[HN Gopher] Why are D-sharp and E-flat considered to be two diff...
       ___________________________________________________________________
        
       Why are D-sharp and E-flat considered to be two different notes?
        
       Author : tobr
       Score  : 334 points
       Date   : 2022-08-28 06:19 UTC (16 hours ago)
        
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       | jimnotgym wrote:
       | I play blues guitar by ear. I don't read music.
       | 
       | The people replying to this thread, the person who wrote this
       | blog are so far away from me it is hard to say we inhabit the
       | same field called 'music'.
       | 
       | I play a lot of improvised lead lines. I know my pentatonic scale
       | shapes on the fretboard, but I also play lots of notes not in
       | those shapes...because I like the way they sound. I also play a
       | lot of 1/4 tone bends (notes between the piano keys) which don't
       | even fit in the traditional system, but sound good. I say this as
       | it is an interesting case of 'more than one way to skin a cat'
        
         | nemo44x wrote:
         | Music is kind of great like that. Much of music theory is over
         | my head but I have spent time to understand a good bit too and
         | I've gained a lot of respect for it. Everything you're doing as
         | a blues guitarist can be explained well by a music theorist who
         | really know their stuff.
         | 
         | I read an interesting article by a music theorist breaking down
         | the song "Smells Like Teen Spirit" and remarking on the genius
         | and uniqueness of the chord progression and how it violates a
         | lot of what theory says would "sound good" and hence why it's
         | genius. It can be presumed Kurt Cobain was not too interested
         | in music theory and if he would have been he may have never
         | even considered the progression and other interesting aspects
         | of that song.
        
           | PaulDavisThe1st wrote:
           | I've said it before, I'll say it again. It's more productive
           | to think of "music theory" as a way for musicians and
           | composers to talk about what they just did, or what they are
           | just going to do, than as a way to generate those things.
        
           | palimpsests wrote:
           | the progression you are referring to is I-IV-bIII-bVI, where
           | are all these chords are "power chords" i.e. dyads comprised
           | of a root and fifth.
           | 
           | it is an awesome progression but violates absolutely nothing
           | in music theory.
           | 
           | we can find examples of similar progressions across jazz and
           | classical music, most of which was composed by folks who have
           | mastered western tonal harmony.
        
           | bonzini wrote:
           | Giant Steps "violates" jazz music theory on the surface but
           | sure enough Coltrane knew his basic chord progressions. If
           | you look close enough Giant Steps builds on traditional ii-
           | V-I progressions and applies (also well known) tritone
           | substitutions to achieve quick key changes.
        
         | beardyw wrote:
         | A lot of those in-between notes hark back to times before the
         | scales were rationalised into the "well tempered" system we
         | mostly use today. Often they are harmonics like the 5th
         | harmonic which lives between the minor and major 3rd on the
         | scale.
        
         | dahart wrote:
         | Blues guitar is kind of the odd one out in terms of the field
         | of music, its one of the few styles where you can get by quite
         | well without note reading or theory. Everything changes if you
         | have a horn section in your blues band though. Music notation
         | exists to facilitate people with different instruments playing
         | together.
         | 
         | As someone who learned the same way you did, on tab and modern
         | pentatonic blues riffs and improv, but over time learned (still
         | learning) more theory and reading music, I'd recommend learning
         | more reading & theory because it really seriously expands on
         | what you can do with blues guitar. A lot of early blues and
         | pretty much all jazz don't stay in the pentatonic scale rut,
         | they move around and mix other scales. It's really helpful to
         | know which diatonic scales you can seamlessly blend with
         | pentatonic, and the reverse: when you can blend pentatonic into
         | a modal song structure, just for two simple examples.
         | 
         | BTW 1/4 tone bends are definitely in the traditional system,
         | they are common even, and in fact are quite directly related to
         | what this article is talking about. The "blue note" in blues is
         | a well known microtone example, but microtonal music in general
         | has theory and notation hundreds of years old, there's a lot of
         | stuff taking these ideas to new levels. Wikipedia's article is
         | just the tip of the iceberg, microtonal music history is bigger
         | and broader than this suggests:
         | https://en.wikipedia.org/wiki/Microtonal_music
        
         | coldtea wrote:
         | > _I say this as it is an interesting case of 'more than one
         | way to skin a cat'_
         | 
         | You're basically skinning the cat the same way, you just don't
         | know the terms of the steps involved or the theory (the "why")
         | behind them, and can't generalize it to ways to skin all kinds
         | of other animals, and even do taxidermy on them - things that
         | the author does.
         | 
         | You however might have picked some special tricks of cat-
         | skinning, and self-taughtingly built your own small
         | conventions, that the author might not know, but which still
         | follow music theory - which, in musicology, is way broader than
         | "common practice" music theory -, (and the author could also
         | delve into them and explain their function theoritically if he
         | played the same genre and bothered to check them out).
        
         | fassssst wrote:
         | Same here, I know how to read music and tabs but gave up on it
         | and now just play by ear, it's way more satisfying. Western
         | music theory is so baroque. The book Brainjo basically killed
         | my interest in it.
        
       | alex_smart wrote:
       | The distinctions between D-sharp and E-flat only make sense in
       | the context of a key.
       | 
       | For instance, you construct a major key in E-flat and not D-sharp
       | for the practical need to represent the scale nicely on the staff
       | - so each tone in the scale should have a unique place in the
       | staff.
       | 
       | You can construct the E-flat major scale with just three flat
       | tones (Eb F G Ab Bb C D), whereas you would need four sharp and
       | two double-sharp(!) tones if you started with D# (D# E# F## G# A#
       | B# C##). And having to use F## and C## to refer to G and D tones
       | is just ugly.
       | 
       | (I had made a mistake in the earlier version of this comment.)
        
         | tzs wrote:
         | If we keep the constraint that each letter has to be used
         | exactly once when naming the notes of a major scale, but drop
         | the constraint that the tonic has to be named using the same
         | letter as the scale name (e.g., we can write G major starting
         | at F##) then that pattern of sharps and flats generalizes
         | nicely.
         | 
         | Number the 12 tones of 12-TET starting with C=0, C#/Db=1, ...,
         | B=11. Then if you write a major scale starting at note N, the
         | sum of all the accidentals counting sharps as +1 and flats as
         | -1 will be equal to 7N mod 12.
         | 
         | For example G is note 7. G major then should have an accidental
         | sum of 7 x 7 = 1 mod 12. We get that writing it G A B C D E F#.
         | But it could also be written with a sum of 13, as F## G## A##
         | B# C## D## E##, or with a sum of -11 as Abb Bbb Cb Dbb Ebb Fb
         | Gb.
         | 
         | Note that because 7 x 7 = 1 mod 12, if we have to answer the
         | question what scale N would have an accidental sum of K mod 12,
         | we can solve 7N = K mod 12 by multiplying both sides by 7,
         | giving N = 7K mod 12.
         | 
         | E.g., what major scale as 3 flats? 7 x -3 = -21 = 3 mod 12,
         | which gives us the major scale starting at Eb.
         | 
         | Personally I find this approach a lot easier than memorizing
         | the circle of 5ths to find key signatures given the key or to
         | find the key given the signature.
         | 
         | A couple of questions naturally arise at this point. Why 7N?
         | Why mod 12. The 12 part is easy to guess--it is because we are
         | picking our major scale out of an underlying 12 tone scale. The
         | major scale has 7 notes out of those underlying 12 notes, so a
         | reasonable guess is that is where the 7 comes from.
         | 
         | But if you think about starting with C major (all white keys)
         | and going up half a step, because the white keys are 0 2 4 5 7
         | 9 11 12 (I've included the octave at 12 to make things
         | clearer), and two of those (4 and 11) are white keys that do
         | not have a black key immediately to the right, it might seem
         | that how many accidentals get added or removed each time you go
         | up in key half a step is going to vary a lot. Going from C to
         | C#, every position goes black except those two. Those two will
         | go black when you go C# to D, and all the ones on black will go
         | to white.
         | 
         | The way the white and black keys are distributed gives you some
         | different regions of the keyboard, each of which has a distinct
         | pattern of adding and removing accidentals as you step through,
         | and the overall pattern of accidentals is a result of those
         | different patterns interacting. So maybe the 7 depends on those
         | regions, and would be different if you had a 7 tone major scale
         | chosen from 12 underlying tones but did not have the same
         | pattern of white/black that we have.
         | 
         | I spent a while trying to show that the patterns would interact
         | in such a way as to make 7N mod 12 work, but utterly failed.
         | 
         | To check that out we can try imagining alien music. Maybe some
         | aliens who also use a 12-TET underlying scale and also have a 7
         | tone major scale have picked 0 2 3 4 7 9 10 as their major
         | scale. Quite a different pattern. However, it turns out that 7N
         | mod 12 works for that too. It also works even with alien music
         | whose major scale is 0 1 2 3 4 5 6. You can have to use a crazy
         | number of sharps or flats in that system!
         | 
         | What the pattern of white/black keys affects is which notes get
         | accidentals when, not the total number of accidentals. By
         | having the white and black keys spread out about as evenly as
         | you can for a 7 white/5 black system we can write every key
         | using the "right" starting note without needing any note to
         | have more than one sharp or flat. Less even distributions of
         | the black keys make it so you need multiple sharps and flats on
         | some notes, but don't change the total number of accidentals
         | mod 12.
         | 
         | Once you realize it really doesn't have anything to do with the
         | pattern of black/white but only on the number of white keys, it
         | is then not too hard to prove that it does indeed only depend
         | on the number.
         | 
         | This can be further generalized. If aliens used a 5 note major
         | scale, then the accidental sum of key N would be 5N mod 12.
         | Since 5x5 = 1 mod 12, they could also go the other way and find
         | the key from the accidental count K via 5K mod 12.
         | 
         | In general for a M note major scale from a T tone underlying
         | scale, transposing that scale to note N uses NM mod T
         | accidentals.
        
           | palimpsests wrote:
           | how would you use this approach in practical application?
           | 
           | i haven't met many working musicians who had much difficulty
           | learning the relationships between different keys, how they
           | connect to the circle of fifths (fourths), and key
           | signatures.
           | 
           | i get that it can seem overwhelming and non-intuitive, but
           | it's really not that complicated once you spend time playing
           | and practicing music that illuminates these relationships
           | (like playing ii-V-I progressions in every key, going around
           | the circle of fifths). very little memorization involved;
           | moreso muscle memory and an accumulation of applied theory in
           | context.
           | 
           | most of the musicians i know are jazz players, where being
           | able to play in any key is a critical aspect of mastering the
           | genre. all the classical musicians i know are professional
           | orchestral musicians, and they don't seem to have any
           | difficulty either.
        
         | tuukkah wrote:
         | > _Also, having to call the G tone F# is just ugly._
         | 
         | I presume you mean having to call the F tone E#.
        
           | alex_smart wrote:
           | Sorry, I had made a mistake. Wanting to create a major key
           | starting with D# would end up looking like D# E# F## G# A# B#
           | C##. The ugliness is even more stark.
           | 
           | - two double sharp keys - F## to refer to G, C## to refer to
           | D, B# to refer to C
           | 
           | Yikes.
        
             | klodolph wrote:
             | D# would be extremely rare. I've only ever seen G#, and
             | that was a temporary modulation within something larger.
             | 
             | Most people write "x" for double-sharp, instead of ##, in
             | order to match how it looks on a score.
        
         | klodolph wrote:
         | Sometimes you call a G as F double-sharp.
         | 
         | I don't think of it as ugly. It's just what happens sometimes.
         | Like if you start in G# minor and then use the leading tone.
         | It's way better to see F-double sharp than to see two different
         | Gs fighting each other on the page. And it's even worse to have
         | to decipher those awful chromatic systems that are all painful
         | to read.
        
           | josteink wrote:
           | > Like if you start in G# minor
           | 
           | Technically speaking that's a Ab minor. New minor scales are
           | constructed by modifying the A-minor scale (which contains
           | the same flat notes as C-major) by adding Bs, not adding #'s.
           | Adding #'s are used for deriving new _major_ scales. At least
           | that's how I understand it.
           | 
           | You can see this on the Wikipedia article on various minor[1]
           | and major scales[2].
           | 
           | [1] https://en.wikipedia.org/wiki/F_minor
           | 
           | [2] https://en.wikipedia.org/wiki/D_major
        
             | bonzini wrote:
             | G# minor is used all the time as the relative minor of B
             | major (5 sharps in the key signature). Ab minor is the
             | relative minor of Cb minor (7 flats) and thus is almost
             | never used except perhaps in passing for a modulation.
             | 
             | > New minor scales are constructed by modifying the A-minor
             | scale (which contains the same flat notes as C-major) by
             | adding Bs, not adding #'s. Adding #'s are used for deriving
             | new major scales.
             | 
             | No, a major scale can have both flats and sharps and the
             | same for minor scales. In fact major scales often start on
             | a flat while minor scales often start on a sharp. Major
             | scales use Db Eb F# Gb Ab Bb as the roots of the scales
             | (rarely C# and Cb), plus the white keys; while minor uses
             | C# D# Eb F# G# Bb (rarely Ab and A#), plus the white keys.
        
             | tripa wrote:
             | Technically speaking, if they said it's G# it's G#.
             | 
             | G# minor is a much better use of the key signature system
             | than Ab: 5 sharps versus 7 flats. In practical terms,
             | that's a proxy for it being more common.
             | 
             | Your vision that minor scales are constructed from A minor
             | is valid; thinking it's by adding flats exclusively is
             | misguided.
             | 
             | I'm not going to go out on a limb and defend the fact that
             | sharps-based minor scales could be more common than flat-
             | based, as that's likely not the case. A much easier
             | argument against your logic is that flats-based major
             | scales _are_ used all the time.
             | 
             | Any given key signature can be either major or minor, be it
             | made of sharps or of flats. It can be seen as altering C
             | major or A minor indeed, but the alteration is allowed to
             | go either way.
        
             | moefh wrote:
             | > New minor scales are constructed by modifying the A-minor
             | scale (which contains the same flat notes as C-major) by
             | adding Bs, not adding #'s.
             | 
             | I think you're confusing two different ways of constructing
             | the minor scales.
             | 
             | One way is to start with the A minor scale (which has no
             | sharps or flats) and to go around the circle of fifths[1]
             | adding sharps or flats. Whether you add sharps or flats
             | depends on whether you're going clockwise or counter-
             | clockwise: for example, D minor[2] (one step from A minor
             | going counter-clockwise) has one flat, and E minor[3] (one
             | step from A minor going clockwise) has one sharp.
             | 
             | Another way to construct a minor scale is to start with its
             | parallel major[4] and add a flat to the 3rd, 6th, and 7th.
             | But note that the result can still have sharps (like in the
             | E example above, where E major has 4 sharps).
             | 
             | In any case, G# minor is definitely a key that is used[5].
             | 
             | [1] https://en.wikipedia.org/wiki/Circle_of_fifths
             | 
             | [2] https://en.wikipedia.org/wiki/D_minor
             | 
             | [3] https://en.wikipedia.org/wiki/E_minor
             | 
             | [4] https://en.wikipedia.org/wiki/Parallel_key
             | 
             | [5] https://en.wikipedia.org/wiki/G-sharp_minor
        
           | alex_smart wrote:
           | That came out different than I had intended.
           | 
           | Of course people use double-sharp keys. And like you said, it
           | is usually done in cases where it is the _simpler_ notation
           | to describe what is happening musically.
           | 
           | Simplicity is beautiful and construction of the major key in
           | E-flat is decidedly simpler than in D-sharp.
        
           | BeFlatXIII wrote:
           | > awful chromatic systems that are all painful to read
           | 
           | The worst ones are the ones that petulantly stick to some
           | theoretically-correct framework and produce a mishmash of
           | accidentals that are canceled on the next note. If it's
           | ascending, add sharps (or cancel the flat) on the second
           | note. Let the key signature do the work instead of making me
           | read all that to discover it's a simple chromatic run.
        
         | OscarCunningham wrote:
         | If you go outside of the diatonic scales it can get even worse.
         | For example E, F, G, A, B, C, D.
        
         | d23 wrote:
         | I get the inclination to make comments like this without
         | reading, but the article goes into far more depth than this.
        
         | InCityDreams wrote:
         | Rule of thirds...for chord construction. 1 3 5 7 9 11 13 C e g
         | b d f a - Cmaj13
         | 
         | Easy to explain to a beginner.
         | 
         | C e g b db f a - Cmaj13b9
         | 
         | C db g b d f a - confusion (for beginners) as that would _not_
         | have a third.... 'd' is the 2nd letter alphabetically.
         | 
         | Any key sig can be represented...
         | 
         | Ie 'E' has to be followed by a g 'of some kind', so even e# can
         | be followed by a gb g or g# to construct a chord.
         | 
         | Easy to see on a guitar, especialky with multiple positions to
         | sound the same note.
         | 
         | e g b d f a c e g b d f a c e....rotates forever, whatever the
         | starting note.
        
         | wumpus wrote:
         | About 80% of the article is devoted to explaining why your
         | comment is missing the point.
        
       | AlbertCory wrote:
       | There's a ton of good information here, but it seems to assume a
       | guitar or piano, where there's only one key or fretted space for
       | each note.
       | 
       | For a fretless stringed instrument, they are indeed different
       | notes, and the _same_ note within a single piece can sound
       | different depending on whether the line is moving up or down.
       | 
       | If that sounds heretical: I got this from the Alexander String
       | Quartet, in the Q&A session after their performance. They have a
       | measurement of microtones (I think they're called "clicks" but I
       | forget), and all four of them have to agree on how many clicks up
       | or down from the center of the note they're using.
        
         | wizofaus wrote:
         | I find that a little odd when vibrato can be as wide as 70
         | cents (70% of a semitone) further up the fingerboard. It makes
         | sense for certain chords in highly tonal music though.
        
           | AlbertCory wrote:
           | They coordinate that, too.
           | 
           | I asked about the movie _A Late Quartet_ (a great movie, btw,
           | with the immortal Phillip Seymour Hoffman), and they said,
           | "in the movie, they say 'our vibratos aren't lining up' and
           | that's something I actually _would_ say in a rehearsal. "
        
         | palimpsests wrote:
         | the unit of measurement is called a "cent".
         | 
         | there are 100 cents between each 1/2 step in 12-tone equal
         | temperament.
        
           | AlbertCory wrote:
           | Thanks. I thought "clicks" didn't sound right.
        
         | [deleted]
        
       | analog31 wrote:
       | My thought is, if you peel back the first layer of music theory,
       | you discover a chaotic, lawless world. The main thing I've
       | noticed is that this is extremely unnerving to engineers, who
       | want to learn it as a precise hierarchical structure. Regular
       | people are more focused on the fact that _somebody_ is somehow
       | making it all sound good, and want to learn how to do that.
       | 
       | On the other hand, most musicians are completely ambivalent to
       | it, or even thrive in the chaos. Yet the "rules" are useful
       | because they provide a common ground for forming ensembles, or
       | connecting composer and performer. We've watched musicians go
       | down the rabbit hole of nonstandard scales, innovative notation
       | systems, etc., only to discover that nobody can play their
       | material.
       | 
       | I'm a double bassist. I'm happy just to be able to coordinate my
       | ears, brain, and hands, well enough to play the same note the
       | same way twice if I want to. Claiming that I have conscious
       | control over temperament would be laughable. I've got too much
       | other stuff to think about: The notes on the page, the non-
       | notated passages (many jazz bass parts are expected to be
       | improvised), tempo and rhythm, connecting with the rest of the
       | band and the audience, who's coming in the front door, and so
       | forth. This stuff is all happening in real time.
        
         | stoeckley wrote:
         | > My thought is, if you peel back the first layer of music
         | theory, you discover a chaotic, lawless world.
         | 
         | That's because some people think the theory comes first, and
         | the music is based on it. But music is just art, like any other
         | art. The rules are soft and broken and hardly gospel. And music
         | theory is an attempt to have some way to communicate about
         | music using ordinary language. It isn't math, it isn't science,
         | it's just some basic terminology and observations, none of
         | which have much to do with the actual artistic act of making
         | music.
        
           | byproxy wrote:
           | Absolutely. Music theory is descriptive, not prescriptive. It
           | just so happens that some things that sounded pleasant to
           | people in the past still sound pleasant to modern ears, so
           | you sometimes get into a bit of "tail wagging the dog" when
           | people use those descriptive academic terms and concepts when
           | creating music today, e.g. saying "I'm gonna write a 16-bar
           | AABA tune that's based on a I-vi-ii-V progression and
           | modulates to the mediant in the B section", and therefore
           | think these are "rules" to abide. One of the more unfortunate
           | misconceptions when it comes to the study of music theory.
        
           | slfnflctd wrote:
           | When you think of songs where 'bending' a note is used, or
           | intentionally hitting a note a little bit flat or sharp for a
           | desired aesthetic effect (or both), this all makes a lot more
           | sense.
           | 
           | Music theory gives us a way to measure & more accurately
           | describe what we were already doing.
        
         | synu wrote:
         | Huh, that's interesting. I bounced off learning music theory
         | because it seemed to be all about putting everything into
         | little boxes, and music doesn't really work that way. What are
         | some of the more interesting elements that you get to after the
         | first layers?
        
           | analog31 wrote:
           | As they say, music theory is descriptive not prescriptive.
           | However...
           | 
           | A really rough analogy is a programming language. The rules
           | of the language don't tell you what kind of program to write,
           | but choosing a language gives you a huge jump start on
           | creating interesting and useful programs. Likewise knowing
           | algorithms and good patterns.
           | 
           | I think that very few people are interested in studying music
           | theory as an end unto itself. Like, I have a friend who is a
           | retired theory professor, and did his PhD in theory. (He also
           | performs music, but treats it as a hobby). For everybody
           | else, the purpose of learning theory is to make you a better
           | musician. So you can take it as far as needed to make that
           | happen within its applicability to the kind of music you're
           | interested in.
           | 
           | And there are different approaches, such as "jazz theory,"
           | that doesn't spend a lot of time with (for instance) the
           | forms of larger musical compositions, or Bach.
           | 
           | So, what aspect of your musicianship are you trying to
           | improve? I can cite one example. I play mostly jazz. I'm not
           | great at theory myself. Everybody I know who can _compose_
           | good jazz, or create written arrangements for larger
           | ensembles, studied theory in college. I 'm stuck with playing
           | their music, which I love, but am not capable of creating my
           | own. The theory probably helps in terms of letting you go
           | from a composition that "almost" works but has awkward bits,
           | and make it really sparkle.
        
       | tomxor wrote:
       | I'm struggling to fully understand this tbh, but was recently
       | exposed to these subtle differences when writing a mini organ
       | synth.
       | 
       | When implementing the draw bars (dictating the harmonics
       | comprising each key) I realised the true harmonics of a note and
       | neighbouring notes calculated in the 2^n/12 way are sometimes the
       | same and sometimes slightly off... organs just kinda ignore this
       | fact and use the closest neighbouring notes for the draw bars
       | anyway so that they don't need a million different oscillators,
       | so technically the draw bars are just chords on the keyboard
       | using the same oscillators and not harmonics (well some of them
       | happen to be exactly the same as harmonics, others not).
        
       | cmur wrote:
       | As a former jazz musician, I always find the classical
       | perspective on theory interesting. This article touches on
       | Pythagorean tuning techniques, which if you ever find yourself in
       | front of a good a cappella choir, they'll be tuning to the true
       | temperament tuning scheme described here. A fun comparison to
       | make in the jazz world is enharmonic usage for the purpose of
       | readability. Jazz chords are very dense and short lived compared
       | to the very clean and predictable counterpoint found in classical
       | music, so "correctness" doesn't really matter as much. Most
       | charts are sight read, so even though the band is sounding some
       | flavor of a B chord, if you're playing the 3rd, there's a chance
       | there may be a written E flat instead of a D sharp simply because
       | E flat is a more commonly written note for horn players.
        
         | klodolph wrote:
         | Pythagorean tuning is somewhat different from what's described.
         | 
         | In Pythagorean tuning, your E would be 81/64 above C, or equal
         | to four fifths minus two octaves. This is slightly higher than
         | E in the article, and the difference (81/80) is called the
         | syntonic comma.
         | 
         | Different tuning systems were invented in order to resolve this
         | discrepancy, and without these advances, jazz would be
         | radically different. One of the things about jazz is that you
         | see distant movements that only really make sense as
         | enharmonics--like how Coltrane's "Countdown" uses the familiar
         | ii-V-I, but modulates in major thirds, which only makes sense
         | when you allow the final modulation te be the same as the first
         | --something that only works enharmonically.
        
           | cmur wrote:
           | For sure, the broad similarity I'm trying to touch on is the
           | focus on mathematical resonance and context of a key. Equal
           | temperament removed a lot of that context, but definitely
           | opened the door for further harmonic experimentation. Giant
           | Steps is also a good example of what you're talking about
           | too.
        
       | tzs wrote:
       | Suppose we start with 12-TET and ask what simple integer ratios
       | each note is close to. To do that we need some notion of what it
       | means for a simple integer ratio to be a good approximation to
       | some arbitrary given number.
       | 
       | Consider trying to approximate some number x with an integer
       | ratio n/m. For a given m all we can guarantee is that we can find
       | some m so to |x-n/m| <= 1/2m. One way to define good
       | approximation is if for a given m, we can get a lot closer than
       | 1/2m to x then that is close.
       | 
       | For example if we want to approximate pi with m = 6, 7, or 8, the
       | closest we can get is 19/6, 22/7, and 25/8. The absolute errors
       | are about 1/40, 1/790, and 1/60, respectively. They are all doing
       | better than 1/2m, but 6 and 7 are only about 3.5 times better
       | 1/2m, but 7 is 56 times better than 1/2m. So we say that 22/7 is
       | a good approximation to Pi. That doesn't mean it is particular
       | close--just that it is way closer than other approximations with
       | similar sized denominators.
       | 
       | For a given number x there is a way to find such good
       | approximations. You figure out the continued fraction for x. For
       | Pi that is 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + 1/(1 + ..., then
       | even though that goes on forever you type ")))))" so that the
       | unbalanced parens don't drive you crazy, and take the sequence
       | you get by taking finite sections from the left side of that
       | continued fraction. So for Pi we get 3, 1 + 1/7, 3 + 1/(7 +
       | 1/15), ..., which when simplified give 3, 22/7, 333/106, 355/113,
       | 103993/33102, .... Note that 22/7 is in there, which is the good
       | approximation from early.
       | 
       | All of those numbers from taking the left parts of the continued
       | fraction, which are called convergents of the continued fraction,
       | are good approximation in the sense above: they are way closer to
       | Pi than anything else with similar denominators.
       | 
       | What we can do then to find good integer ratios that are close to
       | the notes of 12-TET is for each 12-TET note, take its frequency
       | divided by C's frequency, compute the continued fraction of that,
       | and compute the first few convergents. Here are the results. I've
       | omitted convergents with a denominator of 1 or with a denominator
       | > 500.                 C#/Db: {17/16, 18/17, 89/84, 196/185}
       | D:     { 9/8,  55/49}       D#/Eb: { 6/5,  19/16, 25/21,  44/37}
       | E:     { 4/3,   5/4,  29/23   34/27,  63/50, 286/227, 349/277}
       | F:     { 3/2,   4/3, 295/221}       F#/Gb: { 3/2,   7/5,  17/12,
       | 41/29,  99/70, 239/169, 577/408}       G:     { 3/2, 442/295}
       | G#/Ab: { 3/2,   8/5,  19/12,  27/17, 100/63, 227/143, 781/492}
       | A:     { 5/3,  37/22}       A#/Bb: { 7/4,   9/5,  16/9,   41/23,
       | 57/32,  98/55}       B:     {15/8,  17/9, 168/89, 185/98}
        
       | bewaretheirs wrote:
       | Related in a distant way:
       | 
       | https://news.ycombinator.com/item?id=31476078
       | 
       | my TL;DR, as a western classically-trained amateur musician
       | largely unfamiliar with Indian music: Harmonium (a small reed
       | organ) is widely used in Indian classical music but its use is
       | controversial because it doesn't allow for the fine adjustments
       | in pitch (roughly analogous to the D#/Eb distinction discussed
       | here) that is seen as central to most/all Indian styles.
        
       | ur-whale wrote:
       | Are they the same frequency?
       | 
       | Can most humans hear a difference?
       | 
       | Do we need more than the two questions above?
        
         | midenginedcoupe wrote:
         | Are two competing programming languages Turing-complete?
         | 
         | Can end-users of the program tell which one was used?
         | 
         | Do we need more than the two questions above?
         | 
         | If programmers thought like this HN would be empty!
        
         | swores wrote:
         | It would be possible for most humans to notice something but
         | feel indifferent, or for a sizeable minority to really hate
         | something. So just abstractly I'd say that yes you do need more
         | than those two questions.
        
         | PeterisP wrote:
         | No, and yes.
         | 
         | The difference is obvious even those who don't distinguish
         | pitches much (can you hear the difference in the video linked
         | in the article -
         | https://www.youtube.com/watch?v=7GhAuZH6phs&t=21s ) because the
         | 'wrong' one played in a scale or a chord sounds really, really
         | horrible; that's why we have all the work done on 'tempered'
         | tuning to reduce the gap so that everything is just slightly
         | off.
        
         | vnorilo wrote:
         | The relationship between pitch and frequency is not simple. The
         | physical frequency for a pitch can be derived in several ways.
         | 
         | One example is the Pythagorean system where the interval of
         | fifth is set as a frequency ratio of 3/2. This system yields
         | clearly distinct frequencies for D# and Eb.
         | 
         | In 12 tone equal temperament, a semitone is set as a frequency
         | ratio of 2^(1/12). In this system you get the same frequency.
         | 
         | You can also derive frequencies from simple fractions of the
         | scale root. In this instance you would generally obtain D# and
         | Eb from unrelated roots.
        
       | beefman wrote:
       | Great question but some unfortunate errors here.
       | 
       | > Before the advent of temperament systems, D-sharp and E-flat
       | were two different notes.
       | 
       | D# and Eb were defined as elements of a temperament system,
       | namely meantone temperament.
       | 
       | > My track is tuned in a system called five-limit just intonation
       | ... It's the basis for all the tuning systems used in Western
       | Europe between about 1500 and 1900.
       | 
       | The basis for tuning systems in Western Europe between 1400 and
       | 1800 was meantone temperament. 5-limit JI has never been the
       | basis of a common practice music culture anywhere or at any time
       | in world history.
       | 
       | > We can do this because Western people consider octaves to be
       | equivalent.
       | 
       | All people experience octave equivalence.
       | 
       | > Ultimately, split black keys did not catch on.
       | 
       | Split keys were fairly common on keyboard instruments for about a
       | century.
       | 
       | > Bach wrote The Well-Tempered Clavier to show off how one well
       | temperament system (no one knows which one) sounds okay in every
       | major and minor key.
       | 
       | Bach was a proponent of well temperaments in general, not any
       | specific one.
        
       | Aidevah wrote:
       | > _The next level of explanation is to say: "Yes, I recognize
       | that D-sharp and E-flat sound the same, but they function
       | differently, and the spelling communicates this functional
       | difference." This explanation always bothered me, because if the
       | "function" is limited to the page and isn't audible, then is it
       | even a real thing?_
       | 
       | A feature of notated music (which is what most of us mean when we
       | say "[western] classical music") is that there can be things
       | notated and not heard. Similarly, there are also different
       | notations which correspond to the same sound. Notation is
       | ambiguous, and this can be a source of both frustration (for the
       | students) and invention (for the composers). Charles Rosen opens
       | his book _The Romantic Generation_ with a fascinating discussion
       | about music which is seen and not heard which deals with this
       | philosophical issue.
       | 
       | Of course this practice goes back much further. Composers have
       | been playing with notation for a long time and it reached a peak
       | of sophistication in the 15th century, as Emily Zazulia
       | demonstrated in her PhD thesis and book[1]. This quality is
       | obviously absent in musical cultures which do not rely on
       | notation. I imagine to the outsider it appears as if the notation
       | itself has taken on a life of its own to the detriment of the
       | sounding music. Of course there is a certain elitism involved as
       | well since explaining subtleties in notation is also a sure way
       | of ostentatiously demonstrating one's erudition, which may
       | explain why these kind of discussions are perennially popular
       | here ;).
       | 
       | [1] https://global.oup.com/academic/product/where-sight-meets-
       | so...
        
         | vcxy wrote:
         | I would argue the difference _is_ heard in music that broadly
         | follows tonal harmony. Sure, the note it self sounds the same,
         | but the difference is context. That context is there regardless
         | of whether it is heard or seen.
         | 
         | Edit: just to add some detail: you can definitely hear if
         | something sounds Lydian. If it sounds Lydian, you know that's a
         | sharp 4, not a flat 5. Put it in C e.g., then it's an F# and
         | not a Gb, and you can hear that.
        
           | Aidevah wrote:
           | Yes, exactly. A note is rarely found by itself, and looking
           | at the context surrounding the note usually clears up the
           | function of a note pretty quickly. Now that I think about it,
           | the notation actually reduces ambiguity in this case since it
           | specifies the function of notes which have the same sound.
        
           | filoeleven wrote:
           | The author frequently uses the term "same note" when the more
           | accurate term in this context would be "same pitch." Your
           | comment and the next one up both clarify why having
           | differently-named notes that use the same pitch matters.
           | 
           | My favorite illustrstion of this is "Call Me A Hole", a
           | mashup where the vocal track of NIN's "Head Like A Hole" is
           | played atop the music track of Carly Rae Jepsen's "Call Me
           | Maybe." A vocal performance that was originally seething with
           | rage is transformed into a disco pop anthem, and the main
           | reason it works is because "Call Me Maybe" was written in the
           | relative major key to "Head Like A Hole." The same vocal
           | pitches--the whole melodic structure--functions entirely
           | differently, with hilariously effective results.
           | 
           | The mashup is an in-the-large example of the musical context
           | you mention. D-sharp and E-flat is the same principle, just
           | at a much more fine-grained scope.
           | 
           | https://youtu.be/1lkuDm_g2ig
        
       | [deleted]
        
       | Ninn wrote:
       | I recon this Feakonomics podcast includes the answer amongst
       | other interesting related topics:
       | https://freakonomics.com/podcast/mathematician-sarah-hart-on...
       | 
       | It might be worth a listen for anyone who finds the topic
       | interesting, but the answer is obviously already found in the top
       | response too.
        
       | daviddever23box wrote:
       | tl;dr: The notation system predates the modern, commonly-used
       | 12-Tone Equal Temperament, for which there are (at least two)
       | ways to describe any note within the (12-Tone) octave, either by
       | sharps (D sharp) or by flats (E flat). In 12-TET, there are
       | exactly twelve notes in the octave, and sharps and flats can be
       | said to "overlap".
       | 
       | In earlier temperament systems, these notes may have been
       | distinct (or in some cases unavailable), as the relationships
       | between notes were based on non-equal, if not more mathematically
       | perfect, ratios.
        
       | wizofaus wrote:
       | Try sight reading something in D# major and that should tell you
       | the difference!
        
       | elihu wrote:
       | What's weirder is that if you're using just intonation in, say,
       | the key of C major, there's two different D's. One is 9/8, and
       | the other is 10/9. The note we call D in equal temperament is
       | about half-way between the two.
       | 
       | If you want to play these chords in C major: Cmaj, Fmaj, Gmaj,
       | Dmin, Emin, and Amin, you'll need to use both of those D's: 9/8
       | for the 5th of Gmaj, and 10/9 for the root of Dmin. If you try to
       | play Dmin with the 9/8 instead, it sounds absolutely awful.
       | 
       | In other words, if you want to play those six chords that are
       | regarded as belonging to C major, you'll need two different D's.
       | Which means the C major scale should really have 8 notes instead
       | of seven. But we don't have a symbol to distinguish between 9/8
       | and 10/9 in standard notation, they're both just plain D.
       | 
       | Some 12-EDO music makes use of the ambiguity between these two
       | notes (or any two notes with the same relation to each other) to
       | string together chord progressions that don't actually make sense
       | mathematically. If you used those progressions in just
       | intonation, you'd find you don't return to the chord you started
       | on, you actually shifted up or down by a small interval of 81/80.
       | It's sort of the musical equivalent of some formula that only
       | works if you assume that pi is equal to exactly three.
        
       | userbinator wrote:
       | I went to the Wikipedia link in the article to
       | https://en.wikipedia.org/wiki/Five-limit_tuning and saw that the
       | first example there shows two very slightly different
       | frequencies, which is a good way of setting the stage for reading
       | the rest of the article.
        
       | perihelions wrote:
       | The paradox is that you can't create a theory of music whose
       | notes are both (a) evenly spaced and (b) contain the integer
       | ratios.
       | 
       | You want (a) because it you gives you nice algebraic properties
       | (the music structure is invariant under frequency shifts). You
       | want (b) because small-integer ratios are pleasant sounding --
       | partly culturally-acquired taste, partly because physics gives
       | musical instruments acoustic spectra in integral multiples of a
       | fundamental frequency: f, 2f, 3f ... nf. Small-integer ratios are
       | naturally occurring and very recognizable.
       | 
       | Modern tuning (C-f "12-TET" in the article) almost, approximately
       | satisfies (a) and (b) simultaneously. "12" means there's twelve
       | tones between f and 2f; the ratio between adjacent tones is
       | defined to be 2^{1/12}. This tuning can't contain both f and 3f
       | (so it fails (b)), but it *can* contain f and 2^{19/12}f ~
       | 2.9966f, which is actually close enough to 3f to be
       | indistinguishable. (Almost works!) But as you build ratios out of
       | larger integers, it audibly falls apart. The closest you can get
       | to (5/3)f is 2^{9/12}f = ~1.6818f, which is already 10% of the
       | way to the next note. And it rapidly gets worse.
       | 
       | This is why two on-paper-identical notes can end up audibly
       | different, depending on what key you're starting with (and hence
       | how they are approached). There's tension internal to music
       | theory itself.
        
         | 323 wrote:
         | In Go, and Chess, there are a number of "rules": you should
         | never do this (move the same chess piece twice in the opening),
         | you should do that, ... And then AlphaGo appeared and dismissed
         | all this and did just the right thing for the particular game
         | being played. Know the rules, but if you are an expert you can
         | break the rules.
         | 
         | I wonder if AI will do the same thing in music, it will use the
         | "perfect" tuning suitable for a particular piece of music and
         | dismiss this idea of a universal tuning scale.
        
           | nateburke wrote:
           | What would the AI's reward function be?
        
             | 323 wrote:
             | Song gets into Billboard Top 100? Song view count on
             | YouTube?
             | 
             | And for earlier stages you can have human raters or
             | similarity with past successful songs.
        
             | the_third_wave wrote:
             | Feedback from a neural link which indicates satisfaction in
             | the listener?
        
             | xyzzy4747 wrote:
             | It won't get terminated on AWS.
        
             | [deleted]
        
           | pdpi wrote:
           | You can't realistically have a different guitar or a
           | different saxophone for each and every piece you want to
           | play, and those frets and holes can't be freely moved around.
           | It gets that much worse when you consider "installation"
           | instruments like carillons or pipe organs.
           | 
           | AI just literally, fundamentally can't "dismiss the idea of a
           | universal tuning scale", because whatever per-piece
           | optimisations it can come up with still need to be realised
           | by physical instruments at some point. The idea of a good-
           | enough compromise solution that allows you to play a wide
           | variety of pieces on a single instrument is just too damn
           | important.
        
             | a1369209993 wrote:
             | > You can't realistically have a different guitar or a
             | different saxophone for each and every piece you want to
             | play
             | 
             |  _Looks quizzically at 44.1kHz-u16 audio sink._
             | 
             | Pretty sure I can, actually; my computer's speakers
             | certainly do, barring a rare handful of groups of songs
             | that were recorded at the same time and place.
        
             | 323 wrote:
             | There is more to music than just physical instruments.
             | 
             | In popular commercial music you do literally have a
             | different instrument (synth setup) for each song.
             | 
             | But even if we talk about guitars and saxophones, I was
             | speaking about AIs which directly output a sound file, not
             | a music sheet. So they can synthesize a fake saxophone
             | which is tuned in a weird non-physically possible way, as
             | if each note was played by a different physical saxophone
             | that the musician switches to.
        
               | pdpi wrote:
               | You specifically brought up Alpha Go dismissing the
               | conventional wisdom on how Go should be played. Many of
               | the things we thought we knew about the game turned out
               | to be wrong and the game as a whole was turned on its
               | head.
               | 
               | None of that applies to music. Nobody who studies this
               | stuff seriously is under any sort of illusion that 12-TET
               | is the "right" way to play music. I know a fair few
               | professional musicians, and I've "talked shop" with as
               | many of them as I could, and the deficiencies of 12-TET
               | recurringly come up. There is nothing here to "dismiss".
               | 
               | Don't get me wrong: The idea of computationally-optimised
               | tuning sounds really interesting, and the discussion of
               | what we should be optimising for would itself be
               | fascinating to follow. It's just that people are already
               | doing that sort of thing manually today, so there's no
               | big "oh no we're doing it wrong" dismissal of the status
               | quo waiting at the end.
        
               | 323 wrote:
               | > _None of that applies to music._
               | 
               | But how would we know that? People thought music was
               | figured out and then atonal music was
               | invented/discovered/re-discovered (whatever you prefer).
               | 
               | We are somewhat speaking about different things. You talk
               | about people playing instruments, and you are sort of
               | right, all possibilities were explored.
               | 
               | I'm talking about audio files with songs, many of which
               | are currently being produced with software using a
               | specific tuning (typically 12-TET). But in this world the
               | tuning is just an artifact of the production process,
               | it's not fundamental like in your world.
               | 
               | The current picture producing AIs don't start with a
               | blank digital canvas and drag digital brushes over it,
               | they synthesize the image in a holistic way and in this
               | world the "brush" can be unique at each position.
               | 
               | More precisely, I'm thinking that music producing AIs
               | could make music where the first 5 seconds of the lead
               | instrument uses 12-TET and then switches to another, the
               | backing bass track uses a different tuning, the vocal
               | sings to yet another one yet it all comes together
               | beautifully. And the tunings used could morph during the
               | song duration. In a way this means that there is no
               | tuning at all.
        
               | topaz0 wrote:
               | I think the key difference is that playing go is about
               | winning (at least, presumably that's what the AI is
               | optimized for). Music is not.
               | 
               | (I also agree with others in this thread that the popular
               | commitment to equal temperament is exaggerated -- it's
               | not all that uncommon to hear good musicians of various
               | styles playing/singing/synthesizing "out of tune" music
               | for various effects).
        
           | teolandon wrote:
           | People broke conventional rules with success in both Go and
           | chess before AlphaGo and AlphaZero.
           | 
           | In a similar way, people have been using particular tunings
           | for their songs for a long long long time. The idea of a
           | universal tuning scale is relatively new. No need for AI to
           | point us away from it, we already did that ourselves.
        
           | magicalhippo wrote:
           | Your post reminded me of a video[1] Adam Neely made where he
           | explored some (to me) weird tunings, starting with one where
           | A = 432Hz.
           | 
           | As someone who hasn't taken any musical theory or similar, it
           | was quite interesting to hear.
           | 
           | [1]: https://www.youtube.com/watch?v=ghUs-84NAAU
        
             | coldtea wrote:
             | > _where he explored some (to me) weird tunings, starting
             | with one where A = 432Hz_
             | 
             | That's just changing a convention, not a tuning in the
             | sense talked elsewhere in this thread (how we divide
             | notes), but "what our starting frequency is".
             | 
             | A=432 and A=440 is just as arbitrary. They just had to pick
             | something so they would all match.
             | 
             | The main difference is that 432 is associated with a set of
             | new age, healing, "universe", etc. BS claims in certain
             | "spiritual" circles...
        
               | JasonFruit wrote:
               | Though it is true that a lot of older string instruments
               | weren't designed to take the tension of modern strings at
               | modern pitch, and some of them really open up at a
               | slightly lower pitch. I'm building lyres, and many lyre
               | people are from that "A432 resonates with the universe"
               | crowd, so I've been using it -- and I can't deny that
               | there seems to be a sweet spot in sound for a lot of
               | instruments at that pitch. I honestly have wondered if
               | there's some physiological reason so many people prefer
               | it.
        
               | topaz0 wrote:
               | Aside from the universe, there's a very practical point
               | related to this, which is that the instrument has other
               | resonances besides those of the strings. E.g. I have read
               | that the frames of harpsichords are tuned to particular
               | resonances, which is part of what gives different keys
               | different qualities.
        
               | pdpi wrote:
               | The one special thing about A=440 is that it is
               | international law, as defined by the treaty of Versailles
               | (yes, the one that ended World War I)
        
               | 323 wrote:
               | What's the penalty if you make an instrument tuned to
               | A=442? Do you get dragged to the Hague International
               | Criminal Court?
        
               | pclmulqdq wrote:
               | Several orchestras use different A's around 440, and
               | nobody is getting prosecuted. 441 and 442 are popular
               | right now, although some go as low as 438.
               | 
               | In baroque music, ~430 and 415 are also very common since
               | they are thought to be the historical pitches of "A"
        
               | colomon wrote:
               | Friends recorded this album --https://alisonperkinsandnic
               | olasbrown.bandcamp.com/album/all-... -- with A somewhere
               | in the neighborhood of 360Hz.
        
               | coldtea wrote:
               | 360Hz?
               | 
               | That's so low, it's more like playing the piece a three
               | semitones lower than an alternate choice for A4.
               | 
               | If the piece was in A, it would be more like playing it
               | in F# (while still using A=440).
               | 
               | (Of course if you did that, the "sweet-spots of 12TET and
               | its off-notes would be different, than if you played with
               | A=360)
        
               | pclmulqdq wrote:
               | Some late baroque-period harpsichords had a selectable A:
               | you could chose ~430, ~410, or ~390. The adjustment came
               | from sliding the keyboards to the left or right based on
               | which A you wanted. Supposedly A = 390 or even lower was
               | used by the French in the renaissance, so you wanted your
               | harpsichord to be able to accurately play historical
               | music.
        
               | pdpi wrote:
               | None that I'm aware of.
               | 
               | Tuning your orchestra high was sort of the 19th century
               | equivalent of the modern loudness war. The problem is
               | that orchestras tuning to ever higher pitches meant that
               | singers had to sing higher to match, and it was putting
               | serious strain on their voices, which can easily lead to
               | injuries.
               | 
               | Having some sort of agreement setting a standard was just
               | something of an "enough is enough" sort of moment. It
               | just amuses me to no end that this was achieved by
               | writing it into the Treaty of Versailles, of all things.
               | We're settling a freaking world war, so let's make sure
               | we settle the issue of orchestra pitch as part of the
               | treaty.
        
               | [deleted]
        
               | magicalhippo wrote:
               | Well he does go into Pythagorean tuning later in the
               | video[1], both a proper one and one which was made to
               | "look nice", so bit more to it than that from what I
               | understood.
               | 
               | Or I might be wrong, I know nothing about music[2].
               | 
               | [1]: https://www.youtube.com/watch?v=ghUs-84NAAU&t=517s
               | 
               | [2]: https://www.youtube.com/watch?v=s6EaoPMANQM
        
         | bambax wrote:
         | Excellent explanation! It's not certain though that (a) is as
         | desirable as we make it out to be. We accept that transposition
         | is transparent but it could not be. Keys used to have a meaning
         | attached to them and weren't interchangeable. The direction we
         | have chosen made us lose that and it's a little bit sad IMHO.
        
           | [deleted]
        
         | [deleted]
        
         | mort96 wrote:
         | Okay but in 12-TET, there are only 12 notes. D# and E are the
         | same note, because there is only one note between D and E. On
         | paper and in practice, the note between D and E is the same
         | whether you write it as D# or as E. A piano doesn't know how
         | the note is written in the sheet music.
         | 
         | EDIT:to be clear, I'm not disagreeing with most of what you're
         | saying. 12-TET can't represent the desirable perfect fractions,
         | and in a system which can (such as a just intonation system),
         | the starting point does matter. And maybe a vocalist or a
         | violinist would play D# and E subtly differently, I don't know.
         | My main point is just that in a whole lot of contexts, such as
         | when playing a piano, there is no difference between the notes.
         | Your comment made it look like there's always a difference
         | between theory and practice which makes D# and E different in
         | practice, when that's often not the case. We do use 12-TET in
         | practice.
        
           | SkyBelow wrote:
           | For the random piano, you are right, there is no difference.
           | For a paino being used to play a very specific piece, the
           | tuning might be slightly different depending if the intended
           | song is using D# or E, depending upon the key of the song.
           | Though in such a case the piano might be tuned using a
           | different standard that better fits the song.
           | 
           | One more extreme example is two pianos tuned to 12-TET, but
           | one is half off. They are made to be played together by two
           | closely in sync pianists for a few more complex songs that
           | need 24 steps between octaves.
           | 
           | Overall I do find the system confusing enough to wonder if a
           | better one won't one day catch on. And it might already have,
           | I know some musicians who can't read sheet music but play by
           | chords. It seems more limited in the level of detail you can
           | specify, but works plenty well for the songs they want to
           | play.
        
             | pclmulqdq wrote:
             | I worked as a harpsichord tuner during college, and this
             | kind of tuning was generally only used when only string
             | instruments were involved. Once a single instrument with
             | holes, valves, or frets is involved, you have to use equal
             | temperament. Almost nobody does specialty tuning.
        
             | coldtea wrote:
             | > _For a paino being used to play a very specific piece_
             | 
             | That would something that only happens very rarely, like
             | for just 1/10000th the pianos people will encounter in
             | their lives...
        
               | palimpsests wrote:
               | likely 1/100,000 at most. more likely 1/1,000,000
        
           | zarzavat wrote:
           | As a life long string player I can tell you that there is no
           | difference between E flat and D sharp. String players usually
           | play with other instruments that are not so tuneable. Good
           | intonation means playing in tune with the other players, not
           | playing according to mathematics. If you don't have good
           | intonation then you hide it with vibrato. Flats and sharps
           | don't enter into consideration.
           | 
           | The one exception is harmonics which are based upon integer
           | ratios rather than 12-TET.
        
             | zarzavat wrote:
             | I can't edit my comment above but I want to clarify: I
             | don't mean to say that string players _always_ play in
             | 12-TET.
             | 
             | If you're playing a C in C major and I'm playing a G, it
             | may sound best if my G is close to a perfect fifth from
             | your C in just intonation. This is why string sections
             | often sound so sickly sweet, like A Capella.
             | 
             | On the other hand, if you are playing a C _and_ a G on the
             | piano, and I 'm also playing a G, then it will sound best
             | if I play the same G as you in 12-TET. If I were to play
             | the "correct" G against your "wrong" G, it would sound out
             | of tune.
             | 
             | Context is everything.
             | 
             | As you may notice, G doesn't have a sharp or a flat in C
             | major! If string players relied upon accidentals to tell
             | them how to tune a particular note, they would be out of
             | luck seven twelfths of the time.
             | 
             | That process of adjustment: called intonation, happens
             | _after_ resolving which pitch class I want to play. It 's
             | not something that an arranger can control through the use
             | of enharmonic spelling, but it doesn't stop them from
             | trying!
        
           | aikinai wrote:
           | A piano doesn't know the difference and can't differentiate
           | them (on the fly), but a violinist certainly can and does.
           | Most instruments have real time manual control over
           | intonation and skilled musicians will bend pitch to best meet
           | the current key and context.
        
             | xattt wrote:
             | Would there be a specific notation for the merry-middle in-
             | between note (D# and E)?
        
               | wizofaus wrote:
               | You mean D "three quarter" sharp? The name is a bit
               | illogical because it's really "a sharp and a half", or
               | "sharpened three quarters of a tone". The usual
               | representation looks like a sharp with three vertical
               | bars, and there's a unicode symbol for it (tried to cut
               | and paste but no luck). Microtonality is really annoying
               | on a piano though.
               | 
               | As it happens I've been trying to work out what exact
               | intervals are used for the two-chord leitmotif heard in
               | "The Sandman" series, I'm not sure if they're regular
               | microtones or just some sort of eerie detuning
               | (surprisingly I can't find any discussion of it online
               | either).
        
               | palimpsests wrote:
               | the sandman (*) intervals aren't coming from microtonal
               | tuning... it's dynamically modulated detuning in equal
               | temperament, just as you say. it's an extremely common
               | type of modulation, especially if there are synthesizers
               | involved.
               | 
               | * what an incredible show!
        
             | criddell wrote:
             | Is a D-sharp/E-flat played on a piano or guitar closer to
             | D-sharp or E-flat on the violin?
        
               | bombela wrote:
               | It's in the middle between the two!
        
               | elif wrote:
               | Sorry but as a guitarist this just sounds like
               | "violinists miss the half-step notes on purpose"
               | 
               | Which is okay. I like to bend notes too, but just call it
               | what it is.
        
               | criddell wrote:
               | Depends on the temperament you are shooting for, at least
               | that's my understanding after reading the article.
        
               | coldtea wrote:
               | Could also be exactly the same as "the two", as
               | violinists would also often just play those two at the
               | traditional "piano" pitch, when playing alonside a piano
               | and other such instruments.
        
               | criddell wrote:
               | It would be interesting to have an electronic keyboard
               | that watches what you are playing and decides when you
               | press the D-sharp/E-flat key, which note it should play.
        
               | rawling wrote:
               | I'm sure I've see on here something that does not just
               | that, but also remembers what it just did so when you
               | play your next notes it doesn't jump to a different
               | tuning.
        
               | aikinai wrote:
               | There are also digital keyboards that let you bend pitch
               | after you hit a note by shifting the pressure similar to
               | a violin.
        
               | topaz0 wrote:
               | Some old style organs that are not "well-tempered" have
               | split keys for some notes, so that you can choose D# vs
               | Eb (for example), depending what else is going on.
        
             | kimi wrote:
             | ...because if you are playing with a piano, and you play
             | those intervals "right", they will be out of tune.
        
             | HPsquared wrote:
             | That's interesting, so they can get closer to "just
             | intonation" then?
             | 
             | I assume it all breaks down if they need to play alongside
             | a keyboard (or fretted) instrument.
        
               | Tade0 wrote:
               | Fretted instruments, especially electric guitars, are
               | usually not strictly equal temperament and are made to
               | have just intonation in at least some combinations of
               | notes because equal temperament sounds bad with
               | distortion.
               | 
               | There exist equal temperament guitars, but they're
               | usually custom built:
               | 
               | https://guitargearfinder.com/faq/true-temperament-frets/
               | 
               | In any case most people don't mind such small
               | differences, especially that guitars aren't terribly
               | precise to begin with - a player can easily get 10 cents
               | of a semitone on each individual string when playing a
               | power chord with distortion, bringing the whole thing to
               | just intonation.
        
               | david-gpu wrote:
               | Edit: I was wrong below.
               | 
               | ---
               | 
               | Hi! I am not a musician. Did you mean that true
               | temperament guitars are the ones with squiggly frets,
               | instead?
               | 
               | My understanding was that true temperament [0] is not the
               | same as equal temperament [1]. I also believe that both
               | pianos and guitars are typically tuned to equal
               | temperament [2], but you may well be right about guitars.
               | 
               | Maybe somebody can shed some more light on this. Thanks!
               | 
               | [0] https://www.truetemperament.com
               | 
               | [1] https://en.wikipedia.org/wiki/Equal_temperament
               | 
               | [2] https://youtube.com/watch?v=-penQWPHJzI
        
               | Tade0 wrote:
               | True temperament appears to be a marketing term for a
               | fret system providing equal temperament.
               | 
               | A "spherical cow" model of a guitar would be equal
               | temperament, but that ignores the messy reality of how
               | strings behave - chiefly they need to be some distance
               | above the fretboard and pressing them naturally bends the
               | string ever so slightly.
        
               | palimpsests wrote:
               | so slightly that it can be on the range of 0-5 cents,
               | provided the instrument is sufficiently constructed and
               | the player is sufficiently skilled.
               | 
               | this is why a guitar using equal temperment can play
               | consistently in-tune with itself as well as with other
               | instruments tuned in the same system. it's not about
               | perfection according to some abstract mathematical model.
        
               | jayknight wrote:
               | Violins and family(typically) tune their instruments with
               | 3/2 just fifths. You get the A (440) from the oboe and
               | tune the rest of your strings with perfect just fifths.
               | That means sometimes the cellos' C strings will be
               | noticably too low in some circumstances so you'll see
               | them finger an "open C" just above the nut to make it
               | sound right.
        
               | wizofaus wrote:
               | It's 2% of a semitone off by my understanding. I thought
               | I had pretty good ears but I really doubt I could pick
               | that. Open strings do often stick out in general on
               | string instruments though, for a combination of reasons,
               | lack of vibrato and ability to micro-adjust tuning
               | presumably being the main ones (but even the tone is
               | different, I assume based on the difference between
               | having one end fixed by a soft fleshy substance vs the
               | wooden nut).
        
               | palimpsests wrote:
               | the last reason you gave is exactly why open strings
               | sound different. check out zero-fret guitars.
        
               | dbalatero wrote:
               | I actually tune my C string slightly sharp for this
               | reason!
        
               | Bud wrote:
               | Except you very very often don't get an A=440, since a
               | lot of orchestras don't tune to that pitch and early-
               | music orchestras are a full half-tone below that, etc.
        
               | JumpCrisscross wrote:
               | Huh, is that why an open C on a viola always buzzed
               | wrong?
        
               | dumpsterlid wrote:
               | Well yes, the pitch of any violin note except an open
               | string is set by where the finger is placed.
               | 
               | However, being perfectly in tune is also a big red
               | herring kind of thing. People, especially people who like
               | seeing math in music, get obsessed with chasing ideas of
               | perfection in music and music is art... it isn't supposed
               | to be perfect. To have sounds at perfect intervals or
               | sounds perfectly in tune is after a certain point just an
               | annoying detail compared to literally every other aspect
               | of a piece of music.
               | 
               | A lot of advanced digital synthesizers will carefully
               | detune oscillators from each other so they aren't
               | "perfectly in tune" in order to get thicker sounds.
        
               | palimpsests wrote:
               | including multiple methods for the user to detune
               | oscillators is quite common on modern synthesizers,
               | advanced or otherwise. it's almost never a fixed amount
               | of detuning.
               | 
               | one of those methods is called a "chorus" effect. this is
               | extremely common across effect platforms and is not
               | limited to synthesizers / keyboard-type instruments.
        
               | copperx wrote:
               | How does all of that sound to people with absolute pitch?
        
               | Bud wrote:
               | Varies a lot depending on the person. "Absolute" pitch
               | isn't really absolute, in the vast majority of cases.
               | It's a degree of an ability to retain a given pitch and
               | then produce it later without prompting or context.
               | 
               | Keep in mind also that a lot of musicians with "perfect"
               | pitch have to deal with performing situations where the
               | main pitch is not the standard A=440 Hz. For instance in
               | the Baroque repertoire which I perform often, the most
               | common pitch is around A=415, which is around a half step
               | lower, but there are other tunings that pros have to deal
               | with which are both above and below A=440 (European
               | orchestras often tune higher, music before the Baroque is
               | often at A=390, music from the classical period is often
               | around A=430, etc.).
        
               | HelloNurse wrote:
               | > A lot of advanced digital synthesizers will carefully
               | detune oscillators from each other so they aren't
               | "perfectly in tune" in order to get thicker sounds
               | 
               | As noted in other comments, this also applies to singing
               | and arbitrary pitch instruments, possibly at a
               | subconscious level, and it has the opposite
               | "mathematical" implication than you seem to think: any
               | fixed tuning is a serious constraint that makes some
               | chords sound wrong, and only being able to tune
               | individual notes perfectly allows the introduction of
               | aesthetically pleasing imperfections.
        
               | wizofaus wrote:
               | String players have no choice but to learn equal
               | temperament as the vast majority of the time they're
               | playing alongside other musicians, and it's what modern
               | ears (since the late 18th century) expect to hear. It'd
               | be a rare violinist these days that could actually
               | accurately play something in any sort of intonation based
               | entirely on just intervals. Note that almost any sort of
               | vibrato is likely to "smother" the pitch difference
               | between equal and just temperaments anyway - e.g. an
               | equal temperament fifth is 2 cents off a natural fifth,
               | but vibrato can cover a 50 to 70 cent range (opera
               | singers often go over 100, which I find unpleasant to
               | listen to personally - it's basically a trill!)
        
               | joelfolksy wrote:
               | I'm only an amateur, but I doubt there are string players
               | that "learn" equal temperament. I have no idea how I
               | would find 440 * (2^(1/12) ^ n) Hz, for any n not a
               | multiple of 12, in the way that I can find 440 * (4/3)
               | Hz, or 440 * (3/2) Hz, etc. When playing with equaled
               | tempered instruments like piano, you just listen for
               | clashes and adjust dynamically, which is only going to
               | happen in slower, sustained passages.
               | 
               | And you're right, we don't play "based entirely on just
               | intervals." What we do is constantly adjust our
               | intonation depending on whether we need it to be "just"
               | _with respect to_ something else (like other notes in a
               | chord), or whether we are free to use a more  "melodic"
               | intonation. See
               | https://www.youtube.com/watch?v=QaYOwIIvgHg for a good
               | demonstration -- note that he talks in formal terms like
               | "play x in the Pythagorean system," but I think you can
               | largely see this as a rationalization of what players do
               | naturally).
               | 
               | Finally, the presence of vibrato doesn't really obviate
               | intonation concerns, sadly. There's a lot of theoretical
               | debate about how the pitch of a vibrated note is
               | perceived (is it the highest pitch in the range that
               | determines whether the note sounds in tune? etc.), but in
               | practice you can easily verify that adding vibrato to an
               | out-of-tune scale will not make it sound any more in
               | tune, nor will adding it to a shift mask a slightly-
               | missed shift (if only!).
        
               | wizofaus wrote:
               | I chose the word "smother" deliberately, though maybe
               | "blur" would be better. There's quite a bit of debate as
               | to how the pitch of a note with vibrato is perceived. It
               | definitely isn't right in the middle which might be the
               | naive hypothesis.
        
               | chimeracoder wrote:
               | > String players have no choice but to learn equal
               | temperament as the vast majority of the time they're
               | playing alongside other musicians, and it's what modern
               | ears (since the late 18th century) expect to hear. It'd
               | be a rare violinist these days that could actually
               | accurately play something in any sort of intonation based
               | entirely on just intervals.
               | 
               | That's not true at all. A lot of string players learn to
               | play in orchestras or chamber style, which means they're
               | only playing with other stringed instruments, and they
               | absolutely are taught dynamic tuning by ear, which uses
               | just intervals.
        
               | wizofaus wrote:
               | I did say "based entirely on just intervals". But as a
               | composer I most certainly wouldn't want string players
               | choosing their temperament based on whether there
               | happened to be other instruments in the ensemble capable
               | of the same. And it sounds off for music that doesn't
               | largely sit in a single key signature anyway, which is
               | arguably most music composed since Beethoven. Though I
               | did just read a classic example of where just intervals
               | are often used is the opening of Das Rheingold, that sits
               | on an E flat (not D#!) major chord for several minutes.
        
               | chimeracoder wrote:
               | > But as a composer I most certainly wouldn't want string
               | players choosing their temperament based on whether there
               | happened to be other instruments in the ensemble capable
               | of the same.
               | 
               | This is a weird way of looking at it. String players
               | aren't sitting there consciously thinking of their tuning
               | as they play - they're doing it by ear in real-time. The
               | tuning they use will be the one that best harmonizes with
               | the other notes being played at that moment.
               | 
               | > And it sounds off for music that doesn't largely sit in
               | a single key signature anyway,
               | 
               | That's actually where the ability to adapt tuning
               | dynamically is the most powerful - it allows you to be in
               | tune relative to other pitches being played in that
               | moment, not just in tune relative to some absolute
               | benchmark that nobody is going to be able to hear anyway
               | (because almost nobody has perfect absolute pitch).
        
               | wizofaus wrote:
               | Sure, I imagine it's not dissimilar to how we sing as
               | choristers. But I've played on keyboards tuned to exact
               | just temperament in a particular key and it starts to
               | sound very weird very quickly the moment you veer off the
               | reference key signature.
        
               | chimeracoder wrote:
               | > But I've played on keyboards tuned to exact just
               | temperament in a particular key
               | 
               | Well, that's your problem. You're using a keyboard, which
               | doesn't permit you to harmonize dynamically the way an
               | unfretted string instrument does.
               | 
               | Even _within_ a particular key, the pitch that sounds the
               | best for a particular note will depend on which other
               | notes within that key you 're attempting to harmonize
               | with. A keyboard can't do that.
        
               | wizofaus wrote:
               | No and it's possible that as a pianist my ears are more
               | attuned to prefer equal temperament than those of a
               | string player. But I admit when singing a capella there
               | are occasions particular chords just seem to sit better
               | than when having to match a piano accompaniment, and to
               | some extent that's likely to be the ability to use
               | "purer" intervals.
        
               | wizofaus wrote:
               | Btw, this is from the wikipedia article on Equal
               | Temperament, and I'd say it aligns with my general
               | understanding/ expectation:
               | 
               | "Unfretted string ensembles, which can adjust the tuning
               | of all notes except for open strings, and vocal groups,
               | who have no mechanical tuning limitations, sometimes use
               | a tuning much closer to just intonation for acoustic
               | reasons. Other instruments, such as some wind, keyboard,
               | and fretted instruments, often only approximate equal
               | temperament, where technical limitations prevent exact
               | tunings.[4]"
        
               | jnwatson wrote:
               | Exactly. The only fixed-pitch instruments in an orchestra
               | are the piano and the percussion section.
               | 
               | It was routine even in my high school brass section to
               | pitch down the major 3rds.
        
               | wizofaus wrote:
               | Having briefly learned a few wind instruments (flute and
               | horn primarily) I'm aware pitch adjustment is _possible_
               | but the keys /valves are designed around equal
               | temperament - for anything other than slower sustained
               | passages (or potentially repeated notes) constantly
               | trying to approximate just intervals doesn't seem
               | sustainable. And again, absolutely not what I would want
               | or except to hear as a composer.
        
               | palimpsests wrote:
               | skilled instrumentalists are quite capable of
               | consistently reproducing intervals in a given tuning
               | system. particularly thirds in just intonation. it's not
               | an approximation. it's one of the reasons we spend so
               | much time learning ear training in conservatory.
        
               | wizofaus wrote:
               | I argue all just about all intonation is some sort of
               | approximation, unless you're playing an electronic
               | instrument that doesn't allow pitch adjustments! And it
               | does surprise me how little my ears seem to notice
               | despite having zero tolerance for people singing even
               | slightly off-key.
        
               | palimpsests wrote:
               | relative to mathematical perfection, of course it's all
               | an approximation when a human instrumentalist is
               | involved. that's the nature of our physical reality.
               | 
               | the most important element here is how it sounds to our
               | ears. not how closely it tracks to an equation.
        
               | JasonFruit wrote:
               | We actually tend to approach Pythagorean tuning,
               | according to the Catgut Acoustical Society.
        
             | mort96 wrote:
             | Right, I made an edit which accounts for that while you
             | wrote your comment. It's an important detail.
        
             | [deleted]
        
           | progrus wrote:
           | Just consider it technical debt.
        
           | offByJuan wrote:
           | I think to understand the difference between the two notes is
           | context. Like the word 'read'. The same word is pronounced
           | different according to context. 'I read the book' vs 'Did you
           | read the book'. When you read music you expect a e flat not a
           | d sharp and vise versa
        
         | BurningFrog wrote:
         | On a physical piano you have to make these tuning compromises.
         | 
         | A computer generated piano performance could pretty easily pick
         | versions of each note that are in harmony with the other notes
         | played at that moment.
         | 
         | I wonder if that would be worth doing? Has it maybe already
         | been done?
        
           | sporkl wrote:
           | There have been a couple attempts, the term is "adaptive pure
           | intonation." Check out the list at
           | https://en.xen.wiki/w/Adaptive_just_intonation .
           | 
           | Also want to plug my own project, Pivotuner:
           | https://www.dmitrivolkov.com/projects/pivotuner/ . I believe
           | it gives more flexibility and control to the performer than
           | the others on that list. It's not publicly released yet
           | (hopefully soon), but (anyone) feel free to email me if
           | you're curious to try it out!
        
           | shadowofneptune wrote:
           | Tuning an instrument to the rest of the instruments in the
           | ensemble is pretty common outside of Western music. Could be
           | done with a normal piano.
        
             | pclmulqdq wrote:
             | Western music involves a lot of instruments with fixed
             | tunings, like oboes and trumpets, which are made in equal
             | temperament.
        
               | smrq wrote:
               | (Former oboist) You can absolutely adjust the tuning of a
               | note with embouchure, and in a group context will do so
               | all the time to make chords tune better.
        
               | adgjlsfhk1 wrote:
               | wind instruments don't have fixed tuning. intonation
               | allows you to bend notes enough to get the tuning you
               | want. for a dramatic example of this, look at the
               | clarinet solo at the beginning of rhapsody in blue.
        
               | pclmulqdq wrote:
               | The glissando at the opening of rhapsody in blue is not a
               | counterexample to fixed tuning. It is a specific
               | technique availed by having open holes under the fingers:
               | by sliding the fingers slowly off the holes, and
               | partially covering the holes, you can get a glissando
               | effect. This same technique is used to create semitones.
               | 
               | Both of these are very difficult to do precisely, and
               | come at a significant cost in the agility of the player.
               | They are more equivalent to pitch bending on a guitar
               | than adjusting tuning systems on a violin, which has
               | almost no impact. Instruments with valves and hole
               | covers, like bassoons, make techniques like this
               | extremely difficult if not impossible.
               | 
               | However, the holes in the instrument are drilled at
               | specific places along the length of the instrument
               | corresponding to specific notes. This is what gives the
               | instrument its tuning. Hole positions are calculated and
               | drilled very precisely to make sure that the instrument
               | is in tune. It is not accurate to say that these
               | instruments do not have fixed tuning. The tuning is
               | literally drilled into the body of the instrument.
        
               | palimpsests wrote:
               | wind and brass players adjust intonation via embouchure
               | all the time...
        
               | adgjlsfhk1 wrote:
               | Dude I've played clarinet for literally a decade (and a
               | few years of saxophone). Anyone who's even a moderately
               | talented amateur can bend notes enough to bend your note
               | out of equal temperament. Sure you don't do this for
               | anything fast, but if you have a longer chord this is a
               | very common technique.
        
               | pclmulqdq wrote:
               | That is completely true. It is not enough to change the
               | tuning of a piano you are using away from equal
               | temperament, however.
        
             | BurningFrog wrote:
             | I'm talking about tuning the _individual "keys"_ of the
             | piano to harmonize with the other keys being played at
             | every moment.
        
             | nsv wrote:
             | Well, pianos are not as easy to tune as some other
             | instruments. But you're right that it could be done.
        
           | mandmandam wrote:
           | This might be the closest to what you're looking for; it was
           | linked in tfa: https://oddsound.com/
        
             | coldtea wrote:
             | Though, this is more of a "toolset" to do custom tunings
             | and apply them at various times in a DAW, than something
             | actually implementing what the parent asked for.
             | 
             | In other words, it's something someone might use to
             | implement what they asked for - but also lots of other
             | things besides, and it's not meant specifically for that
             | purpose.
        
         | MichaelDickens wrote:
         | > The paradox is that you can't create a theory of music whose
         | notes are both (a) evenly spaced and (b) contain the integer
         | ratios.
         | 
         | I don't know much about this, but isn't (b) impossible even if
         | you satisfy (a)? There is no sequence of numbers that contains
         | any arbitrary integer ratio because there are infinitely many
         | possible ratios but only finitely many ratios you can make out
         | of a sequence of numbers.
         | 
         | (Obviously some ratios like 2:1 and 3:1 are more important
         | than, say, 52697:16427. 12-TET chooses to permit 2^n:1 at the
         | cost of all other ratios, which seems like a good tradeoff to
         | me.)
        
         | wyager wrote:
         | > You want (b) because small-integer ratios are pleasant
         | sounding -- partly culturally-acquired taste, partly because
         | physics gives musical instruments acoustic spectra in integral
         | multiples of a fundamental frequency
         | 
         | I'd say it's more likely because intermodulation distortion
         | between frequencies with low-complexity fractions tends to be
         | low-frequency.
        
         | emerged wrote:
        
         | noncovalence wrote:
         | In the context of the difference between D# and Eb, 19-TET is
         | very interesting to play around with. It adds an extra black
         | key between every pair of white keys, and most songs intended
         | for 12-TET still work fine, _as long as you play sharps and
         | flats as written_. If you play a D# instead of an Eb, you
         | suddenly get a very different sounding interval.
        
           | bonzini wrote:
           | Also as long as sharps and flats are written in a very
           | pedantic manner. For example a diminished C chord only sounds
           | "right" if it's notated as C-E-G-B rather than C-E-G-A.
           | 
           | On top of this, harmony may or may not work the same in
           | 19-TET and 12-TET. With the same example of diminished
           | chords, the diminished chord does _not_ divide the octave in
           | four equal parts in 19-TET. Adim and Cdim are enharmonic in
           | 12-TET, but Adim in 19-TET is A-C-E-G; that is, only C and E
           | are the same.
        
         | evrydayhustling wrote:
         | Now that we can have electronic instruments that "tune"
         | themselves, could we compute song-optimal tunings that preserve
         | the intervals used most in that song? Does this have a name?
         | 
         | As a guitarist we often swap guitars or retune to make certain
         | songs easier to play, or to be able to get a certain tamber put
         | of the note. But I never considered it as a way to address
         | temperament.
         | 
         | It's interesting to think how much of music theory emerges out
         | of reconciliation with available instruments, as opposed to
         | reconciliation with the ear.
        
           | golergka wrote:
           | Apple Logic Pro has this function built in as Hermode tuning.
        
           | bluGill wrote:
           | Maybe, but it needs to be the whole band not just one
           | instrument. What notes the bass us hitting changes how the
           | guitar needs to sound and vice versa. If you have a large
           | orchestra it's gets hard, and even worse if someone hits a
           | wrong note.
        
           | mrob wrote:
           | You can even dynamically adjust the tuning to maximize
           | consonance throughout the song, e.g.:
           | 
           | https://sethares.engr.wisc.edu/mp3s/three_ears.html
        
             | still_grokking wrote:
             | I just learned: This seems to be related to that "Hermode
             | Tuning".
             | 
             | https://en.xen.wiki/w/Adaptive_just_intonation
             | 
             | But there seem to be differences. Some demos have those
             | tonal glides (that I don't like) but some don't (and sound
             | just great).
             | 
             | Could someone explain in a "TL;DR" what's going on here?
             | 
             | But I see, that wiki I just found seems to be full of info.
             | But it will take time to read all that... Would prefer to
             | have some VSTs to just play around with. Any tips?
        
             | [deleted]
        
             | dcow wrote:
             | This is really cool. It sounds weird for about the first
             | 45-90 seconds but then my mind adjusts and it sounds really
             | pleasant. Would make a good context/theme for a video game
             | soundtrack.
        
               | drdeca wrote:
               | To me the individual notes sound fine and usually normal-
               | ish (except for the really extended ones), but I have
               | difficulty hearing the overall tune? Or, it sounds like
               | there are parts of a tune with other parts on top which I
               | don't hear how they fit?
               | 
               | I think a clearer demonstration might be to have a side
               | by side comparison of a fairly simple tune in 12TET vs in
               | this dynamical tuning.
        
               | thewebcount wrote:
               | Agreed! I'm not hearing a very definable or memorable
               | melody or harmony. The synth sounds chosen are kind of
               | grating, which doesn't help. I'd love to hear something
               | more coherent in this sort of tuning to get a better
               | understanding of it.
        
               | AnonCoward42 wrote:
               | It really is kool. However, I have the feeling you can
               | transport only a very limited range of emotions with it
               | as we are accustomed to certain harmonics I guess.
               | 
               | Still, it's kinda like alien music and it's certainly
               | creative.
        
             | still_grokking wrote:
             | Is "maximized consonance" what causes those extreme sharp
             | sounding ring tones? (After listening to this peace my ears
             | are still ringing; 2 min. after the fact).
             | 
             | Also the tonal glides sound like an old broken record
             | player. (This creates a sensation of "wobbling speed",
             | which sounds just wrong).
             | 
             | Hmm, my ears are still ringing, even while writing this;
             | that was not a pleasant experience to be honest...
             | 
             | I guess I need some ear-bleach. Psytrance to the rescue!
             | Let's see, maybe, hmm, Talpa1, or maybe better that old
             | Atma set2?
             | 
             | ___
             | 
             | 1 https://www.youtube.com/watch?v=wErFe-1dlg4
             | 
             | 2 https://www.youtube.com/watch?v=HU9FDStUoT8
        
           | smrq wrote:
           | Not trying to be "that guy", just figured you might want to
           | know-- although it's pronounced "tamber" it's spelled
           | "timbre". Thanks, english.
        
             | kqr wrote:
             | I think this one you can blame on the French.
        
               | m-p-3 wrote:
               | The word sounds exactly how it is written when you say it
               | in French tho, not our fault you adopted the word and say
               | it differently ;)
        
               | Sharlin wrote:
               | Huh, I'm pretty sure that it doesn't sound like [timbre]
               | in French either :D
        
               | zdragnar wrote:
               | I blame the English aristocrats. Why eat cow like a
               | peasant when you could have some _beef_ like a fancy
               | person?
        
               | kibwen wrote:
               | And why spell it "color" like the Romans did when you can
               | blithely attempt to imitate the French aristocracy by
               | injecting arbitrary "u"s into random words, thus giving
               | you license to complain about CSS keywords for the rest
               | of recorded history? :P
        
               | willnonya wrote:
               | You're my new favorite person.
        
               | dudeguy3301 wrote:
               | also, think the french started this. a name for the
               | animal in the field, a different name for the animal on
               | your plate.
        
             | Tagbert wrote:
             | The pronunciation is highly variable and the spelling has
             | historically also been variable. When French words are
             | imported to English, sometimes people try to retain the
             | French pronunciation and other times they anglicize it.
             | This word seems to have been handled both ways.
             | 
             | Another thing that happens is that both English and French
             | change their pronunciation over time. After English imports
             | a word, the French pronunciation may change making the
             | English word look odd or not even look connected. Not sure
             | that this happened to "timbre" but it did happen to words
             | like "chief" and "chef". Both were imported from French but
             | at different times. "Chief" when French used the hard 'ch'
             | sound and "chef" when French had switched to the soft 'sh'
             | sound.
             | 
             | https://www.merriam-webster.com/dictionary/timbre
             | https://en.wiktionary.org/wiki/Timbre
        
           | xhevahir wrote:
           | You might like to hear this proprietary algorithm:
           | http://www.hermode.com/index_en.html
           | 
           | Since you're a guitarist, there's also this Swedish guitar,
           | which purports to solve the tuning problem (which I tend to
           | think is not a problem but an essential part of the
           | instrument's sound) https://youtu.be/-penQWPHJzI
        
             | still_grokking wrote:
             | OK, now I'm also sold on this "Hermode Tuning". Sounds
             | indeed great!
             | 
             | How to tune synthesizers this way? What and where to buy?
        
               | xhevahir wrote:
               | A license has to be purchased, and I think only
               | Steinberg's Cubase and Apple's Logic Pro offer it as a
               | feature. Since Steinberg is owned by Yamaha I suppose
               | they might be allowed to use it in a hardware
               | synthesizer, but as far as I know they do not.
               | 
               | Edit: this table says that Access have hardware synths
               | with Hermode tuning: http://www.microtonal-
               | synthesis.com/micro_af.html . Elsewhere I see Waldorf
               | listed as having offered Hermode in some models.
        
               | still_grokking wrote:
               | Oh, cool! Thanks for the list!
        
             | dehrmann wrote:
             | I think this is the company that makes it:
             | https://www.truetemperament.com/products/
        
             | still_grokking wrote:
             | Wow, this guitar sounds so ultra-clean! Depending on song
             | this could be pretty nice.
             | 
             | But the normal, "imperfect" guitar does not sound bad. I
             | would also say, this "imperfection" gives a guitar its
             | typical sound in the first place, so it's not a "problem".
             | 
             | Both guitars in that video are great, but indeed quite
             | different.
        
               | smitty1e wrote:
               | The humanity is in the imperfections.
               | 
               | Prediction: society demotes all of the auto-tuning and AI
               | art to training status, and actual art produced by himans
               | with pulses is preferred.
        
               | still_grokking wrote:
               | Here we're not on the same page, frankly.
               | 
               | My favorite style of music (Psytrance) almost _requires_
               | digital  "perfection".
               | 
               | It's even not really possible to create a "properly
               | sounding" Psytrance bass-line1, not even a most basic
               | variant, without doing some math (or using tools that
               | will do that math for you). Frequencies, pitch, tempo,
               | and phase need to match constantly and absolutely
               | perfect, or it won't sound properly. Any "humanization"
               | on any preset would kill the sound instantly!
               | 
               | For that reason creating Psytrance is a very "mechanical"
               | task that only machines can perform with the required
               | precision. (And not every machine is good enough for that
               | actually. You need for example oscillators with very high
               | precision or you will experience unwanted artifacts,
               | especially on higher frequencies, that could destroy the
               | sound).
               | 
               | Something that could create "perfectly matching" chords
               | that don't include any dissonance would be really useful
               | to get the (most of the time) desired "ultra-clean"
               | Psytrance sounds. The usual alternative is to filter out
               | all dissonance. But that's a lot of work, or in "bigger"
               | chords or soundscapes outright impossible (even when you
               | slice the sound in the frequency spectrum with all kind
               | of tricks; filters also produce artifacts... And trying
               | to get rid of those artifacts, like phase imperfections,
               | changes the sound again in often undesired ways. A
               | "perfect" tuning form the get go would maybe help with
               | such things).
               | 
               | ___
               | 
               | 1 Here two of the better tutorials for Psytrance bass-
               | lines:
               | 
               | https://www.youtube.com/watch?v=m40xkEkrEKo
               | 
               | https://www.youtube.com/watch?v=-4B1NcdNJjE
               | 
               | And if you're lazy see here for a VST plugin send form
               | the gods:
               | 
               | https://fx23.net/psylab-pro/
        
           | MikeBattaglia wrote:
           | This is called "adaptive just intonation." Logic Pro X has
           | this feature built in, using a particular algorithm called
           | Hermode Tuning. It sounds great
        
             | thebeardisred wrote:
             | /me goes to explore this in Ableton...
        
           | ajross wrote:
           | > Now that we can have electronic instruments that "tune"
           | themselves, could we compute song-optimal tunings that
           | preserve the intervals used most in that song?
           | 
           | We've had self-tuning instruments for thousands of years.
           | Vocal harmony has almost always been perfectly tuned for its
           | key. Likewise orchestral strings are fretless and can produce
           | perfect intervals. Equitemperment was an innovation in the
           | 17th century because it approximated the perfect intervals
           | very well ("sounded good") but also permitted the ability to
           | simultaneously represent scales based on every note in the
           | circle of fifths ("sounded interesting"). But the "real"
           | chords were always (well, since the late middle ages)
           | understood to be integer ratios.
        
             | tengwar2 wrote:
             | Brass instruments (not just the trombone) can have micro-
             | adjustments in pitch through the embouchure (lip
             | position/tension) of the musician.
        
               | squarefoot wrote:
               | Does this apply also to sax? I've listened to some
               | (mainly old) recordings where the sax seems clearly out
               | of tune; sometimes it's subtle but there are recordings
               | in which it's so off that one wonders if it's done on
               | purpose (1) and personally I really dislike it. Back in
               | the day there weren't digital effects or they were so
               | primitive that applying pitch correction on the fly while
               | maintaining sound quality and spectral integrity was out
               | of question, still tape recorders allowed to finely set
               | their speed, so tuning the song to a sax being recorded
               | would have been trivial.
               | 
               | (1) Example: "get up an get out" by Iggy Pop.
               | https://www.youtube.com/watch?v=R1ld5jG3f-M
        
               | palimpsests wrote:
               | retuning via tape velocity modulation would be easiest if
               | the instrument in question was consistently out of tune
               | with the rest of the band - like if the sax was always 15
               | cents flat relative to the harmonic structure.
               | 
               | usually that's not the case though. typically it's
               | individual notes. much harder to precisely and accurately
               | modulate tape velocity (especially by hand).
        
               | colomon wrote:
               | As far as I know it applies to both brass and woodwinds,
               | though the degree of difficulty involved probably varies
               | between types of instruments and also (at least on the
               | woodwinds I'm familiar with) note to note.
        
               | mr_tristan wrote:
               | A sax is _really_ easy to control (or lose control) of
               | the pitch. And in fact, many saxophonists will just shift
               | various ranges around sharp or flat to suit their style
               | (cough _Phil Woods_ cough).
               | 
               | So basically, a woodwind like a sax will tune a few notes
               | with a piano or whatever, but it's really up to the
               | player to keep playing in tune. I would not even bother
               | trying to autotune or use post-processing; it'll just
               | sound weird.
               | 
               | This is also how you can get a room full of student
               | musicians "tuned" but it still sounds like a disaster.
        
               | analog31 wrote:
               | Also, the tubes for the individual valves have their own
               | tuning slides. A trumpet will typically have a little
               | thumb-operated lever for one of those slides, to help
               | with some of the notes. I saw a video of a tuba solo, and
               | the tubist was working the tuning slides almost as much
               | as the valves.
        
               | dbcurtis wrote:
               | With valved brass instruments you are trying to
               | approximate a logarithmic relationship with a linear sum
               | of components. Trumpets have a high resonant Q, so not
               | using the valve slides is going to produce out of tune
               | notes. I played horn once upon a time. Horns have low
               | resonant Q, so you just "lip it in".
        
               | palimpsests wrote:
               | one of my favorite aspects of learning the tuba was when
               | we covered logarithmic approximations via linear summing.
        
               | jnwatson wrote:
               | Thumb-operated levers on trumpets are uncommon (though,
               | IMHO ergonomically superior). More common are a ring in
               | which you place your left ring finger. The ring is
               | directly attached to a slide on the third valve, so you
               | can flatten notes by extending your left ring finger.
        
               | bewaretheirs wrote:
               | What I've seen is a thumb lever for the 1st valve, finger
               | ring for the 3rd valve.
        
               | bewaretheirs wrote:
               | Yep. And - where musically appropriate - if you know
               | which note of the chord you're playing, you can tweak the
               | pitch towards the Pythagorean tuning and get the harmony
               | to "ring" as the harmonics of each note reinforce each
               | other.
               | 
               | This sort of hybrid tuning is common in barbershop
               | quartet singing as well.
        
             | evrydayhustling wrote:
             | This is a cool insight! Can choruses be shown to
             | dynamically adopt "optimal" tunings for a particular song?
             | I.e. the singers settle onto frequencies that make the
             | song's intervals sound best?
             | 
             | To be clear, I'm trying to explore the idea that individual
             | songs have optimal tunings because they only use certain
             | intervals. So, something more fine grained even then
             | singing for a particular key.
        
               | geofft wrote:
               | Singers will do this via intuition - you don't think of,
               | say, a perfect fifth as 2^(7/12) = 1.4983x over the root.
               | You think of it as a particular pair of sounds that
               | resonates well, much like when you picture "red" in your
               | mind you're not thinking of exact HSV or Pantone values.
               | At most, you'll think of a perfect fifth as exactly
               | halfway between the octaves (1.5x over the root). As the
               | sibling comment points out, this isn't the singers
               | choosing a particular temperament for the entire song;
               | it's them constantly tuning individual chords and
               | intervals to each other and to their previous notes as
               | the song goes on. The same note on paper can be several
               | slightly-different frequencies in different parts of the
               | song, and most singers won't even be able to tell you
               | that they're doing that.
               | 
               | (This is also the same mechanism at work when an entire
               | choir singing an unaccompanied piece goes flat without
               | realizing it. Someone will not quite make an ascending
               | interval, and everyone else will adjust to cover it.)
        
               | AlbertCory wrote:
               | Thanks, that explains why singers, when they go wrong,
               | are almost always on the flat side.
        
               | ajross wrote:
               | You can absolutely sing a perfect chord. That's most of
               | the idea behind styles like barbershop, for example. But
               | things start to fall apart when chords transition between
               | each other. The first and third notes of the central
               | chords in a key will line up on top of each other, but
               | the middle notes of the chords and triads based on other
               | notes don't. So just like an equitempered scale sounds a
               | tiny bit off, harmony gets wonky too if you try to do
               | interesting things.
               | 
               | So the compromise we've all settled on is that we play
               | music in the equitempered scale, and only adjust a little
               | bit here and there to exploit perfect tunings in limited,
               | style-dependent ways.
               | 
               | Which is to say: perfect chords are interesting flavor,
               | but at the end of the day kinda boring in isolation;
               | "real" music needs more rules.
        
               | evrydayhustling wrote:
               | Awesome appreciate you explaining this. Hadn't considered
               | the idea that transitions vs simultaneous notes "compete"
               | on what the optimal note frequencies are. And very cool
               | to understand that people are dealing with this
               | pragmatically all the time.
        
               | kofejnik wrote:
               | For a demo, you can search YouTube for "Jacob collier g
               | half-sharp"
        
           | andrepd wrote:
           | There is a very similar thing: Just intonation http://alumni.
           | media.mit.edu/~bdenckla/thesis/texts/htthe/nod...
        
       | psyc wrote:
       | I started asking my father, a concert pianist, composer, and
       | teacher - this question when I was 4. He explained. In my head I
       | said, "Bullshit." I continued to press him on it periodically
       | until I was a teenager. I still shook my head and thought, "What
       | is wrong with these people." Now, I can read sheet music just
       | fine, but I still feel like ... never mind. I've done a ton of
       | composing without once taking any notice of what key any of it
       | was in. And it all sounds fucking great. I prefer to do as much
       | as possible "by ear". I'm unbelievably stubborn.
       | 
       | tl;dr - Somebody really should have picked up on the autism when
       | I was 4, and MIDI rolls don't give a shit about keys and
       | accidentals.
        
         | PaulDavisThe1st wrote:
         | MIDI rolls don't, by themselves, make any noise or even
         | inherently define any note frequencies at all.
         | 
         | The frequency of the sound produced by a given synthesizer when
         | it receives any particular MIDI note number is up to the
         | synthesizer. This is part of the point of the MIDI tuning
         | system. The synthesizer and/or the tuning system may very much
         | care about keys and accidentals.
        
           | [deleted]
        
         | Nemrod67 wrote:
         | do share! I'm a "MIDI composer" myself and love to hear what
         | others do :)
         | 
         | obligatory self-promotion,
         | https://www.youtube.com/channel/UCUmdU7WpuhAv3imtVqkGpIA
        
           | psyc wrote:
           | That's good stuff! Reminds me very, very vaguely of:
           | 
           | https://www.youtube.com/watch?v=vapZZdog0NI
           | 
           | Here's a small sampler. I include one that's maybe a bit
           | similar, the one called 'crsh'
           | 
           | https://soundcloud.com/w37hlwyq0a/sets
        
             | Nemrod67 wrote:
             | I liked that Overworld theme a lot, reminded me of the
             | Nexomon Evolution theme
        
       | bazhova wrote:
       | Instruments without frets don't have this problem. I played
       | violin for many years. When you play a double stop (two strings
       | at the same time), since there are no frets, you can play true
       | 3rds, 6ths etc. The harmony is so "pure" that it causes a third
       | harmonic to ring (which is how you know you're doing it right).
       | My violin teacher always insisted that e-flat and d-sharp are not
       | the same. When you're playing in different keys you have to put
       | your finger in a slightly different place.
        
         | tadhgpearson wrote:
         | Right. I had this too, but because I never got the explanation
         | this post provides, I had to live with "because it's a
         | different key" - but could never quite understand why it made
         | me out of tune with an accompanying pianist. Now I know... this
         | is awesome!
        
       | vram22 wrote:
        
       | kortex wrote:
       | Anyone who is interested in going down the beyond-12-equal-
       | temperment rabbit hole:
       | 
       | - xeharmonic wiki: https://en.xen.wiki/w/Main_Page
       | 
       | - xenharmonic playlist:
       | https://open.spotify.com/playlist/1OcPPq0ohnUarvDCERaxaR?si=...
       | 
       | - Tolgahan Cogulu and his awesome microtonal guitar creations:
       | https://youtu.be/iRsSjh5TTqI
       | 
       | Some bands with more "approachable" sounds (vs the xenharmonic
       | playlist, which gets spicy) known for microtonal work:
       | 
       | Psychedelic rock:
       | 
       | - King Gizzard and the Lizard Wizard (namely albums Flying
       | Microtonal Banana, KG, LW)
       | 
       | - Altin Gun
       | 
       | - Gaye su Akyol
       | 
       | Classic blues rock (Led Zeppelin and the like, but also OG blues
       | like Robert Johnson, that's another rabbit hole) also has a
       | surprising amount of off-12Tet notes, because of the blues scale
       | 
       | In the electronic realm, Aphex Twin does some interesting stuff
       | with microtones
       | 
       | - Jacob Collier - musical prodigy, mostly a capella/vocal
       | arranging, but is a genre polymath, does some incredible stuff
       | with just harmony
       | 
       | If anyone has anything to add, please do! I can't get enough of
       | this stuff
        
       | moogly wrote:
       | It would be remiss of me not to mention the archicembalo[0],
       | which was a keyed instrument that allowed a musician to
       | experiment with this distinction to a degree.
       | 
       | [0]: https://en.wikipedia.org/wiki/Archicembalo
        
       | willnonya wrote:
       | "This confusion applies to all of the black keys"
       | 
       | Music theory must be racist!!!
       | 
       | /sarc
        
       | coldtea wrote:
       | For a similar reason that "upslope" and "downslope" describe
       | walking upon the same stretch of road on a hill: context.
        
       | lloydatkinson wrote:
       | You can tell they are different because of the way they are
        
       | mabbo wrote:
       | Given that integer ratios tend to sound better, are there songs
       | edited to use notes that maximize the number of integer ratios
       | rather than the standard tuning?
       | 
       | It would seem an easy hack to make people like your new pop track
       | better. But then, I'm no musician, so maybe I'm oversimplifying.
        
       | tzs wrote:
       | Guitarist might find three videos recently posted to classical
       | guitarist and lutist Brandon Acker's YouTube channel interesting.
       | 
       | Lutes and early guitars (before around 1800) did not have metal
       | frets. Instead they used pieces of string tied around the neck.
       | 
       | They did this because the strings were very expensive, with a set
       | of strings for a lute often costing more than the rest of the
       | lute, and strings were not as robust as more modern strings. With
       | metal frets strings would wear out faster. You could easily end
       | up spending more per year on strings than you had initially spent
       | on your instrument. By making the frets of the same material as
       | the strings they didn't need to change strings as often.
       | 
       | Acker and luthier M.E. Brune took a classical guitar Brune was
       | building but had not yet put frets on and played around with
       | putting on tied gut frets and gut strings. In the first video [1]
       | they just go over the history of tied on frets, and do some
       | comparisons with metal frets.
       | 
       | With tied on frets it is relatively easy to try tunings other
       | than 12-TET. You can change the position of a fret, or you can
       | add extra frets. You can also add partial frets. Renaissance
       | lutists would often glue on small pieces of string behind or in
       | front of a fret. The fret would give them some particular note
       | from a sharp/flat pair, and the little mini fret, called a
       | tastino, would give them the other note from that pair.
       | 
       | The second video [2] explores the tuning possibilities of tied on
       | frets and tastinos. Acker plays a bunch of things in 12-TET and
       | in other tunings more suitable for the particular piece, and also
       | gives some examples of how bad other tunings can sound when you
       | are playing a piece in a key that doesn't fit the key your
       | instrument was tuned for.
       | 
       | The third video [3] is just playing around after the tied on fret
       | experiment is over but the guitar has not yet had its metal frets
       | installed. Acker tries to play it without frets. That turns out
       | the be quite a mixed bag.
       | 
       | [1] https://www.youtube.com/watch?v=--y_vf-Kg-w
       | 
       | [2] https://www.youtube.com/watch?v=tiKCORN-6m8
       | 
       | [3] https://www.youtube.com/watch?v=RIQaRqr5T5U
        
       | AlbertCory wrote:
       | I searched the whole thread for "Autotune" and didn't find it, so
       | let me start:
       | 
       | I'm assuming, but I want to check with you all: does Autotune
       | always "correct" to the exact center of the note? I assume the
       | answer is probably Yes.
       | 
       | If so, that's a bug, is it not?
        
         | MikeBattaglia wrote:
         | You are correct. For instance, traditionally, in barbershop
         | vocal music, singers are trained to deliberately deviate from
         | 12 equal, towards an ever-shifting kind of just intonation, in
         | order to maximize the extent to which the voices blend. Auto
         | tune, on the other hand, just tunes things straight to 12
         | equal. Melodyne fares a little bit better in that it lets you
         | tune to custom microtonal scales, or fudge things a little bit
         | here and there, etc. Interestingly, Logic Pro X has a "Hermode
         | Tuning algorithm" that will basically do the dynamic adjustment
         | toward just intonation for you, but it only works for MIDI
         | instruments and not auto tune as far as I know.
        
         | filoeleven wrote:
         | Autotune software has different parameters available to it.
         | These include pitch correction speed, how close a singer has to
         | be to the note in order to start/stop pitch-correction, which
         | pitches to correct for.
         | 
         | The T-Pain effect, which is the autotune sound you're probably
         | thinking of, cranks most of those parameters all the way up in
         | order to get to that robot voice: "instantly lock the vocals to
         | one of these set pitches, if the singer goes lower than X,
         | immediately switch to the next lower pitch in the set." More
         | subtle usage makes for a performance that is more in tune
         | overall but keeps much more of the vocalist's expression and
         | pitch variation intact. Its goal usually is to not be noticed.
         | 
         | I don't think I understand your question (edit: about it being
         | a bug), so I won't attempt to answer it directly, but maybe the
         | above info is helpful in thinking about it.
        
           | AlbertCory wrote:
           | > about it being a bug
           | 
           | The comment was asserting (or questioning) the T-Pain effect.
           | I honestly didn't know if that was what everyone was using in
           | Autotune or not.
        
       | fxtentacle wrote:
       | Because for most instruments, it is. A violin player won't move
       | up for a full half tone for a D sharp, so there'll remain a small
       | pitch difference between them.
       | 
       | It's only for the small subset of keyed instruments like pianos
       | that pitch is quantized into 12 subtones. But even there, organs
       | use a different pitch to key mapping than keyboards.
       | 
       | For a very interesting rabbit hole, search for "Wolfsquinte",
       | which is a chord that sounds nice on keyboard but horrible on
       | organ.
        
         | wumpus wrote:
         | I am not aware of any manuscript having different tuning of
         | organs vs other keyboards in the Renaissance or Baroque eras...
         | can you cite one?
         | 
         | The Wikipedia article for Wolfsquinte makes it clear that it
         | has nothing to do with keyboards or organs: it's a feature of
         | your choice of tuning. Perhaps you're used to organs and
         | keyboards with different tuning choices?
        
           | CHY872 wrote:
           | I don't think that's quite GP's claim. They're not
           | necessarily saying that organs and keyboards of the same
           | heritage had different tuning (though it's well documented
           | that instruments had different tuning according to region
           | even through the 1700s and 1800s), rather that historic
           | organs which retain their original temperament sound very
           | different to modern keyboards. Here's an article supporting
           | this. It refers to different rates of beating in different
           | tuning regimes, comparing equal temperament to 'cornet-ton'
           | type things.
           | 
           | Because it's common for organs to be hundreds of years old,
           | and it's common for people to want historic organs to sound
           | as close to how they did when they were made as possible
           | because it's uncommon for them to play in non-vocal ensemble,
           | this leads to a relatively common situation where an organ
           | played today may well be tuned very differently to a piano
           | played today. Depending on the organ.
           | 
           | https://www.eunomios.org/contrib/francis2/francis2.pdf
           | 
           | Here is a second article on organs by one manufacturer tuned
           | in 'meantone' https://www.bach-
           | cantatas.com/Topics/Meantone.htm. It's also the case that
           | harpsichords were commonly tuned in meantone
           | https://www.harpsichord.org.uk/wp-
           | content/uploads/2015/04/te... which might actually support
           | the claim that historic non-organ keyboards sounded different
           | from organ keyboards (specifically, if Bach didn't like the
           | mean-tone organs he played and it was common to tune
           | harpsichords in meantone, that would seem to provide some
           | evidence for both temperaments existing and sounding
           | different on the different types of instrument in the same
           | historic period).
        
             | wumpus wrote:
             | > Perhaps you're used to organs and keyboards with
             | different tuning choices?
        
               | CHY872 wrote:
               | I don't think GP was particularly making the point that
               | it was innately impossible to tune an organ and a piano
               | the same, just that it's common for them to be tuned
               | differently (especially in European churches). Same with
               | harpsichord and piano (where a harpsichord is not tuned
               | to concert A).
               | 
               | Either way, hope you enjoyed the citations - I found them
               | interesting - the one about Bach writing in specific keys
               | so as to match the instruments he's working against
               | reflects a different kind of craftsmanship and concern
               | than one would see from most composers in the 21st
               | centruy!
        
               | magnaton wrote:
               | I tune organs professionally, and in the US most
               | instruments are tuned to equal temperament. For the
               | performance of pieces originally composed on unequal-
               | tempered instruments, though, something is lost on equal-
               | tempered organs: the movement through harmonic
               | progressions on unequal temperaments creates a dramatic
               | tension between consonance and dissonance, with
               | dissonance increasing the farther you get from the more
               | "in-tune" keys and decreasing as the progression returns
               | to them. Similarly, pieces composed in keys that are some
               | distance away from the "purest" key, gain their own
               | distinctive colors. If you're used to equal temperament
               | and then hear a big major chord in the temperament's home
               | key on an organ with a historic temperament, the impact
               | is really quite something as the thirds and fifths are
               | much closer to the natural overtones of the unisons and
               | the whole chord draws together into a gloriously-coherent
               | tonality.
               | 
               | Pipe organs often contain stops called mutations (whose
               | frequencies are non-integer multiples of unison-rank
               | frequencies), and others called mixtures (where there are
               | multiple such pipes per note, generally rather small and
               | high-pitched). These are both intended to reinforce
               | natural harmonics, and as such are tuned pure -- even on
               | equal-tempered instruments! The exception is
               | highly-"unified" instruments where one rank has been
               | wired to play at both unison and mutation pitches (to
               | save money and/or space); this sorta works for quints
               | (fifths), but is pretty bad for tierces (thirds), and
               | don't even try it with a septieme (seventh).
               | 
               | While electronic tuners are often used to set an initial
               | temperament on a reference rank (it can also be set by
               | listening to the contrasting rates of the differential
               | waves between fourths and fifths), we generally tune
               | other ranks to the reference rank, listening to the
               | differential waves created by the two ranks to discern
               | in/out-of-tuneness. For mixtures and mutations, the trick
               | is to be able to recognize differential beating with
               | partials of the reference rank that are higher than the
               | fundamental; and for very high pitches, listening for
               | sub-harmonics comes into play (frequencies can align in a
               | way that creates the illusion that they are harmonics of
               | a fundamental that's not actually being played, and our
               | brains fill in the fundamental; this phenomenon is
               | sometimes used to create the illusion of extremely low
               | "resultant" Pedal-division ranks sounding an octave lower
               | than the root of the fifth that the pipes are actually
               | playing, and the use of an independent pure-tuned quint
               | rank produces the most convincing result).
        
               | fuzzfactor wrote:
               | >Why are D-sharp and E-flat considered to be two
               | different notes?
               | 
               | Officially, it's only on paper.
               | 
               | It kind of makes the key signatures come out more
               | sensible because you don't want to have a signature where
               | there are both sharps & flats in one key.
               | 
               | >electronic tuners are often used to set an initial
               | temperament on a reference rank
               | 
               | >tune other ranks to the reference rank, listening to the
               | differential waves created by the two ranks to discern
               | in/out-of-tuneness.
               | 
               | The equivalent on guitar is to use the tuner for
               | reference on the high E string only, then tune the low E
               | to match perfectly by ear. You're going to be hearing a
               | lot of these two, and they better be able to make you
               | happy to begin with.
               | 
               | Then tune the middle 4 strings according to what the
               | hands will be doing in relation to the reference strings,
               | as well as who you will be playing with and how they are
               | tuned.
               | 
               | Without an electronic tuner a single tuning fork is
               | enough for this, and it's actually better than having a
               | set of 6 forks at the nominal even tempered frequencies.
               | 
               | E=329.6 is the fork you want so you don't have to fret
               | the high string to match an A=440 fork.
        
               | wumpus wrote:
               | This discussion definitely sets a record for "people
               | writing the most words to explain to me things I already
               | know". Hopefully some spectators got something out of it.
               | 
               | Fun story, I once volunteered to play a piece at 440 and
               | a piece at 415 in the same concert, not realizing that it
               | would take a long time for the instrument (a viola da
               | gamba) to "settle" after that drastic of a change.
        
           | fxtentacle wrote:
           | The organs made by the Silbermann family are tuned with non-
           | equal key spacing. And those are among the ones Bach played
           | on. So if you play the same notes on a digital organ, or on a
           | keyboard, the harmonies won't work as intended.
           | 
           | Native Instruments also offers to switch the tuning mode for
           | their virtual/digital instruments, BTW, so that you can
           | compensate for that in software if needed.
        
       | rawling wrote:
       | Can't D# and D# be two different notes too, depending on what key
       | you're in?
       | 
       | Hell, doesn't this apply to the white keys too?
        
         | tgv wrote:
         | By that kind of logic, D# in the key of G# should indeed sound
         | different than D# in the key of C# or B, depending on the
         | temperament.
        
         | TheOtherHobbes wrote:
         | Yes, depending on the temperament.
         | 
         | Not in 12-TET because the ratio between every semitone is the
         | same.
         | 
         | In other temperaments the frequency of every note can be
         | different in every key.
        
       | exabrial wrote:
       | With TTET, we really need to drop note names just use scale
       | degrees (aka 'Nashville Number System'). This would remove a ton
       | of confusion when texting music theory.
        
       | wforfang wrote:
       | D-sharp and E-flat are two different notes used to describe the
       | same physical vibration for the same reason "father" and "son"
       | are two different words that could describe the same person. It's
       | just a way to communicate contextual relation.
        
         | marton78 wrote:
         | This is false. D-sharp and E-flat have (slightly) different
         | frequencies. Read the article!
        
           | dehrmann wrote:
           | ...in certain temperaments, but not the ubiquitous 12-TET.
        
             | noslenwerdna wrote:
             | ... as thoroughly explained in the article.
        
       | petewailes wrote:
       | Obviously Ethan knows this and just isn't going into it because
       | this is more a history lesson than a theory lesson, but the same
       | applies to white keys. So B# and F are perfectly valid notes. C#
       | major for example contains B#, despite that there's no black key
       | between B and C.
        
         | chrismorgan wrote:
         | For that matter, F (F double sharp) and A (A double flat) are
         | both legitimate alternatives/equivalents to G in some
         | situations, by extrapolating the sequences. (And if you
         | extrapolate far enough, _any_ note has multiple possible
         | alternatives--for example, you could get a G that's kinda more
         | G# or G# than just straight G, to use super fuzzy terminology.)
        
       | seanhunter wrote:
       | Short answer: they aren't. This is the musical equivalent of the
       | fact that English has "guarantee" and "warranty" and they mean
       | the same thing.
       | 
       | Long answer: they aren't. They are enharmonic equivalents in the
       | vast majority of music that uses any of the conventional Western
       | systems of tuning (as the author sort of goes out of their way to
       | demonstrate in the article), and if you use or invent a different
       | system then what you call the notes is kind of up to you since
       | it's your system.
        
         | iainmerrick wrote:
         | _They are enharmonic equivalents in the vast majority of music
         | that uses any of the conventional Western systems of tuning (as
         | the author sort of goes out of their way to demonstrate in the
         | article)_
         | 
         | I don't think that's correct -- they are identical in 12-TET,
         | but all the other tuning systems either treat them as different
         | notes, or attempt to compromise between the alternatives in a
         | way that favours certain keys over others.
         | 
         | Maybe this is isn't critical info for a lot of people, but it
         | is important foundational knowledge if you're a music student,
         | or just interested in music theory.
        
           | seanhunter wrote:
           | Actually most of the time if you're playing in a different
           | tuning (eg quarter-comma meantone or pythagorean or whatever)
           | where they would be different, you're playing a type of music
           | where you exclusively would play one note or the other, so
           | the fact that they are theoretically different doesn't arise.
        
             | iainmerrick wrote:
             | But then wouldn't the fact that they're theoretically the
             | same also not arise?
        
         | boffinism wrote:
         | Today is a great day for you, because you get to learn
         | something new! Specifically, that if you derive pitches of
         | notes from harmonics, D sharp and E flat are slightly different
         | pitches! There's actually a great article about exactly this
         | you might want to read, and it's handily linked above.
        
           | seanhunter wrote:
           | Today is a great day for you, because you get to feel good
           | about yourself by being a first-order pedant and making basic
           | assumptions about what I know and don't know and whether or
           | not I've read the article.
           | 
           | I actually did read the article and even prior to that do
           | know about deriving pitches from harmonics. What I posted was
           | still correct in spite of the downvotes.
        
             | yesseri wrote:
             | The problem is you are incorrect. The deeper your knowledge
             | of music theory, and the more experience you have with a
             | capella choir music or certain instruments where they can
             | be played differently, The more apparent this will become.
             | 
             | Trying to sing a D# in a B major chord the same way you
             | would a Eb in a C minor won't be a great experience.
             | 
             | Most of the adjustments will happen automatically if you
             | listen to your fellow singers and have experience. But they
             | do happen.
        
         | nine_k wrote:
         | Addition: when you choose a tonality in which you write a piece
         | of music, it may define its standard set of flats and sharps,
         | to simplify building chords using uniform rules. Because of
         | this, it is convenient to name the same note using different
         | names, relative to its neighbors.
         | 
         | Expansion: in non-tempered, natural tuning, such as often used
         | when playing a violin, there _are_ differences between some
         | sharps and flats built from different notes, because natural
         | harmonic intervals, based on frequency ratios like 3:2, do not
         | split the frequency range in a completely log-linear way. This
         | is why, say, G# and Ab may be _not_ the same for purposes of
         | pure natural harmony [1].
         | 
         | Equal temperation was invented to overcome this. J.S.Bach wrote
         | a great showcase for it, Woll-Tepmeriertee Klavier, which
         | involves harmonies and chord progressions that are hard or
         | impossible to achieve with natural tuning without producing
         | weird dissonances.
         | 
         | [1]: https://pages.mtu.edu/~suits/WhyG.html
        
           | mrob wrote:
           | It's unknown whether Bach wrote the WTK for equal temperament
           | (the modern standard) or for a well temperament (something
           | that tempers all keys enough to be usable but does not make
           | all keys sound identical).
        
             | jakzurr wrote:
             | Whoa, I didn't know!
             | 
             | Now I'm wondering if I was told wrong 50 years ago, or if
             | this is new research?
             | 
             | https://en.m.wikipedia.org/wiki/The_Well-
             | Tempered_Clavier#We...
        
               | tripa wrote:
               | 50 years ago, unless you were studying at the highest
               | levels of theoretical/historical music research, you'd
               | likely have been taught wrong.
               | 
               | The "Bach standardized the world on 12TET" trope is old
               | and enjoyable enough to make a good story that
               | unspecialized music teachers have parroted along for
               | generations.
               | 
               | We've got better access to information now. I've
               | corrected music teachers on this specific topic in the
               | past. Some gratefully accept. Some pull out the "but the
               | teacher here is _me_ card", so I 'm sure a few more
               | generations are going to be needed.
        
         | midenginedcoupe wrote:
         | Correct answer: they are.
         | 
         | Not on a piano, but for all the other instruments with variable
         | pitch (e.g. fretless strings, voice, trombones) they are. The
         | enharmonic is useful information and we'll know whether to
         | place that note just a little under or above its usual pitch to
         | make the chord more in tune. We don't need to invent a new
         | system to do this, we do it every day within the 12-tet system
         | we already have.
        
           | seanhunter wrote:
           | Theoretically yes but actually not really.
           | 
           | Most of the time, even if you're playing a variable pitch
           | instrument you're going to be tuning to fixed pitch because
           | you'll have at least one fixed pitch instrument (eg a piano)
           | and if you don't you'll just sound out of tune.
           | 
           | In cases (eg a consort group or string quartet or something)
           | where you're all variable pitch, you'll be tuning to each
           | other and to the scale/key as appropriate to the music and
           | whatever sounds good. You may well sweeten the thirds or
           | widen the fifths a bit etc but that doesn't apply to this
           | question here because you're really not going to see the
           | enharmonic equivalents in the same piece the absolute vast
           | majority of the time for stylistic reasons and if you ever
           | did you would just be tuning to each other to make the
           | vertical incidences sound good rather than thinking
           | consciously of tuning a d-sharp one way and an e-flat another
           | way.
           | 
           | Source: Have a degree and postgrad in music, used to be a
           | professional double bass player[1], spouse has a degree and
           | postgrad in music and teaches at 2 conservatoires in London
           | as well as performing professionally, mostly early music in
           | small consort groups where this sort of tuning thing comes up
           | a lot.
           | 
           | [1] So yeah you can make the standard joke about what do
           | double bass players know about tuning.
        
             | midenginedcoupe wrote:
             | Sometimes yes, sometimes no.
             | 
             | Even if playing with a fixed-pitch instrument, it only
             | really sounds out of tune if they're playing the same
             | notes. Which in the styles I play isn't an issue.
             | 
             | So I guess how often this happens in practice varies
             | between styles and eras of music, which would make sense to
             | me. I haven't ever done early music and know nothing about
             | it (other than trombones used to be designed terribly and
             | we now know how to make better ones ;)
             | 
             | Source: Also have a postgrad in music, probably from one of
             | the conservatories your spouse teaches at, and still play
             | trombone professionally.
        
             | davidnhouse wrote:
             | I guess it really depends on your instrument, taste, style
             | and the group you are playing with. While studying Cello I
             | actually had a lot of lessons with string quartet where we
             | were analysing the score (harmony) for intonation and it
             | happens quite often in modulations that enharmonic
             | equivalents were used to distinguish whether a chord
             | belongs to the old or the new harmony. And sometimes we
             | really needed to make a difference between an e flat and a
             | d sharp to match an open string or to get a desired
             | tension.
             | 
             | For me the enharmonic equivalent is usually just a totally
             | different harmony, so that is what I tune to. As a result
             | they are quite different notes. I try to do that
             | consciously - also while playing with fixed pitch
             | instruments when possible (like the grandparent comment
             | explained).
        
         | grumpyprole wrote:
         | > Long answer: they aren't.
         | 
         | This is not true in general. It is only true for instruments
         | that use the well tempered tuning, e.g. a piano. But for
         | example, the violin and cello do not.
        
           | hilbert42 wrote:
           | Right, the Circle of Fifths and the Pythagorean comma stop
           | perfect alignment.
        
       | im3w1l wrote:
       | > The usual answer is that you are only supposed to use each
       | letter name once in any given scale.
       | 
       | And why is that important? Answer: This lets you write the key
       | signature once, and then not have to bother with accidentals in
       | front of notes.
        
         | dahart wrote:
         | Perhaps more succinctly, you always write any two consecutive
         | notes of a diatonic scale on two different lines of the staff.
         | It would be bad if your in-key scale looked like it had two
         | notes on the same line and then a jump of a third. Note this is
         | true even when you have accidentals! It's a way to keep the
         | intention or semantics of notes more clear, and more easily
         | readable, regardless of the pitch interval. Like how the
         | article talks about the distinction between an augmented 2nd
         | and a diminished 3d, the notation is designed to help clarify
         | that distinction.
        
         | thaumasiotes wrote:
         | Well, no, that would only work if you were committed to never
         | using notes that weren't in the key signature. That would be an
         | unusual choice.
        
           | im3w1l wrote:
           | Not having to use accidentals for in-key notes still reduces
           | the needed number substantially.
        
           | iainmerrick wrote:
           | Right, but if your tune _mostly_ uses conventional major and
           | minor scales (which most do!) you mostly won't need
           | accidentals.
           | 
           | Also, you'll be able to transpose to any other key just by
           | shifting the letter names up or down and changing the key
           | signature. That's a really interesting and useful property.
           | 
           | Also also, the notes with accidentals won't change when you
           | transpose (although the accidentals themselves will need
           | rewriting).
           | 
           | Transposing music would be hellish without this system!
        
           | PeterisP wrote:
           | Depends on the music genre probably, there are oh so many
           | song arrangements that never use notes outside of the key
           | signature.
        
       | rdtennent wrote:
       | >Bach wrote The Well-Tempered Clavier to show off how one well
       | temperament system (no one knows which one) sounds okay in every
       | major and minor key. The keys closer to C sound sweeter and more
       | euphonious, while the more distant keys sound darker and edgier.
       | 
       | Fairly recent research has shown that Bach may have been very
       | explicit in specifying a temperament system. A series of what
       | appear to be decorative swirls at the top of the title page of
       | the WTC has been conjectured to actually be instructions for
       | tuning to the temperament system he favoured.
        
         | ethanhein wrote:
         | I wrote a blog post summarizing this research. The idea is that
         | the swirls specify turns of the tuning pegs to modify meantone
         | temperament. It's more or less pure speculation, but it does
         | produce a very nice-sounding tuning, almost equal temperament
         | but not uniform across the keys.
         | https://www.ethanhein.com/wp/2020/what-does-the-well-tempere...
        
       | MikeBattaglia wrote:
       | There is some basic information that is very wrong in this
       | article. For example:
       | 
       | "My track is tuned in a system called five-limit just intonation
       | via the magic of MTS-ESP. It's the basis for all the tuning
       | systems used in Western Europe between about 1500 and 1900."
       | 
       | No - at no point in the last 500 years was 5-limit just
       | intonation ever the predominant tuning system used anywhere in
       | Western Europe. The real predominant tuning system was called
       | "meantone temperament," to which this article sadly devotes only
       | about 3 words - and those words are only about 12 tone meantone
       | keyboard layouts, not about the bigger, abstract idea of meantone
       | temperament in general as it was understood and taught by
       | practitioners of the day.
       | 
       | There is a very important difference between meantone and just
       | intonation. The goal of meantone was to have four tempered
       | perfect fifths (approximately a 3/2 frequency ratio) add together
       | to approximate the fifth harmonic (or a 5/1 frequency ratio).
       | Thus, the major third from the circle of fifths would approximate
       | a 5/4 ratio with the tonic, and the major chord would approximate
       | a very crunchy sounding 4:5:6 ratio. In order to do this, fifths
       | are all flattened slightly to make the tradeoff - flattening the
       | fifths by 1/4 of a "syntonic comma" was typical, or "quarter-
       | comma meantone". Even though keyboard instruments evolved in a
       | more well-tempered direction, meantone was the way that teachers
       | of the common practice era (such as Leopold Mozart) still taught
       | and thought about this stuff.
       | 
       | Meantone sounds noticeably different from just intonation, where
       | the major third from the circle of fifths is a syntonic comma
       | sharp of a 5/4 ratio (about 22 cents). In just intonation, if you
       | want your major chords to be 4:5:6, you need to bring in this
       | other, different, independent 5/4 major third that is not on the
       | circle of fifths. As a result, certain chord progressions that
       | are common in Western music will tend to exhibit strange sounding
       | "comma drifts" if you play them in just intonation. Adam Neely
       | has a good video on "Benedetti's Puzzle" about this for those who
       | are interested.
       | 
       | Of course, there is nothing wrong with just intonation, and comma
       | shifts can sound interesting if you want to deliberately use them
       | in some kind of modern microtonal setting, but it simply isn't
       | the tuning historically used in common practice Western music.
       | 
       | Anyway, though, if you go through the article with a marker and
       | replace all instances of "just intonation" with "meantone," the
       | general idea is mostly correct.
        
         | ethanhein wrote:
         | Hi, I'm the author of the blog post. I said that 5-limit is the
         | basis for systems like meantone, which is true. Meantone
         | systems take 5-limit as their starting point and then modify
         | it. I deliberately skated over the specifics of how meantone
         | works on purpose, because I have too much experience watching
         | my students' eyes glaze over when I talk about this kind of
         | thing. I'm trying to strike a balance between giving correct
         | information and not turning people away.
        
           | MikeBattaglia wrote:
           | I can't comment regarding how you think is best to teach your
           | students. This is now a popular blog post that has gone viral
           | on HackerNews to a much wider audience of well-educated
           | people, so you should expect people will clarify these things
           | on here. I'm talking mostly about stuff like this:
           | 
           | > Five hundred years ago, however, it would have made a very
           | big difference. Before the advent of temperament systems,
           | D-sharp and E-flat were two different notes. They weren't
           | just written differently; they sounded different. You can
           | compare the historical versions of these notes yourself in
           | this track I made... My track is tuned in a system called
           | five-limit just intonation
           | 
           | ^ These are not the historical versions of those notes.
           | 5-limit just intonation was not in widespread use in Western
           | Europe 500 years ago. 500 years is not before the advent of
           | temperament systems. And so on. Teach this to your students
           | however you think is best, but people on here may be
           | interested to know that.
        
       | tobbob wrote:
       | It's the same note, but musicians are anoraks. I know because I
       | used to be one.
        
         | klodolph wrote:
         | Kind of like saying that "cell" and "sell" are different words.
         | Obviously they're different words, even though you can't hear
         | the difference. Just like it's obvious that Ab and G# are
         | different notes, even though they may sound the same.
         | 
         | Ask an English speaker to interpret a text about a sails man
         | who sales around the world and cells sell phones, at have price
         | for any guessed who sends him a facts to his office in grease.
         | 
         | It's harder to read when you use the wrong words, just like how
         | a score is harder to read if you use the wrong notes.
        
           | tobbob wrote:
           | No
        
       | powersnail wrote:
       | The explanation of enharmonic equivalent (though the author
       | didn't use this term) is right, but I do take problem with this
       | sentence:
       | 
       | > but what musical difference does it make? In the present day,
       | the answer is, none whatsoever.
       | 
       | This is not quite right. On all fretless instruments, including
       | most bowed strings and the human voice, enharmonic equivalent
       | notes still have different pitches. The subtle differences in
       | intonation is incredibly important and noticeable on the violin,
       | for example.
        
         | sgustard wrote:
         | In practice what's the difference in finger location between
         | these almost identical notes on a violin? A millimeter?
        
           | powersnail wrote:
           | Usually the difference is a slight roll of the finger. But
           | you can hear it. You might not know you can hear the
           | difference in pitch, but you can hear one performer being
           | cleaner than another and intonation accuracy is a huge
           | factor.
        
           | palimpsests wrote:
           | it depends on where it is on the fretboard.
           | 
           | the higher you go in frequency, the physical distance between
           | each interval on the fretboard becomes smaller. so if a +/- 5
           | cent adjustment is 0.5 mm at the first "fret" after the nut,
           | it will be something like be 0.1 mm when you are at the 7th
           | "fret" location (i.e where the interval of perfect fifth,
           | relative to the open string, is played).
        
         | VBprogrammer wrote:
         | Out of interest, is this still the same when a violin is
         | playing alongside fretted instruments? Wouldn't they sound out
         | of tune in that case?
        
           | wumpus wrote:
           | Some players of fretted instruments move the frets to match
           | individual pieces of music.
           | 
           | In modern rock music, some musicians will change guitars
           | every song to have sweeter chords depending on the particular
           | chords in that song.
        
             | coldtea wrote:
             | Which "modern rock musicians" do that? It surely is not
             | widespread in rock.
             | 
             | Rock musicians change guitars (in a live or even studio
             | situation) mostly to get a different sound or a different
             | tuning (like going from "standard" to an open tuning). Not
             | for microtuning adjustments, or because they have moved the
             | frets to match an individual piece.
             | 
             | Some prog musicians might do it, but it surely is not a
             | "rock" custom.
             | 
             | In arabic music, on the other hand, or renaissance music,
             | and other genres, it is, and instruments there often have
             | movable frets.
        
           | beardyw wrote:
           | Physical instruments can't be perfectly in tune even within
           | themselves. Perfectly in tune is the preserve of electronic
           | instruments. Even so I have a software synth that can adjust
           | its own tuning within a chord to provide a more pleasing
           | sound.
        
             | yellowapple wrote:
             | > Physical instruments can't be perfectly in tune even
             | within themselves.
             | 
             | No, but they can sidestep the need to be perfectly in tune
             | within themselves by allowing the player to produce notes
             | unbounded by discrete steps or subdivisions thereof, e.g.
             | fretless string instruments and trombones.
        
               | coldtea wrote:
               | > _by allowing the player to produce notes unbounded by
               | discrete steps or subdivisions thereof, e.g. fretless
               | string instruments and trombones_
               | 
               | Then you have the problem that the player will himself be
               | off, unwillingly, most of the time. Often more than the
               | offsets of 12-tet to the "ideal" note.
        
               | squeaky-clean wrote:
               | > Often more than the offsets of 12-tet to the "ideal"
               | note.
               | 
               | Any proof to this? 12 tet can vary by 15 cents from just
               | intonation. Even an amateur musician can hear how out-of-
               | tune a 15 cent difference is.
        
               | coldtea wrote:
               | > _Even an amateur musician can hear how out-of-tune a 15
               | cent difference is._
               | 
               | Judging from all kinds of out-of-tune players in live
               | settings, and youtube videos (especially guitar, which I
               | follow a lot) I kind of doubt that...
        
               | squeaky-clean wrote:
               | 15 cents is huge. It's 15% of the way to the next note.
               | Even 5 cents sounds noticeably out of tune. Trained
               | musicians can easily tune to less than 2 cents without
               | using tricks like beating to get even more accurate
               | tuning.
               | 
               | Guitarists may be out of tune, but chances are more
               | likely you're hearing a poorly intonated guitar. You can
               | tune the open strings perfectly, but if your string
               | scale-length deviates from what your fretboard expects,
               | you'll have notes that progressively get more out of tune
               | the further down the neck you play. You can't correct
               | this with tuning, you need to adjust the tensions in your
               | bridge saddles, and most amateur guitarists are afraid to
               | do this.
               | 
               | Also you mention live settings, it depends on how big the
               | group is I guess, but at smaller venues and smaller bands
               | the stage monitoring is often so bad you can't hear your
               | own guitar.
        
               | criddell wrote:
               | Why does fretless matter? Doesn't string bending also let
               | you play off-note tones?
        
               | chucksmash wrote:
               | Having to bend up to a given note each time you need to
               | hit it will be slower and less precise.
               | 
               | Generally the bend is done after the fretted note is
               | struck as well. I guess it would be possible to always
               | pre-bend to a given alternate note if you wanted a
               | constant tone, but it definitely seems like working
               | against the grain of the tool versus just using a
               | fretless instrument.
        
               | paulmooreparks wrote:
               | Eddie Van Halen was known to do this, though he was
               | admittedly a freak of nature. He tuned the B string a few
               | cents flat so that barre chords played up the neck would
               | sound more in tune. If he needed to play, for example, a
               | D chord in first position, he'd bend the D fretted on the
               | B string slightly sharp.
        
               | criddell wrote:
               | There's a video of a Van Halen concert where the synth
               | track for Jump was played back at the wrong bitrate.
               | Eddie worked furiously to find it on the guitar but
               | couldn't. It's pretty wild to watch.
        
               | coldtea wrote:
               | Because in fretless it can be done all the time - and
               | picking the note manually by exact finger placement _is_
               | done all the time.
               | 
               | In fretted instruments, bending is done for effect, not
               | for adjusting each and every note.
        
               | criddell wrote:
               | There are some players of guitars with a scalloped
               | fretboard who do so to experiment with tempered tunings.
               | It's definitely uncommon, but it's not unheard of.
        
             | mrob wrote:
             | A tonewheel organ could be amplified acoustically, e.g. by
             | physically touching an appropriately sized resonant chamber
             | to the wheel when you press a key. The exact size of the
             | resonator does not matter because it's mode locked to the
             | wheel, which turns at a speed determined only by the gear
             | train. Tonewheel organ gears traditionally do not have
             | perfectly accurate tuning, but there's no reason they
             | couldn't be built to match any tuning system within the
             | limits of human hearing (at greater cost and complexity).
        
             | timc3 wrote:
             | Early electronic instruments, particularly before the 1980s
             | had tuning all over the place, and you would have to wait
             | 30 minutes to get anything resembling stability, even then
             | nothing was guaranteed.
             | 
             | Think it would be possible to mockup some really
             | interesting tunings/temperaments in BitWigs grid or
             | Max4Live.
        
           | lucas_codes wrote:
           | Yes and no, a violinist has to use their taste and experience
           | to match the intonation of the fretted instrument in some
           | cases (for example, when playing the exact same note) and not
           | other cases (for example, perhaps a piano plays a C and a G
           | and violin plays an E, the violinist will likely want to play
           | a lower E than the piano would to get the exact ratios
           | described in the article.)
        
           | Arathorn wrote:
           | You definitely risk a clash between a well-tempered
           | instrument (like a piano) and a violin, given the piano is
           | just one big compromise whereas the violin can hit the
           | theoretically correct note. Either the violin (typically
           | subconsciously) tweaks the tuning of a given note to match
           | the piano, or the note is too short to notice (given the main
           | way to notice the difference is by spotting pulses, or
           | "beats", which is the phase difference between the two notes
           | - which could be measured in seconds if it's <1Hz
           | difference).
           | 
           | Khachaturian loved playing with enharmonics - the violin
           | concerto has runs where you get D# and Eb (or similar) in
           | different parts of the same run - or worse, two different
           | Bb's, as the run implicitly moves through different keys as
           | it goes. This is then made particularly fun in the lead-up to
           | the cadenza, where the violin duels with the clarinet, and to
           | sound correct, you have to explicitly coordinate on which key
           | the various phrases are actually playing in (given it
           | effectively switches implicit key faster than the explicit
           | key signature). From memory, you end up with the clarinet
           | deliberately playing very different enharmonics to the
           | violin, giving it an incredibly otherworldly feeling.
           | 
           | edit: to clarify, you literally have to say: "so play this Bb
           | as the Bb in a G-minor scale, and this Bb as the Bb in a Ab-
           | major scale" or similar - as they have different frequencies.
           | Or more accurately "play this subphrase as if it's in
           | G-minor, and this phrase as if it's in Ab-major". Despite the
           | Clarinet having fixed stops, you still "lip" the notes up and
           | down to get the right frequency.
        
         | coldtea wrote:
         | > _This is not quite right. On all fretless instruments,
         | including most bowed strings and the human voice, enharmonic
         | equivalent notes still have different pitches._
         | 
         | Not because we want it or it is some ideal situation, though.
         | 
         | Just because 12-tet can't get a single note to be in the exact
         | right ratio. If it could, we'd play D# and Eb exactly the same.
         | 
         | Besides, if the fretless instrument is not soloing, it might
         | still play it as the 12-tet single note compromise, to match
         | what others play at the same time.
        
         | algesten wrote:
         | One great example of this is vocalist groups. The Enya/Lord of
         | the Rings track "May it Be" as sung by Voces8.
         | https://www.youtube.com/watch?v=x7M5ZqFSynQ
         | 
         | Notice how the fifths are perfectly "still", no beating. It can
         | almost sound out of tune if you're too used to tempered tuning.
        
           | DiggyJohnson wrote:
           | This is also what makes Barbershop magical.
        
         | tralarpa wrote:
         | This is indeed a very weird thing to say by the author. Your
         | "not quite right" is too kind to the author. As you wrote, good
         | fretless instruments and singers will absolutely play/sing
         | those notes differently, although maybe unconsciously.
        
           | coldtea wrote:
           | More often than note (sic), they'll play them the same as a
           | piano would, to match the regular instruments they play along
           | with.
        
             | ninkendo wrote:
             | In a given orchestra (for example), what instruments have
             | fixed tuning? A piano yes (although lots of orchestral
             | music doesn't have piano.) The harp? I struggle to think of
             | others.
             | 
             | Wind instruments essentially have continuous tuning because
             | the player can adjust the pitch with their lips and vocal
             | shape. Orchestral string instruments are all fretless (and
             | thus continuously pitched.) Singers, same thing. Even
             | fretted instruments are often played with a lot of vibrato
             | that masks any true pitch problems.
             | 
             | I think the inability to play with a perfect pitch is more
             | the exception than the rule (at least in "classical"
             | music), it's just that piano is such a popular instrument
             | in the modern era that this becomes a problem.
        
               | coldtea wrote:
               | > _what instruments have fixed tuning?_
               | 
               | Not that many: the piano, the harp, the glockenspiel,
               | etc.
               | 
               | But the thing is, most modern music, is not with a
               | classical orchestra, but can still have violin (and in
               | some genres, like bluegrass, irish, country, etc. it
               | often does).
        
         | throwaway287391 wrote:
         | Huh...can I get a source on this that delves into it more? I
         | played the cello in an orchestra, solos, and chamber music for
         | about 10 years growing up and I've literally never heard anyone
         | mention I or anyone else should've been putting my finger in a
         | slightly different place for C# and Db. I suspect this is for
         | all intents and purposes not true in the 21st century.
        
           | wumpus wrote:
           | You probably were "sweetening" chords without realizing it.
        
           | analog31 wrote:
           | You didn't miss out on much. My cello teacher mentioned it to
           | me early on, in passing, but it's basically useless trivia
           | until you actually have enough control for it to make a
           | difference. From observing my kids go through music study,
           | I'd say it emerges as something to actually think about at
           | the college level.
           | 
           | Instead, I switched to the double bass, joined the jazz band,
           | and majored in physics. ;-)
           | 
           | I think "sweetening without realizing" may be a thing. You've
           | assimilated the sound of classical (or whatever) music
           | through listening. You can hear how you want the note sound
           | in your head, and your finger goes there.
        
           | alar44 wrote:
           | It's not the difference between C# or Db per se, it's a
           | function of what note in the chord it is occupying.
        
             | throwaway287391 wrote:
             | I'm responding to this part of the parent's post: _On all
             | fretless instruments, including most bowed strings and the
             | human voice, enharmonic equivalent notes still have
             | different pitches. The subtle differences in intonation is
             | incredibly important and noticeable on the violin, for
             | example._
        
               | kzrdude wrote:
               | Yes exactly, and one would intonate it slightly
               | differently by ear depending on what role the note has in
               | the current harmony is the idea.
               | 
               | Presume a base note of A is being played and the violin
               | plays a C# functioning as the major third of an A major
               | chord. The ear would want to play the C# justly intonated
               | to the root note A, or maybe a compromise somewhere
               | between equal temperament and just intonation.
               | 
               | See for example
               | https://music.stackexchange.com/questions/113812/violin-
               | tuni...
               | 
               | there's a lot of nuance. A lot of playing it by ear. :)
        
               | rawling wrote:
               | Would that not just manifest as... you feel like you're
               | out of tune, so you adjust minutely?
        
           | algesten wrote:
           | You will adjust without even realizing. You'll change your
           | pitch to sound right in relation to everyone around you. This
           | probably means that in practice your finger is slightly up or
           | down depending.
           | 
           | It is also a reason why when playing an A, many prefer moving
           | the hand to 4th position on the D string, rather than using
           | the A-string with no finger. Partly because you can make a
           | better tone (add vibrato if wanted), but you can also
           | intonate.
        
             | dahart wrote:
             | > You will adjust without even realizing. [...] This
             | probably means
             | 
             | This _might_ be true once in a while on very slow chords or
             | the final resolving chord of a piece, maybe, but this
             | sounds like assumption to me based on it being
             | theoretically possible, and not evidence that it actually
             | happens often. From experience, it sure seems like years
             | upon years of equal tone muscle memory, from having to play
             | with other instruments, is far more likely to dominate
             | finger placement. Not to mention everyone being used to
             | equal tone - having equal tone sensibility as to what
             | sounds right. Sounding right in relation to everyone around
             | you is still valid in 12-TET. Enharmonic micro intonations
             | are almost certainly not happening during fast sequences,
             | and because of that, the argument that it's subconscious
             | and imperceptible seems implausible - professional
             | musicians absolutely would notice a change in finger
             | placement depending on context, because of key changes,
             | because of abrupt fast-slow resolutions, because of chords
             | and arpeggios and situations where open strings are called
             | for, etc. etc..
        
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