[HN Gopher] Why are D-sharp and E-flat considered to be two diff...
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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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