8 ms·

Why can't you tune your guitar? (2019)

247 points by digitallogic 7mo ago

drunken_thor 7mo ago
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.
deleted 7mo ago
[deleted]
sgarrity 7mo ago
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 7mo ago
  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.
  - deleted 7mo ago
    [deleted]
  - jval43 7mo ago
    Yes exactly. Although I didn't buy a new guitar, but a dozen tuners. It finally clicked when I got one that was "real time" enough to see how the tuning shifts from high to low. This was before smartphones could do it. Doesn't help that most tuners are still dog slow, none of the beginners courses properly tell you how the guitar actually works, or what a "chord" really is. They're all just "play this and don't worry about it". To be fair it does get you going.
- goblin89 7mo ago
  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 7mo ago
    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 7mo ago
      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 7mo ago
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 https://www.youtube.com/shorts/NJDgpw2jIdc
- a4isms 7mo ago
  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 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 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 7mo ago
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 7mo ago
  Have you heard of even tempering, on piano?
- bob1029 7mo ago
  > 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 7mo ago
  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.”
PunchyHamster 7mo ago
[flagged]
- xandrius 7mo ago
  Can you elaborate? Just to make your comment less of a useless knee-jerk reaction but rather a discussion started for someone else.
  - a4isms 7mo ago
    Generous of you to assume that someone who walks in, sees something somebody else has written and immediately calls it shit... Has something of value to say. If they did, why did they hold it back just to speak so contemptuously of a subject that is actually interesting and reasonably well explained?
    - sillysaurusx 7mo ago
      Technically they called it testicles, not shit, but your point stands. Generosity is worth having by default, though. Filter people out when they burn it explicitly.
      - a4isms 7mo ago
        There is a quantum of earned generosity. Someone saying, "This doesn't seem right" has jumped to a conclusion, but they aren't getting personal about the author or the work. Whether it's testes or testy language, getting personal and insulting does not meet my personal standard for assuming good intent and being worthy of an open-minded attempt to create constructive dialogue. But I applaud you for wanting to lift the standard of discourse!
    - bronlund 7mo ago
      I think I see where he is coming from. Using math to prove that you can’t tune stuff, will to some, sound like using a laser leveling tool to prove that you can’t make a perfect pizza.
amelius 7mo ago
> 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 7mo ago
  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 7mo ago
    Or in the middle of a song -- lots of songs modulate between different keys.
  - amelius 7mo ago
    Ok, does this explain why singers drift to a different key when there is no accompaniment?
    - soyyo 7mo ago
      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 7mo ago
        Yes, I mean would it be an additional factor?
- 7mo ago
bmacho 7mo ago
https://web.archive.org/web/2019if_/http://www.ethanhein.com/wp/2019/why-cant-you-tune-your-guitar/ https://web.archive.org/web/2019if_/http://www.ethanhein.com...
the__alchemist 7mo ago
Relevant MinutePhysics video which dives deep: https://www.youtube.com/watch?v=tCsl6ZcY9ag https://www.youtube.com/watch?v=tCsl6ZcY9ag
xcf_seetan 7mo ago
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_ 7mo ago
  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 7mo ago
    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.
    - allears 7mo ago
      Peterson guitar tuners can do custom tunings, and have the James Taylor tuning built in as a preset. (On Peterson tuners, it's called the 'acoustic' preset, but is actually the JT tuning.)
- ses1984 7mo ago
cpursley 7mo ago
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 7mo ago
  This article is relevant to a theoretic perfectly designed and built guitar.
- rondini 7mo ago
  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 7mo ago
  Weird to describe 99%+ of all guitars, including some of the best made guitars in the world, as "poorly made."
- lillesvin 7mo ago
  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 7mo ago
> 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 https://youtu.be/XOCGb5ZGEV8 [1] https://youtu.be/6sgI7S_G-XI https://youtu.be/6sgI7S_G-XI
- RealityVoid 7mo ago
  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 7mo ago
  > 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 7mo ago
  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 7mo ago
  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.
KuSpa 7mo ago
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 7mo ago
  Indeed, and another factor is that a fingered note has a different tone quality. Disclosure: String player.
  - shermantanktop 7mo ago
    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 7mo ago
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 7mo ago
  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 7mo ago
    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 7mo ago
      > 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.
deckar01 7mo ago
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 7mo ago
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 7mo ago
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/ 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 7mo ago
  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 7mo ago
dahart 7mo ago
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.
- thaumasiotes 7mo ago
  > 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. Note this this is normally called the "Pythagorean comma". https://en.wikipedia.org/wiki/Pythagorean_comma https://en.wikipedia.org/wiki/Pythagorean_comma
  - dahart 7mo ago
    Yes, thanks! And that article points at the “problem” setup in the article: the syntonic or diatonic comma, or the discrepancy between four stacked perfect fifths and two octaves plus a major third. I like how the Pythagorean comma simplifies to 3^12 / 2^19 - pure powers of three vs pure powers of two. That makes it so obvious (to me anyway) why we can’t have perfect fifths.
jama211 7mo ago
Isn’t there a similar issue with pianos?
- fuzzfactor 7mo ago
  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 7mo ago
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 7mo ago
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 7mo ago
  This sensitivity to intonation is why all the great quartet composers were either deaf, Hungarian, or both.
- semitones 7mo ago
  fretless and continuous instruments are not confined to 12-TET
  - wrs 7mo ago
    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 7mo ago
I’m surprised they don’t show true temperament frets. https://strandbergguitars.com/en-WW/magazine/true-temperament 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 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 7mo ago
  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/ https://projectionsliberantes.ca/en/guitars-tuning-system/ You can see that rather than squiggles, different strings have frets in completely different places.
  - dagmx 7mo ago
    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-temperament https://www.thatguitarlover.com/blog/what-is-true-temperamen... But this is also why I mention both fret compensation systems in my original post.
semitones 7mo ago
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
- recursive 7mo ago
  John Frusciante claims this case was originally unintentional. https://www.guitarworld.com/news/john-frusciante-paul-davids-scar-tissue https://www.guitarworld.com/news/john-frusciante-paul-davids...
timbaboon 7mo ago
I read the title and felt personally attacked :(
Nition 7mo ago
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.
- Underphil 7mo ago
  In heavy metal, especially in modern down-tuned genres, this is often used as an artistic choice.
hn_throwaway_99 7mo ago
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 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 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 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 https://youtu.be/VJ8Bg9m5l50
fortran77 7mo ago
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 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 7mo ago
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 7mo ago
Close enough for rock'n roll, as it is called.
jakzurr 7mo ago
Great article. Also, awesome comments; thanks everyone.
rzzzt 7mo ago
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 7mo ago
  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
lukeinator42 7mo ago
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.
- sparky_z 7mo ago
  If only we had just slightly increased the length of each day so that the year divided perfectly into 365 days. Then it would be an even better analogy.
leni536 7mo ago
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.
deleted 7mo ago
[deleted]
haberman 7mo ago
> Not everyone in history thought that 12-TET was an acceptable compromise. Johann Sebastian Bach thought we should use other tuning systems This is presented as fact, but as I understand it there is no conclusive evidence for what Bach intended wrt temperament. There is a theory that the title page of the Well-Tempered Clavier encodes Bach’s preference in the calligraphic squiggles, but this is a recent theory and speculative. I don’t believe there are any direct statements by Bach as to his intention.
dhosek 7mo ago
Instruments which have a non-discrete set of pitches (as well as voices) will tend towards the more harmonious (so to speak) tuning when playing in harmony. You’ll notice this in choirs, for example, where singing a capella, the chords will follow nice integral ratios of frequencies. Fretless string instruments and the trombone are obvious cases of instruments which can do micro-tuning, but it’s worth noting that brass instruments have finger loops on some of the valve loops to allow adjustment of pitch. Micro-tuning of the pitch can also be managed in wind instruments through adjustment of the embouchure so while woodwinds seem like they would be only capable of discrete pitches, there is some ability to adjust the pitch during performance. On a church gig in the 90s, I encountered an organ which was not tuned in equal temperament so that playing guitar with the organ always sounded out of tune (something I only discovered once Mass began since we had rehearsed with a piano) and I had to switch to bass to be able to play an accompaniment that sounded decent.
- mnw21cam 7mo ago
  Brass instruments have a finger loop on the third valve loop, but it's not primarily for adjusting to just temperament. Most brass instruments have three valves. The first lowers the pitch by a tone. The second lowers the pitch by a semitone. The third lowers the pitch by a tone and a half. If you need to lower the pitch by two tones, then you press the second and third valves at the same time, and that works fine. However, if you need to lower the pitch by three tones, then you need to press all three valves at the same time. However, that adds the length of all the valve loops together to the total length of the instrument, whereas to lower the pitch by a fixed interval you need to multiply the length of the instrument by a certain amount, and so to truly lower the pitch by three tones you need to add a little bit more length beyond that supplied by pressing all three valves together. That's what the finger loop on the tubing for the third valve is for, so you can slide it out a bit for certain low notes.
  - dhosek 7mo ago
    And this is why I never rose above being a mediocre tubist.
woozyolliew 7mo ago
I like the music of Aloboi who makes electronic music, often with just intonation https://m.youtube.com/watch?v=WkYJb21hpyA https://m.youtube.com/watch?v=WkYJb21hpyA
webprofusion 7mo ago
The most surprising thing is that everyone here is an expert on true temperament. Who would have guessed.
coldtea 7mo ago
>The best-sounding note combinations (to Western people) are the ones derived from the first few harmonics. In other words, you get the nicest harmony (for Western people) when you multiply and divide your frequencies by ratios of the smallest prime numbers: 2, 3, and 5. He keeps writing "for western people" but some parts of these are inherent in the human ear evolution and rather universal. All around the world we can find pentatonic music for example, even from ancient peoples, and this includes e.g. West African cultures, China, etc. And traditions that have microtonal inflections will still place the same emphasis on the octave, the fifth, major/minor third, etc the microtones add different flavors but it's not some widely different thing, which is why e.g. middle eastern or Indian songs e.g. can still be played on pianos, simplified (to the nearest approximation) but still retaining a lot, just losing their full flavor.
- porridgeraisin 7mo ago
  Nit: Mostly the octave and the fifth in Indian music. Thirds aren't as much of a structural pillar.
  - coldtea 7mo ago
    Yeah, they opt for more microtonal/modal flavors. Though yaman raga is very popular and has a regular third, while other ragas still have a third-ish note, but microtonically adjusted up/down from the major and minor variants.
DonHopkins 7mo ago
"You can tune a filesystem, but you can't tune a fish." -tunefs(8), 4.2BSD and later
- mghackerlady 7mo ago
  unless you run it on an OpenBSD system, in which case you can
fifticon 7mo ago
did they mention that you can cheat this when e.g. singing, by changing pitch dynamically to fit the chords you are working with? In theory, a synthesizer or sound card could do the same. Of course, this could have other undesirable side effects. Maybe this was implied by the "just tuning"?
davidee 7mo ago
Like most things in music there's a real distinction between technical perfection (tuning is one, rhythm another) and music feeling alive. It's why perfectly quantized rhythms and music sound lifeless. Our perception of these things (for most, not all) is incredibly fluid, much like our perception of time. Music that moves us tends to have the right "technical imperfections". Too much and it comes off as amateur, too little, and it comes off as sterile. Even on a production-level, the right amount of harmonic distortion/non-linearity can be a huge benefit to how sounds are perceived. The amount of soft-saturation tooling in modern electronic/in-the-box music production is wild. Almost every modern plugin seems to include some kind of "warmth" control now. Yet another example how perfect reproduction doesn't sound quite right.
mghackerlady 7mo ago
probably because I don't have a guitar
bashkiddie 7mo ago
> Why can’t you tune your guitar? You can. (1) Movable frets https://www.youtube.com/watch?v=EZC69A8TsJ8 https://www.youtube.com/watch?v=EZC69A8TsJ8 (2) No frets https://www.youtube.com/watch?v=92TxCGBNEVg https://www.youtube.com/watch?v=92TxCGBNEVg (3) force the string sideways to a higher pitch https://www.youtube.com/watch?v=kbALdNDhKYE&list=RDkbALdNDhKYE&start_radio=1 https://www.youtube.com/watch?v=kbALdNDhKYE&list=RDkbALdNDhK... But the long answer is: It will stay out of tune for a given definition of "in tune", because there is no perfect string. A perfect string has a diameter of zero. > The math of harmonics is really simple If a string only had harmonics on it, the oscilation would form a stationary wave that never leaves the string and resonates between bridge and head. It is the non-harmonics that create the sound. A sound is made of a base frequency and overtones. Overtones are never perfect multiples of the base frequency, because they are influenced by (1) string length (2) material bending stiffness Because of bending stiffness, overtones have a lower frequency than their theoretical haromnics. > The second harmonic is the one you get from the string vibrating in halves. True in theory, false in practice due to bending stiffness. > Guitars can’t be perfectly in tune I don't see why. Overtone series are impossible to solve, but base frequencies can be tuned to your liking.

247 points by digitallogic 7mo ago

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.

deleted 7mo ago

[deleted]

sgarrity 7mo ago

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 7mo ago
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.
- deleted 7mo ago
  [deleted]
- jval43 7mo ago
  Yes exactly. Although I didn't buy a new guitar, but a dozen tuners. It finally clicked when I got one that was "real time" enough to see how the tuning shifts from high to low. This was before smartphones could do it. Doesn't help that most tuners are still dog slow, none of the beginners courses properly tell you how the guitar actually works, or what a "chord" really is. They're all just "play this and don't worry about it". To be fair it does get you going.
goblin89 7mo ago
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 7mo ago
  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 7mo ago
    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 7mo ago

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 https://www.youtube.com/shorts/NJDgpw2jIdc

a4isms 7mo ago
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 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 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 7mo ago

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 7mo ago
Have you heard of even tempering, on piano?
bob1029 7mo ago
> 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 7mo ago
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.”

PunchyHamster 7mo ago

[flagged]

xandrius 7mo ago
Can you elaborate? Just to make your comment less of a useless knee-jerk reaction but rather a discussion started for someone else.
- a4isms 7mo ago
  Generous of you to assume that someone who walks in, sees something somebody else has written and immediately calls it shit... Has something of value to say. If they did, why did they hold it back just to speak so contemptuously of a subject that is actually interesting and reasonably well explained?
  - sillysaurusx 7mo ago
    Technically they called it testicles, not shit, but your point stands. Generosity is worth having by default, though. Filter people out when they burn it explicitly.
    - a4isms 7mo ago
      There is a quantum of earned generosity. Someone saying, "This doesn't seem right" has jumped to a conclusion, but they aren't getting personal about the author or the work. Whether it's testes or testy language, getting personal and insulting does not meet my personal standard for assuming good intent and being worthy of an open-minded attempt to create constructive dialogue. But I applaud you for wanting to lift the standard of discourse!
  - bronlund 7mo ago
    I think I see where he is coming from. Using math to prove that you can’t tune stuff, will to some, sound like using a laser leveling tool to prove that you can’t make a perfect pizza.

amelius 7mo ago

> 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 7mo ago
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 7mo ago
  Or in the middle of a song -- lots of songs modulate between different keys.
- amelius 7mo ago
  Ok, does this explain why singers drift to a different key when there is no accompaniment?
  - soyyo 7mo ago
    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 7mo ago
      Yes, I mean would it be an additional factor?
7mo ago

bmacho 7mo ago

https://web.archive.org/web/2019if_/http://www.ethanhein.com/wp/2019/why-cant-you-tune-your-guitar/ https://web.archive.org/web/2019if_/http://www.ethanhein.com...

the__alchemist 7mo ago

Relevant MinutePhysics video which dives deep: https://www.youtube.com/watch?v=tCsl6ZcY9ag https://www.youtube.com/watch?v=tCsl6ZcY9ag

xcf_seetan 7mo ago

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_ 7mo ago
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 7mo ago
  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.
  - allears 7mo ago
    Peterson guitar tuners can do custom tunings, and have the James Taylor tuning built in as a preset. (On Peterson tuners, it's called the 'acoustic' preset, but is actually the JT tuning.)
ses1984 7mo ago

cpursley 7mo ago

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 7mo ago
This article is relevant to a theoretic perfectly designed and built guitar.
rondini 7mo ago
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 7mo ago
Weird to describe 99%+ of all guitars, including some of the best made guitars in the world, as "poorly made."
lillesvin 7mo ago
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 7mo ago

> 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 https://youtu.be/XOCGb5ZGEV8 [1] https://youtu.be/6sgI7S_G-XI https://youtu.be/6sgI7S_G-XI

RealityVoid 7mo ago
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 7mo ago
> 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 7mo ago
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 7mo ago
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.

KuSpa 7mo ago

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 7mo ago
Indeed, and another factor is that a fingered note has a different tone quality. Disclosure: String player.
- shermantanktop 7mo ago
  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 7mo ago

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 7mo ago
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 7mo ago
  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 7mo ago
    > 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.

deckar01 7mo ago

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 7mo ago

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 7mo ago

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/ 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 7mo ago
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 7mo ago

dahart 7mo ago

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.

thaumasiotes 7mo ago
> 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. Note this this is normally called the "Pythagorean comma". https://en.wikipedia.org/wiki/Pythagorean_comma https://en.wikipedia.org/wiki/Pythagorean_comma
- dahart 7mo ago
  Yes, thanks! And that article points at the “problem” setup in the article: the syntonic or diatonic comma, or the discrepancy between four stacked perfect fifths and two octaves plus a major third. I like how the Pythagorean comma simplifies to 3^12 / 2^19 - pure powers of three vs pure powers of two. That makes it so obvious (to me anyway) why we can’t have perfect fifths.

jama211 7mo ago

Isn’t there a similar issue with pianos?

fuzzfactor 7mo ago
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 7mo ago

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 7mo ago

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 7mo ago
This sensitivity to intonation is why all the great quartet composers were either deaf, Hungarian, or both.
semitones 7mo ago
fretless and continuous instruments are not confined to 12-TET
- wrs 7mo ago
  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 7mo ago

I’m surprised they don’t show true temperament frets. https://strandbergguitars.com/en-WW/magazine/true-temperament 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 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 7mo ago
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/ https://projectionsliberantes.ca/en/guitars-tuning-system/ You can see that rather than squiggles, different strings have frets in completely different places.
- dagmx 7mo ago
  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-temperament https://www.thatguitarlover.com/blog/what-is-true-temperamen... But this is also why I mention both fret compensation systems in my original post.

semitones 7mo ago

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

recursive 7mo ago
John Frusciante claims this case was originally unintentional. https://www.guitarworld.com/news/john-frusciante-paul-davids-scar-tissue https://www.guitarworld.com/news/john-frusciante-paul-davids...

timbaboon 7mo ago

I read the title and felt personally attacked :(

Nition 7mo ago

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.

Underphil 7mo ago
In heavy metal, especially in modern down-tuned genres, this is often used as an artistic choice.

hn_throwaway_99 7mo ago

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 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 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 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 https://youtu.be/VJ8Bg9m5l50

fortran77 7mo ago

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 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 7mo ago

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 7mo ago

Close enough for rock'n roll, as it is called.

jakzurr 7mo ago

Great article. Also, awesome comments; thanks everyone.

rzzzt 7mo ago

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 7mo ago
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

lukeinator42 7mo ago

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.

sparky_z 7mo ago
If only we had just slightly increased the length of each day so that the year divided perfectly into 365 days. Then it would be an even better analogy.

leni536 7mo ago

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.

deleted 7mo ago

[deleted]

haberman 7mo ago

> Not everyone in history thought that 12-TET was an acceptable compromise. Johann Sebastian Bach thought we should use other tuning systems This is presented as fact, but as I understand it there is no conclusive evidence for what Bach intended wrt temperament. There is a theory that the title page of the Well-Tempered Clavier encodes Bach’s preference in the calligraphic squiggles, but this is a recent theory and speculative. I don’t believe there are any direct statements by Bach as to his intention.

dhosek 7mo ago

Instruments which have a non-discrete set of pitches (as well as voices) will tend towards the more harmonious (so to speak) tuning when playing in harmony. You’ll notice this in choirs, for example, where singing a capella, the chords will follow nice integral ratios of frequencies. Fretless string instruments and the trombone are obvious cases of instruments which can do micro-tuning, but it’s worth noting that brass instruments have finger loops on some of the valve loops to allow adjustment of pitch. Micro-tuning of the pitch can also be managed in wind instruments through adjustment of the embouchure so while woodwinds seem like they would be only capable of discrete pitches, there is some ability to adjust the pitch during performance. On a church gig in the 90s, I encountered an organ which was not tuned in equal temperament so that playing guitar with the organ always sounded out of tune (something I only discovered once Mass began since we had rehearsed with a piano) and I had to switch to bass to be able to play an accompaniment that sounded decent.

mnw21cam 7mo ago
Brass instruments have a finger loop on the third valve loop, but it's not primarily for adjusting to just temperament. Most brass instruments have three valves. The first lowers the pitch by a tone. The second lowers the pitch by a semitone. The third lowers the pitch by a tone and a half. If you need to lower the pitch by two tones, then you press the second and third valves at the same time, and that works fine. However, if you need to lower the pitch by three tones, then you need to press all three valves at the same time. However, that adds the length of all the valve loops together to the total length of the instrument, whereas to lower the pitch by a fixed interval you need to multiply the length of the instrument by a certain amount, and so to truly lower the pitch by three tones you need to add a little bit more length beyond that supplied by pressing all three valves together. That's what the finger loop on the tubing for the third valve is for, so you can slide it out a bit for certain low notes.
- dhosek 7mo ago
  And this is why I never rose above being a mediocre tubist.

woozyolliew 7mo ago

I like the music of Aloboi who makes electronic music, often with just intonation https://m.youtube.com/watch?v=WkYJb21hpyA https://m.youtube.com/watch?v=WkYJb21hpyA

webprofusion 7mo ago

The most surprising thing is that everyone here is an expert on true temperament. Who would have guessed.

coldtea 7mo ago

>The best-sounding note combinations (to Western people) are the ones derived from the first few harmonics. In other words, you get the nicest harmony (for Western people) when you multiply and divide your frequencies by ratios of the smallest prime numbers: 2, 3, and 5. He keeps writing "for western people" but some parts of these are inherent in the human ear evolution and rather universal. All around the world we can find pentatonic music for example, even from ancient peoples, and this includes e.g. West African cultures, China, etc. And traditions that have microtonal inflections will still place the same emphasis on the octave, the fifth, major/minor third, etc the microtones add different flavors but it's not some widely different thing, which is why e.g. middle eastern or Indian songs e.g. can still be played on pianos, simplified (to the nearest approximation) but still retaining a lot, just losing their full flavor.

porridgeraisin 7mo ago
Nit: Mostly the octave and the fifth in Indian music. Thirds aren't as much of a structural pillar.
- coldtea 7mo ago
  Yeah, they opt for more microtonal/modal flavors. Though yaman raga is very popular and has a regular third, while other ragas still have a third-ish note, but microtonically adjusted up/down from the major and minor variants.

DonHopkins 7mo ago

"You can tune a filesystem, but you can't tune a fish." -tunefs(8), 4.2BSD and later

mghackerlady 7mo ago
unless you run it on an OpenBSD system, in which case you can

fifticon 7mo ago

did they mention that you can cheat this when e.g. singing, by changing pitch dynamically to fit the chords you are working with? In theory, a synthesizer or sound card could do the same. Of course, this could have other undesirable side effects. Maybe this was implied by the "just tuning"?

davidee 7mo ago

Like most things in music there's a real distinction between technical perfection (tuning is one, rhythm another) and music feeling alive. It's why perfectly quantized rhythms and music sound lifeless. Our perception of these things (for most, not all) is incredibly fluid, much like our perception of time. Music that moves us tends to have the right "technical imperfections". Too much and it comes off as amateur, too little, and it comes off as sterile. Even on a production-level, the right amount of harmonic distortion/non-linearity can be a huge benefit to how sounds are perceived. The amount of soft-saturation tooling in modern electronic/in-the-box music production is wild. Almost every modern plugin seems to include some kind of "warmth" control now. Yet another example how perfect reproduction doesn't sound quite right.

mghackerlady 7mo ago

probably because I don't have a guitar

bashkiddie 7mo ago

> Why can’t you tune your guitar? You can. (1) Movable frets https://www.youtube.com/watch?v=EZC69A8TsJ8 https://www.youtube.com/watch?v=EZC69A8TsJ8 (2) No frets https://www.youtube.com/watch?v=92TxCGBNEVg https://www.youtube.com/watch?v=92TxCGBNEVg (3) force the string sideways to a higher pitch https://www.youtube.com/watch?v=kbALdNDhKYE&list=RDkbALdNDhKYE&start_radio=1 https://www.youtube.com/watch?v=kbALdNDhKYE&list=RDkbALdNDhK... But the long answer is: It will stay out of tune for a given definition of "in tune", because there is no perfect string. A perfect string has a diameter of zero. > The math of harmonics is really simple If a string only had harmonics on it, the oscilation would form a stationary wave that never leaves the string and resonates between bridge and head. It is the non-harmonics that create the sound. A sound is made of a base frequency and overtones. Overtones are never perfect multiples of the base frequency, because they are influenced by (1) string length (2) material bending stiffness Because of bending stiffness, overtones have a lower frequency than their theoretical haromnics. > The second harmonic is the one you get from the string vibrating in halves. True in theory, false in practice due to bending stiffness. > Guitars can’t be perfectly in tune I don't see why. Overtone series are impossible to solve, but base frequencies can be tuned to your liking.