[HN Gopher] Why can't you tune your guitar? (2019)
___________________________________________________________________
Why can't you tune your guitar? (2019)
Author : digitallogic
Score : 150 points
Date : 2026-03-04 22:30 UTC (4 days ago)
(HTM) web link (www.ethanhein.com)
(TXT) w3m dump (www.ethanhein.com)
| sgarrity wrote:
| My first guitar teacher told me that someday I'd start to notice
| that you can't get all strings perfectly in tune. At that point,
| he said, you'll know you're getting somewhere on the guitar.
| kgwxd wrote:
| Get obsessed over the perfect tuning. Blame the imperfections
| on the quality of the guitar. Don't play until you get a better
| guitar. Repeat until you give up. Then actually start playing
| the damn thing.
| goblin89 wrote:
| With an ordinary fretted guitar, you can sort of perfectly tune
| it to what you play but not perfectly tune it in a global
| sense.
|
| That's an issue with tuning instruments in general, and why
| pianos are generally slightly out of tune as a compromise.
|
| As you get used to a particular guitar and strings, as you
| train your ear, you can also learn to work around the
| imperfections by adjusting how you hold down the strings (even
| with a fretted guitar, you can slightly repitch a string by
| holding it differently).
| Zuider wrote:
| Classical guitarists are used to pushing nylon strings into
| consonance by compressing the string either towards the nut
| or the bridge. Not so easy with steel, where players will
| just preemptively retune to whatever chords are most
| prominent in the song.
| jmkr wrote:
| I play with generally lighter strings. 8.5-40 mighty slinky
| fender scale. I noticed when I switched my fingers pay much
| more attention to pressure, and being in tune with
| microbends.
|
| Been thinking of going a bit lighter recently, and also
| getting a classical.
| RickJWagner wrote:
| Interesting.
|
| Advanced banjo players will sometimes use harmonics for a 'bell'
| effect. Here's a short video from Alison Brown, a great player.
|
| https://www.youtube.com/shorts/NJDgpw2jIdc
| a4isms wrote:
| Steve Hackett takes advantage of guitar harmonics in a piece
| inspired by Bach's prelude to the first suite for solo
| violincello:
|
| https://www.youtube.com/watch?v=ubadQ1jcWOM
|
| And the late Jaco Pastorius with the bass harmonics song that
| would have broken the Internet if we had had the internet when
| he released his first solo album:
|
| https://www.youtube.com/watch?v=nsZ_1mPOuyk
|
| Speaking as a person who owns basses... I like the sound of
| harmonics on a bass better. I think it's something to do with
| the longer strings giving more play to the overtones.
| 52-6F-62 wrote:
| Absurd. A guitar within tolerance _is_ in tune. It 's a
| fundamental feature of the instrument. Not a flaw.
|
| Music doesn't live in an abstract realm of perfections, it is an
| expression however formed. The fact that we can measure it is one
| thing. But the music or instruments do not need conform to
| discrete measurements to satisfy.
|
| I know engineers _hate_ this, but ask any musician. It 's like
| arguing that a sitar and its scales aren't right. Absurd.
| Synaesthesia wrote:
| Have you heard of even tempering, on piano?
| bob1029 wrote:
| > Music doesn't live in an abstract realm of perfections
|
| I agree with this in spirit, but there are practical
| ramifications of getting the frequency domain wrong. The human
| brain is very particular in this space. Even for completely
| untrained listeners. It's nothing like the human visual system.
| You're working on timescales measured in microseconds with
| auditory signals. Even where the instruments are physically
| positioned on stage is significant. Getting their pitch
| slightly wrong can be catastrophic.
| Copyrightest wrote:
| I am a jazz guitarist and am sympathetic to this comment: the
| way I tune my guitar these days is hitting an E tuning fork,
| playing a particular E7 chord, and deciding if it sounds good:
| e --0- B --0- G --7- D --6- A --7-
| E --0-
|
| Learned it from Jimmy Bruno. I despise digital tuners. However
| it is worth noting: a properly-tuned guitar will never be able
| to play a "barbershop seventh," which hits the natural harmonic
| dominant 7th and is so flat compared to TET that it's really
| almost a 6th. The chord itself sounds more bittersweet and less
| "funky" than a TET dominant 7th. OTOH the TET chord is an
| essential part of modern blues-influenced music: being "out of
| tune" makes the chord sharp and strong, almost like a blue
| cheese being "moldy." So I'm not beaten up about the
| limitations, it's just worth keeping in mind: no instrument can
| beat a group of human voices.
|
| In general your ears do not hear these little arithmetical
| games around mismatched harmonies. They hear things like "this
| chord sounds warm and a little sad, this one is bright and
| fun."
| fuzzfactor wrote:
| There's more than one way to be sympathetic :)
|
| With 12 of the strings on a sitar having equal (thin)
| diameter, but different lengths so they can be tuned to the
| 12 notes in the scale, these are also unplayed strings which
| contribute to the sound by resonating underneath the main
| course of strings which are the ones fretted and manually
| played on.
|
| That's so endearing I guess that's why they call them
| sympathetic strings ;)
|
| While my guitar gently weeps, etc. . .
| criddell wrote:
| Engineers hate it and so they invented the true temperament
| guitar. It's like a regular guitar except the frets are a bit
| funky.
| tadfisher wrote:
| Even those are not "true-temperament" instruments like a
| piano, they adapt a "well-temperament" tuning system like
| Bach's keyboard tuning [0]. The end result is closer to true-
| temperament in some keys, and farther in others.
|
| Oh, and that applies to standard tuning only. YMMV with
| alternative tunings, especially the open tunings.
|
| 0: https://www.guyguitars.com/truetemperament/eng/tt_techdeta
| il...
| relaxing wrote:
| Any musician with enough training will tell you which notes are
| out of tune on their well-tuned instrument, and how they
| correct for it as they play.
|
| Just because we live with the trade-off doesn't make it correct
| in any other sense.
| YZF wrote:
| I don't think this is generally true for the guitar. There
| are even songs that have notes intentionally out of tune
| (e.g. Scar Tissue by the Red Hot Chili Peppers).
|
| Agree with the OP that the characteristics of the guitar,
| including its "out of perfect tune", is what gives its music
| its unique characteristic. It's not a bug it's a feature.
| There might be some people with perfect pitch who get annoyed
| but for most people that's "colour" and the sound they expect
| and associate with their favorite music. If you played those
| songs on an "ideal" guitar they would not sound right.
| kjkjadksj wrote:
| Outside of people like van halen also pretty much no one is
| exploring the entire neck on a single song. So the issue of
| the guitar not being perfectly intonated is irrelevant
| since they are using just a piece of its range.
| YZF wrote:
| A lot of simple songs are just open "cowboy" chords for
| sure. But those are played on the first frets while the
| guitar is typically intonated at the 12th fret and tuned
| with open strings. I would expect those first frets to be
| fairly "out" vs. the open strings.
| f17428d27584 wrote:
| This article is just an introduction to the math behind 12-TET,
| why it exists, the tradeoffs, etc.
|
| The only thing that is absurd here is your bizarre strawman
| that discussing equal temperament is somehow non-musical and
| that engineers can't understand what music is because they want
| to measure things.
| dahart wrote:
| Many musicians can readily confirm that the difference between
| temperaments can be felt and heard by trained ears. A guitar
| tuned to equal temperament has major thirds that warble
| audibly. It _feels_ different when you use just intonation,
| which isn't generally possible on a guitar.
| kjkjadksj wrote:
| Why can't you use intonation? Isn't that just confirming the
| note is the same on different strings? And also the goal of
| bridge adjustment?
| dahart wrote:
| For the reasons the article explains. You can use "just
| intonation" a bit on a guitar, but it will only work for
| certain chords in certain positions. BTW note that just
| intonation is different from string intonation - I wasn't
| talking about making sure the 12th fret is the same note as
| the 12th fret harmonic on a single string, I was talking
| about the tuning system called "just intonation" that
| defines what certain intervals are, and allows for perfect
| thirds and perfect fifths in _some_ keys. But it won't work
| everywhere on a guitar. It's not possible to get (for
| example) perfect fifths on all string combinations in all
| positions, but it is possible to tune the guitar so you
| have a perfect fifth when crossing 1 string while in 5th
| position.
|
| The goal of regular guitar intonation and bridge adjustment
| is to get the guitar as close as possible to 12 tone equal
| temperament (TET), which is slightly 'out of tune' as the
| article describes. 12 TET is the best you can do if you
| want something equally close to perfect fifths (or thirds,
| etc.) in all positions in all keys across all string
| combinations; that's what 12 TET is for, it's designed to
| minimize the worse case, at the expense of losing the best
| case.
| amelius wrote:
| > If thirds and fifths are so out of tune in 12-TET, why do we
| use it? The advantage is that all the thirds and fifths in all
| the keys are out of tune by the same amount. None of them sound
| perfect, but none of them sound terrible, either.
|
| Can't we have a system that is optimized for the notes that are
| actually played in a song rather than the hypothetical set? And
| what if the optimization is done per small group of notes rather
| than over an entire song?
| chpatrick wrote:
| That's how it works when you sing! But if you have an
| instrument you need to tune it would be annoying if you had to
| retune it between every song.
| wallstprog wrote:
| Or in the middle of a song -- lots of songs modulate between
| different keys.
| amelius wrote:
| Ok, does this explain why singers drift to a different key
| when there is no accompaniment?
| soyyo wrote:
| Singers drift because they use relative pitch, because most
| musicians dont have perfect pitch.
|
| With relative pitch music sounds the same even if you
| deviate from the original equal temperament pitch of the
| key you started singing even changing the key.
|
| For the same reason if there is a fixed instrument playing
| at the same time, like a piano accompaniment, it's sound
| would be used as a reference and the singers would not
| drift
| amelius wrote:
| Yes, I mean would it be an additional factor?
| liveoneggs wrote:
| I think you can only be "perfectly" in tune for a single mode
| so a multi-modal song would become very difficult to play?
| soyyo wrote:
| You can with instruments without fixed pitches, like human
| voice and string instruments, in fact choirs and string
| quartets do play this way, adjusting each note.
|
| But for instruments with fixed pitches, like guitar or
| pianos,12 equal temperament is the best compromise to be able
| to play in all keys.
| Filligree wrote:
| > Can't we have a system that is optimized for the notes that
| are actually played in a song rather than the hypothetical set?
| And what if the optimization is done per note rather than over
| an entire song?
|
| You can. It's called adaptive tuning, or dynamic just
| intonation, and it happens naturally for singers with no
| accompanying instruments.
|
| It's impractical on a real instrument, but there's a commercial
| synthesiser implementation called hermode tuning.
|
| You're trading one problem for another, though. No matter how
| you do this, you will either have occasional mis-tuning or else
| your notes will drift.
| rectang wrote:
| In addition to singers, adaptive tuning is something which
| happens naturally for fretless stringed instruments (violin,
| etc), brass instruments with slides (most prominently the
| slide trombone but in fact many (most?) others), woodwind
| instruments where the pitch can be bent like saxophone, and
| so on.
|
| I used to play fretless bass in a garage hip hop troupe that
| played with heavily manipulated samples that were all over
| the place in terms of tuning instead of locked to A440,
| forcing adaptations like "this section is a minor chord a
| little above C#".
|
| Adaptive tuning is hard to do on a guitar because the frets
| are fixed. String bending doesn't help much because the
| biggest issue is that major thirds are too wide in equal
| temperament and string bending the third makes pitch go up
| and exacerbates the problem.
|
| You can do a teeny little bit using lateral pressure (along
| the string) to move something flat. It's very difficult to
| make adaptations in chords though. A studio musician trick is
| to retune the guitar slightly for certain sections, though
| this can screw with everybody else in the ensemble.
|
| Attempts to experiment with temperament using squiggly frets
| make it clear how challenging this problem is:
| https://stringjoy.com/true-temperament-frets-explained/
| wilsonnb3 wrote:
| I highly recommend the book "How Equal Temperament Ruined
| Harmony (and Why You Should Care)" if you are interested in
| this subject.
| penr0se wrote:
| The higher the variety of notes (out of the overall 12 sounds
| in an octave) in the song, the less this becomes possible.
|
| If your song is really simple, e.g. only consists of the 3
| notes that make up a major triad (root, third, fifth), then
| this is definitely possible and you can just use natural thirds
| and natural fifths.
|
| But as you start adding more notes, more chords and perhaps
| change of keys etc, it starts to break down.
|
| That's the reason why J. S. Bach wrote The Well-Tempered
| Clavier. It's a collection of 24 preludes and fugues, in each
| possible major and minor key.
|
| The basic idea was that if every prelude and fugue sounded good
| on an instrument (organ, harpsichord etc.), than it meant that
| the instrument was "well-tempered".
|
| Using natural tuning instead of 12-TET would have resulted in
| some pieces sounding very good and other sounding very bad.
| coherentpony wrote:
| It doesn't work per-song. Songs have multiple chords, some even
| with alterations. If you tune an E so that it is perfectly a
| major third above C, then that E won't be a perfect fifth above
| an A note. The Am chord has the notes A, C and E, so Am has
| notes that all belong to C major.
|
| Additionally, some songs even change keys, which makes "per-
| song" not enough of a constraint.
| steppi wrote:
| Yes, people try this. Check out dynamic tonality. It doesn't
| necessarily need a system. Experienced guitar players often
| find themselves unconsciously making little microtonal
| adjustments through bends and other techniques when playing
| leads. I found myself doing this just because it sounded better
| to me. I didn't even notice there was a consistent pattern
| until I eventually learned the math. For example I'd always
| want to bend minor thirds slightly sharp and bend the neck to
| slightly detune major thirds.
|
| https://en.wikipedia.org/wiki/Dynamic_tonality
| marshmellman wrote:
| Logic Pro has Hermode tuning, which does this per chord:
| https://support.apple.com/guide/logicpro/hermode-tuning-lgcp...
| GRiMe2D wrote:
| Actually Bach's Well Tempered Clavier IS a book written in a
| single set of tuning system that actually lost/forgotten. We
| still have discussions about how it's constructed. For more
| information google "Well Tempered Clavier interpretation"
|
| You can listen to variations here:
| https://youtu.be/kRui9apjWAY?t=622
| tadfisher wrote:
| Neither lost nor forgotten! It's the basis for the "Thidell
| Formula 1" temperament [0], which is what produces those
| squiggly frets on expensive guitars. It also works well for
| multiple keys (at the expense of others), making it a
| compromise for a range of music rather than a single song.
|
| 0: https://www.guyguitars.com/truetemperament/eng/tt_techdeta
| il...
| zahlman wrote:
| You may be interested in:
|
| https://en.wikipedia.org/wiki/Just_intonation
|
| https://en.wikipedia.org/wiki/Comma_pump
| yoctonaut wrote:
| Kyle Gann's _Arithmetic of Listening_ goes deeply into this.
| Given an infinite number of ways of dividing the range from _f_
| to _2f_ , some other equal-division temperaments (31 or 53, for
| example) get closer than 12TET to maintaining low-integer
| ratios across key centers, but each additional pitch adds
| complexity. I'd recommend that book in particular.
| https://www.kylegann.com/Gannbooks.html
| Wolfenstein98k wrote:
| Not really, because notes do double duty.
|
| You might play a G# note in the context of an E chord (where
| it's the third), and then you might play it in the context of a
| C# (where it's the fifth).
|
| These are discernably different pitches, but the same "note",
| in the same key, in the same song!
| bmacho wrote:
| https://web.archive.org/web/2019if_/http://www.ethanhein.com...
| the__alchemist wrote:
| Relevant MinutePhysics video which dives deep:
| https://www.youtube.com/watch?v=tCsl6ZcY9ag
| xcf_seetan wrote:
| Actually is not a guitar problem, but all 12-TET tuned
| instruments have this, it is just a side effect of harmonic math.
| In the guitar case it is not only the tuning that counts, also
| the material the string are made and the diameter of the strings
| count to the final frequency, and we are using parallel frets so
| applying the same distance to different strings. There are
| guitars with not parallel frets that try to compensate for the
| diameter variation. But that's all math and understanding, cause
| when you tune your guitar and just play you are in another world
| were "thought is the killer of flow"; so just play and enjoy the
| sound. :D
| _alternator_ wrote:
| Another thing that's not been mentioned here: there is a
| relationship between volume and pitch. In short, you strike a
| string hard and it goes a bit sharp. The issue is that the
| tonal math makes a linearization of the string physics, but the
| highly activated string is effectively a little tighter than
| the idealized version.
| tadfisher wrote:
| Humans are also not perfect at fretting with the exact same
| pressure every time, or without inducing some bend in the
| strings. This is really noticeable with the G string which
| always sounds out of tune while playing, because our tuning
| system gives it a half-step-down intonation as a trade-off to
| make it easier to form chords.
|
| James Taylor compensates by tuning everything down a few
| cents, between -12 at the low E and -3 at the high E, with a
| little break in the pattern with -4 cents at the G to deal
| with its weirdness. Good electronic tuners have "sweetened"
| presets which do something similar.
| ses1984 wrote:
| There are two type of "not parallel" frets and neither have
| anything to do with the diameter of the strings.
|
| Different guitarists use different diameter strings because the
| diameter determines the tension when you tune to pitch.
| Different people prefer different tension. Most shredders
| prefer light tension. Most jazz players prefer high tension.
|
| The diameter is compensated at the bridge and in some guitars
| the nut. When you press a thin string to a fret, the center of
| the string is closer to the fret than when a thick string is
| pushed to the fret. Thicker strings compensate for this by
| using slightly longer length which you can adjust at the
| bridge.
|
| One type of non parallel frets are called true temperament
| frets. They are sort of parallel but squiggly. This results in
| better intonation closer to that of a piano.
|
| Another type of non parallel frets is multi scale or fanned
| frets. This allows the bass strings to have a longer scale
| length, which allows you to use relatively thinner strings for
| bass notes. This is important because when strings get thicker
| relative to their length, they start to behave more like
| cylinders with thickness rather than ideal springs, and sound
| rather nasty because harmonic overtones are out of tune with
| the fundamental.
| fuzzfactor wrote:
| Yes, the diameter is compensated at the same time as the
| tension.
|
| When the string's action is higher above the frets, the
| tension increases more when fretted than open, to a greater
| degree than low action.
|
| So the saddle for that string needs to be positioned such
| that the plucked portion of the string is slightly longer
| than it would need to be if the tension were the same as the
| open string.
| cpursley wrote:
| Fixed it: "Why can't you tune your poorly made guitar?"
|
| The most guitars today are still made in the style of the 1950s
| Gibsons and Fenders, including the neck and tuner layout. Most
| guitar buyers focus on the aesthetic and not the quality. I
| switched to a headless guitar where the tuners are at the bridge
| and it has a fanned fretboard giving the strings more natural
| tensions, the thing stays in tune and is intonated at the frets
| extremely well.
| yesb wrote:
| This article is relevant to a theoretic perfectly designed and
| built guitar.
| rondini wrote:
| You're assuming that the goal for a guitar player is to have
| perfectly optimal instrument when in reality many players want
| an instrument that feels and sounds like the artists that
| inspire them. Aesthetics is part of that but if they enjoy the
| sound of the instrument then who's to say that another one is
| "better"?
| post-it wrote:
| Weird to describe 99%+ of all guitars, including some of the
| best made guitars in the world, as "poorly made."
| lillesvin wrote:
| Even your fancy guitar is not exempt from harmonics math. TFA
| has nothing to do with the quality of a guitar and everything
| to do with 12-Tone Equal Temperament.
| post-it wrote:
| > If you watch slow-motion video of a guitar string vibrating,
| you'll see a complex, evolving blend of squiggles. These
| squiggles are the mathematical sum of all of the string's
| different harmonics.
|
| This is incorrect. If you watch a video like [0], the squiggles
| aren't real, they're an artifact of a rolling shutter camera. A
| real slowmo camera will correctly show the entire string
| vibrating[1].
|
| The rest of the article is correct, but you can't _see_ harmonics
| happening to the string.
|
| [0] https://youtu.be/XOCGb5ZGEV8 [1] https://youtu.be/6sgI7S_G-XI
| RealityVoid wrote:
| While you're of course righ, in a certain way, the squiggles
| _are_ a function of the frequnencies that the chords are
| vibrating at. What you see is the interaction of the two
| frequencies, your the interaction depends on both frequencies.
| throwaway27448 wrote:
| > the squiggles aren't real, they're an artifact of a rolling
| shutter camera. A real slowmo camera will correctly show the
| entire string vibrating
|
| How do you distinguish vibration from squiggles? To me these
| seem like the same concept, at the very least over time. The
| moment simply doesn't matter except to neurotic people without
| a solid understanding of harmonics and especially of sound.
| fuzzfactor wrote:
| Interestingly, with an oscilloscope you can see the harmonics
| in all their gory detail :)
|
| Actually depending on microphone or instrument interface, you
| can see stuff that's beyond the range of hearing too.
|
| Also, on a low-frequency long-string like an upright bass, if
| it is bowed at the halfway node, you still hear mainly the
| fundamental but the second harmonic is naturally emphasized
| more than usual, and you can also see half the string making
| its contribution as pictured, with the naked eye.
| dahart wrote:
| Hold on. Your first video is indeed a rolling shutter artifact.
| But your second video never shows enough of the string to see
| the harmonics. When you (for example) pluck with a finger on
| the 12th fret, you absolutely do have a real physical squiggle
| vibrating in the string, with one node and two antinodes. With
| a 7th fret harmonic, there are 3 antinodes, with a 5th fret
| harmonic there are four. There are squiggles, and you can see
| them with real slowmo.
| engine_y wrote:
| Yes, I think that with all these videos what you actually see
| is aliasing...
| actsasbuffoon wrote:
| Not sure if I'm misunderstanding your claim. A string does
| vibrate as the sum of the string's harmonics. That's how pinch
| harmonics work, and they wouldn't work if that wasn't the case.
|
| You poke a spot where a given harmonic doesn't vibrate, and
| that takes energy away from the other harmonics that _do_ need
| to vibrate at that spot.
|
| If we're just talking about visually being able to see them, I
| suppose that's a different question. Maybe on an incredibly low
| pitched string, or with a strobe light playing at a synced
| frequency? But in terms of what the string is doing, it _is_
| vibrating as the sum of its harmonics.
| phkahler wrote:
| >> but you can't see harmonics happening to the string.
|
| But you absolutely can if you rest a finger on a node and pick
| it, producing primarily the harmonic. You can even see the
| lesser vibration at the nodes with your eyes.
| jMyles wrote:
| > If you watch a video like [0], the squiggles aren't real,
| they're an artifact of a rolling shutter camera.
|
| ...is this correct? You can say this about any oscillating
| phenomenon - that doesn't mean it's not 'real'. The "squiggles"
| are an artifact of the frequency of the string and the scan
| rate of the rolling shutter. You'll also see artifacting from a
| global shutter camera, where the "squiggles" will be an
| artifact of the string frequency and the frame (rather than
| scan) rate.
|
| Or do I misunderstand?
|
| I've been playing guitar for 25 years, and it seems to me that
| I can look at the "squiggles" from a rolling shutter capture of
| a string and tell you which string it is (and possibly, if I'm
| having a particularly sharp day, whether it's E or drop-D).
| I've never tested myself this way - am I certain to fail? :-)
| ses1984 wrote:
| How could you tell the note by looking at a string? Unless
| you're talking by about marking timestamps and measuring the
| time between peaks. A 42 gauge string tuned to E or D or any
| other note are going to look basically the same.
| markrages wrote:
| GP is talking about seeing the string oscillations alias
| against the 30 Hz camera frame rate.
|
| I've never tried it.
| KuSpa wrote:
| This is why string instrument players sometimes prefer to play a
| note not on the empty string (let's say play a A on the A-string
| on a cello), but instead on a lower string (e.g. first finger,
| fourth position on the lower D string) to accord for these
| imperfections. As a string instrumemt player, you pretty much
| only have to worry about these notes on empty strings, every
| other note you can "wiggle into place".
| analog31 wrote:
| Indeed, and another factor is that a fingered note has a
| different tone quality.
|
| Disclosure: String player.
| shermantanktop wrote:
| And the thicker strings sound a bit different as well.
|
| And the fingering for a given melody may just lay across the
| strings better one way than another.
| JohnMakin wrote:
| I was born with something not quite like perfect pitch, but when
| something is even slightly off tune it caused physical discomfort
| for me.
|
| My cs department had a cool project class where you built what
| was basically a raspberry pi with a microcontroller by hand, and
| you had to use the dumb speaker and controller to make your own
| music firmware to produce notes. the challenge involved, was
| basically, the processor's clock wasnt fine grained enough to
| produce perfect notes. I wanted to make a simon says toy but the
| notes were off. I approached my professor with my problem and he
| said I could cheat the processor clock in a clever way to get
| what i wanted and it was such a "oh wow computers are magic" to
| me, i got the notes i wanted. disappointingly the TA grader wasnt
| that impressed but that proff ended up offering me a job before I
| graduated.
| RealityVoid wrote:
| Do say more! What was the problem with the clock, more exactly?
| I believe you, I've had issues caused by clock skew and CAN bus
| for example, when you have a small error that is amplified on
| beach bit enough time, errors add up and you eventually get out
| of synch.
|
| But in the case if sound, I would have expected the skew to be
| less of a problem. Also surprised how the orof instantly know.
| It took me a while to figure out. How did you fix it? Cool
| story!
| analog31 wrote:
| One simplistic way is to successively add a small constant to
| a large integer, and generate the waveform from the most
| significant bits. A "cent," which is 1/100 of a semitone, is
| a factor of about 580 parts per million, so you can work out
| the precision needed for the constant. On a microcontroller,
| you can control the timing with a PWM, which runs
| independently of the processor and its timing foibles.
|
| Proof is left as an exercise to the student. ;-)
| RealityVoid wrote:
| > On a microcontroller, you can control the timing with a
| PWM, which runs independently of the processor and its
| timing foibles.
|
| That is not really true. You usually have a couple of clock
| sources on a MCU, but the clock gets propagated down the
| clock tree and the source, and most of the times, the PWM
| has the same source clock as the CPU. Indeed, I think if
| you're before the PLL the clock is more accurate as in you
| get less jitter but the overall drift is the same. You
| might have distinct clock sources but you need a specific
| hw and a specific configuration.
| analog31 wrote:
| Is it enough to have an audible effect? We're not talking
| cesium clock levels of stability here. Now my curiosity
| is piqued, I have to figure out a way to measure this.
| PaulDavisThe1st wrote:
| > I was born with something not quite like perfect pitch, but
| when something is even slightly off tune it caused physical
| discomfort for me.
|
| Define off tune? 12 TET? Just intonation? Bohlen-Pierce (56
| TET) ?
|
| The "in tune" notes are as much a function of culture as
| physics.
| PaulDavisThe1st wrote:
| I've been doing audio software for 25-30 years. I have no idea
| what sort of synthesis you'd be doing where the processor clock
| played any roll at all. Waveform synthesis is normally done in
| buffers (8 to 8192 samples), and the "clocking" to convert the
| sample stream into an analog waveform is done by the audio
| interface/DAC, not the CPU. If you were basically implementing
| a DAC, then yes, the clock would matter a lot ... is/was that
| the issue?
| NobodyNada wrote:
| > you built what was basically a raspberry pi with a
| microcontroller by hand, and you had to use the dumb speaker
| and controller to make your own music firmware to produce
| notes
|
| This sounds like they were most likely bit banging square
| waves into a speaker directly via a GPIO on a microcontroller
| (or maybe using a PWM output if they were fancy about it). In
| that case, the audio frequency will be derived directly from
| the microcontroller's clock speed, and the tolerance of an
| internal oscillator on a microcontroller can be as bad as
| 10%.
| deckar01 wrote:
| Even if you tuned two string to ensure that two specific notes on
| them vibrated at a perfect interval, there are non-multiplicative
| overtones modulated by resonance with the rest of the instrument.
| Those intervals are ideals for minimizing dissonance.
| Practically, the dissonance of 12TET intervals falls below the
| noise floor of all the other acoustic distortions that give
| instruments character.
| fuzzfactor wrote:
| Well, there's only 6 knobs and if you want to be "in tune with
| the world" those six knobs can only be in one place.
|
| However if you want more notes than that to be their best you're
| going to have to compromise and work at it a bit.
|
| Now if you want the instrument to sound its absolute best on its
| own solo, a slightly different place for some strings.
|
| And then depending on other musicians you are playing with and
| the way their tuning has achieved perfection (or not), some
| further tweaking can make a big difference.
|
| And that's after accepting that the "knobs can only be in one
| place".
|
| For students to get really good at the tuning process can require
| a few extra years of everyday practice more than it does to learn
| to play a few pieces.
|
| Part of the limitation is the way only a few minutes of tuning
| are spent for every hour of practice, if that.
| kazinator wrote:
| There is no way to tune your guitar so that all the successive
| open fourths (and the one major third) are pure, without the high
| E being quite off pitch relative to the low one.
|
| But, unless you mainly play stacked fourths, why would you make
| it a requirement? You can, for instance, tune instead to get pure
| fretted fifths between adjacent strings, and fretted octaves
| between strings one removed.
|
| The real reason you can't get your guitar in tune is one which
| makes none of the above matter. Most guitars don't have good
| intonation. Most acoustic guitars don't have movable saddles to
| set intonation at the bridge. Electric ones do. For accurate
| tuning, you need not only compensation at the bridge, but also at
| the nut.
|
| https://guitarnutcompensation.com/
|
| On my main axe, I installed a small screw next to the nut, right
| under the G string. Just doing the G string makes a huge
| difference!
|
| Here is a test: play an open D power chord (open D, A on G
| string, D on B string) it is very clean. Now release the A to
| play a 1-4-8 G power chord (open D, open G, D).
|
| On my compensated guitar, both of them are crisply in tune.
| Without nut intonation, one of the two will have ugly beats. If
| you tune one, the other goes wonky.
|
| When I first heard how good it is after putting in the
| compensating screw, I was astonished and at the same time filled
| with the regret of not having done it decades earlier.
|
| Why the G? The unwound G string on electrics is the most
| susceptible to bad intonation at the nut, because it undergoes
| the greatest pitch change when it is fretted. Guitarists like to
| bend that one for the same reason. Fretting it at the first or
| second frets makes it go markedly sharp; for that reason we need
| to shorten the distance between the nut and the first fret to get
| that sharpened interval back down to a semitone.
|
| This is less of a problem on guitars with a wound G, which has a
| lot more tension in it to compensate for its weight, and doesn't
| pitch-bend nearly as easily.
| coliveira wrote:
| It doesn't matter how good the intonation at the bridge or nut.
| There's the mathematical fact that we cannot get pure thirds
| and even fifths in modern equal temperament system. If you have
| a good ear you'll feel the subtle difference between notes, and
| they can never get exactly where you want. It's something you
| have to live with in modern music.
| kazinator wrote:
| > _It doesn 't matter how good the intonation at the bridge
| or nut._
|
| Yes, it does.
|
| > _There 's the mathematical fact that we cannot get pure
| thirds and even fifths in modern equal temperament system._
|
| Those are the pennies that don't matter, if your instrument
| has dollar problems.
|
| If you don't have good intonation, then you can't even
| properly get the approximations provided by equal
| temperament.
|
| With good intonation, compensated on both ends, you have a
| much better experience making tuning adjustments to get
| better compromises for the music you are playing.
| coliveira wrote:
| Intonation is just the beginning. It won't solve the deeper
| issues with equal temperament.
| LegionMammal978 wrote:
| The thing is, unless you're playing with other instruments,
| _no one is forcing you to tune to equal temperament_. E.g.,
| it 's very common to tune a violin's A string to an A440
| reference, then tune the other strings to 3:2 perfect fifths
| by ear. It just gets more complicated for fretted instruments
| like the guitar.
| coliveira wrote:
| If you tune the strings in a guitar to a perfect 4th, which
| is the case except the 3rd between strings b-e, the lower e
| will significantly differ from the high e open string.
| There's no way to get around it.
| dahart wrote:
| > You can, for instance, tune instead to get pure fretted
| fifths between adjacent strings, and fretted octaves between
| strings one removed.
|
| No, you can't. If you tune so that octaves with one string
| between are correct everywhere on the neck, that will force the
| tuning to be 12 tone equal temperament, and a fifth in 12 TET
| cannot be a perfect fifth.
| dahart wrote:
| For some reason it's taken me decades of playing guitar to become
| good enough at tuning and also sensitive enough to really feel
| the fact that I can't tune the guitar. Recently I finally grokked
| the simple reason that 12 TET cannot be perfect, and it doesn't
| take a long article to see it. I was kind-of aware of the major
| third problem, but I naively thought fifths were still perfect.
|
| A 12 TET chromatic is 2^(1/12), and a 12 TET fifth would be
| 2^(7/12). A perfect fifth is a 3:2 ratio. Those numbers are
| slightly different, and that's enough to understand it. Another
| way of thinking about it is that if you were to complete the
| cycle of fifths purely by stacking fifths, you should end up on
| the note you started with but many octaves higher. But you should
| be able to see that starting on C1 and going by octaves will
| produce a number that is purely powers of 2, whereas stacking
| fifths will necessarily involve powers of both 2 and 3, so they
| can never be equal, I can stack fifths and never land on my
| original note's octaves.
| jama211 wrote:
| Isn't there a similar issue with pianos?
| fuzzfactor wrote:
| Yes, and besides that no matter what you do you just can't get
| these virtuosos to tune their pianos on the spot ;)
|
| So you've got to tune your guitar to sound good with them and
| probably not just matching your open strings to their
| corresponding notes.
|
| While your electronic tuner flashes an ugly warning or the
| strobe tuner won't stand still :(
| rustyhancock wrote:
| Article reads like a well akchuallly to is your guitar in tune.
|
| I probably haven't tuned my guitar to concert tuning for a long
| time.
|
| I tried rocksmith and often tuned to that otherwise I just keep
| it in tune with itself and what approximately sounds right to me.
|
| My fingers are too fat for any precision to matter too much. So
| long as it's in tune with itself intonation is vaguely right and
| the action is acceptable no one will notice my solo playing in
| the garage by myself is out of tune are the fifth harmonic.
| wrs wrote:
| Not all instruments are limited to a fixed set of pitches. A good
| classical string player micro-adjusts each individual note to
| adapt to its harmonic context. For example, making all the thirds
| and fifths sound good even when the key changes, or adjusting a
| leading tone up or down very slightly to make it even more
| leading.
|
| Another way to think of it is that they have to hit every pitch
| without assistance from the instrument anyway, so they learn to
| make every note sound "good" rather than hitting a mathematically
| defined frequency.
| Zuider wrote:
| This sensitivity to intonation is why all the great quartet
| composers were either deaf, Hungarian, or both.
| semitones wrote:
| fretless and continuous instruments are not confined to 12-TET
| wrs wrote:
| Yes! If you broaden your scope beyond "Western diatonic" you
| get even more opportunity. "Why can't you tune your Turkish
| microtonal guitar" would also be an interesting follow-up.
| dagmx wrote:
| I'm surprised they don't show true temperament frets.
|
| https://strandbergguitars.com/en-WW/magazine/true-temperamen...
|
| They solve exactly for this issue, and sound amazing in use. The
| downside is that you are somewhat locked into a given tuning.
|
| Alternatively you can take the approach of guitars with movable
| frets so you can adjust them per tuning.
|
| https://youtu.be/EZC69A8TsJ8?si=7hUIb7FEKb45eV_L
|
| These are generally used for microtonal playing but can also
| effectively be true temperament as well.
|
| Guitars with gut frets used to have adjustable positions, which
| allowed for some mitigation via changing fret positions too
| semitones wrote:
| True temperament solves for a _different_ issue than what OP's
| post talks about. From the strandberg true temperament page:
|
| > Let's begin by describing the issue with standard equal
| tempered frets; standard fret spacing is calculated from one
| single piece of information about the guitar, the scale length.
| This principle ignores that the frequency of a vibrating string
| is calculated by three factors: the mass of the string, the
| tension applied and the speaking length. All three of these
| factors are affected to different degrees each time a string is
| pressed down on a fret. The only way to correctly compensate
| for all three of these parameters is to adjust each string-to-
| fret connection point independently, until each note plays the
| correct frequency. This issue, which is impossible to solve
| with standard tempered frets, is what True Temperament solves.
|
| So the true temperament system is compensating for the fact
| that a thicker string behaves differently when fretted than a
| thinner string. It still provides a 12 TET system however.
|
| What you are probably thinking of, is a _just intonation_
| fretboard, which exists and looks very different:
| https://projectionsliberantes.ca/en/guitars-tuning-system/
|
| You can see that rather than squiggles, different strings have
| frets in completely different places.
| dagmx wrote:
| A true temperament isn't just about compensating for the
| string mass differences but also for their differing
| intonation points. A true temperament won't get to the same
| level as a movable fret system but it does also compensate to
| a certain degree for the differing intonation points across
| strings at different tunings (what it refers to as speaking
| length which captures both point to point length and mass
| related deformation length). They're different but inherently
| associated issues.
|
| More information is here
| https://www.thatguitarlover.com/blog/what-is-true-
| temperamen...
|
| But this is also why I mention both fret compensation systems
| in my original post.
| busterarm wrote:
| TT necks are an absolute waste of money. At least if you went
| with the Earvana nut you only wasted $5 and the time to
| replace the thing.
|
| I've known a lot of musicians that have used the necks but
| mainly only while sponsored and none of them prefer them. Big
| names in the guitar world.
|
| You're better off spending that money on a better-constructed
| guitar. And lessons.
|
| So many people mistakenly think that gimmicks will make them
| sound better. TT necks. Fanned frets/multiscale. The right
| effects chain...
| dagmx wrote:
| This feels like a really puritanical take on things. Fanned
| frets and multiscale absolutely help with the playability
| of an instrument. It's physics, there's nothing mystical or
| gimmicky about it.
|
| Maybe YOU don't want it, but it prevents strings from going
| flabby without needing much heavier gauges. Which does help
| with a wide range of playing styles and genres.
| xenophonf wrote:
| Here's the YouTube link without that tracking code for those of
| us on mobile:
|
| https://youtu.be/EZC69A8TsJ8
|
| (I wish Firefox on iOS had a "open clean link" option, but I'd
| wish Mozilla would fix other more important stuff first, like
| letting me search/open bookmarks from a private tab.)
| semitones wrote:
| fun fact: some bands, like red hot chilli peppers, will tune the
| G string slightly flat such that major thirds become just, for
| some of their riffs. Listen to "scar tissue" for example
| timbaboon wrote:
| I read the title and felt personally attacked :(
| Nition wrote:
| The other problem I always notice on top of all this is that when
| you pluck a string, it adds tension to it temporarily, so the
| pitch when you first play it is a little higher than the pitch as
| it settles down. The louder you play it, the more the effect.
| hn_throwaway_99 wrote:
| Woah, so cool when a topic I was going into in depth gets to HN.
|
| I'm a relatively new adult beginner on the violin, and one of the
| fascinating (and extremely difficult) things about un-fretted
| string instruments is the player has the freedom to shift the
| tuning around to fit the context. On the violin, we normally play
| melodies and scales using Pythagorean tuning (which is actually a
| misnomer as Pythagoras didn't invent it, the ancient
| Mesopotamians did), which is based on the circle of fifths and
| leads to wider whole steps and narrower half steps than equal
| temperment tuning. But then for double stops (i.e. chords), and
| especially when playing in a string quartet, just intonation,
| which is based on the harmonic series, is used so the notes sound
| concordant. This page describes all the different tuning systems
| a violinist may use, also including 12 TET when trying to match a
| piano: https://www.violinmasterclass.com/posts/152.
|
| This video shows how challenging it can be when trying to adjust
| intonation when playing in a string quartet:
| https://youtu.be/Q7yMAAGeAS4 . Interestingly, the very beginning
| of that video talks about what TFA discussed that when you tune
| all your strings as perfect fifths your major thirds will be out
| of tune.
|
| I'll also put in a plug for light note, an online music theory
| training tool that was mentioned on HN a decade ago:
| https://news.ycombinator.com/item?id=12792063 . I'm not related
| to the owner in any way, I just bought access a few years ago and
| think it was the first time I really understood Western music
| theory. The problem with music theory is that the notation is
| pretty fucked up because it includes all this historical baggage,
| and lots of music theory courses start with what we've got today
| and work backwards, while I think it's a lot easier to start with
| first principles about frequency ratios and go from there.
|
| Other notes (pun intended!): The violin is great for learning
| music theory because you can actually see on the string how much
| you're subdividing it - go one third of the way, that's a perfect
| fifth, go halfway, that's an octave, etc. Harmonics (where you
| lightly touch a string) are also used all the time in violin
| repertoire. Finally, the article mentions Harry Patch, but you
| should also check out Ben Johnston, a composer who worked with
| Patch and was famous for using just intonation. Here is is
| Amazing Grace string quartet, and you can really hear the
| difference using just intonation: https://youtu.be/VJ8Bg9m5l50
| fortran77 wrote:
| Piano tunings are also "stretched" so that the harmonics are more
| in tune. This is especially needed on verticals and short "baby"
| grands. See https://en.wikipedia.org/wiki/Stretched_tuning
|
| I have software I use when I tune my Bosendorfer 290 that
| calculates the stretch. Of course, the final tweaks are done by
| ear.
| rurban wrote:
| Tuning guitar strings by hand is trivial. Try to tune a piano.
| There have up to 3 strings per key, and quite a lot of keys.
| Cannot be perfect, but should sound "warm" enough.
| TrackerFF wrote:
| Close enough for rock'n roll, as it is called.
| jakzurr wrote:
| Great article. Also, awesome comments; thanks everyone.
| rzzzt wrote:
| I always thought it's an optimization problem: the headstock is
| pulled by the strings towards the guitar's body, and whenever you
| get one string in tune, the change in (the distribution of) force
| changes the tuning of all other strings as well. So ideally they
| should be moved into an acceptable configuration collectively.
| People with six hands should be able to do it.
| bandrami wrote:
| If you've been storing it with strings loose and are bringing
| it into tune you definitely gradually tighten all the strings
| rather than just doing it in sequence, for that reason
| drunken_thor wrote:
| I wondered why this article was so high on the front page but now
| I realize it's simply because everyone else wanted to "um
| actually" it. I guess that makes sense.
| lukeinator42 wrote:
| A good analogy for equal temperament might be the Gregorian
| calendar, as a year does not evenly divide perfectly into 365
| days. So in order to compensate for that we adjust the calendar
| by a leap year every so often to make the calendar more accurate
| in the longer term. That's kinda similar to how every note is a
| little off in equal temperament so that at the larger scale of
| being able to play all intervals works out.
| leni536 wrote:
| I thought this was going to be about stiffness of the strings and
| how the modes even on a single string are not in tune compared to
| the mathematical model, which assumes infinitely flexible
| strings.
| cmckn wrote:
| I've read several articles over the years about Joni Mitchell's
| renowned tunings. There's a lot of info on her website about
| them: https://jonimitchell.com/music/tuningpatterns.cfm
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