> 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.
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.
RealityVoid 1 hours 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.
fuzzfactor 15 minutes 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.
throwaway27448 53 minutes 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.
xcf_seetan 2 hours 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
ses1984 1 hours ago [-]
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.
_alternator_ 1 hours 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.
JohnMakin 1 hours 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 57 minutes 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 41 minutes 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. ;-)
sgarrity 2 hours 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.
goblin89 57 minutes 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).
kgwxd 1 hours 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.
40 minutes ago [-]
kazinator 14 minutes 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.
Without some compensation at the nut, you will never get good tuning.
KuSpa 1 hours 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 1 hours ago [-]
Indeed, and another factor is that a fingered note has a different tone quality.
Disclosure: String player.
amelius 2 hours 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?
penr0se 2 hours ago [-]
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.
steppi 1 hours ago [-]
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.
> 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 56 minutes ago [-]
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.
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"
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.
yoctonaut 22 minutes ago [-]
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
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 2 hours ago [-]
Or in the middle of a song -- lots of songs modulate between different keys.
amelius 1 hours ago [-]
Ok, does this explain why singers drift to a different key when there is no accompaniment?
soyyo 1 hours 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 35 minutes ago [-]
Yes, I mean would it be an additional factor?
wilsonnb3 2 hours ago [-]
I highly recommend the book “How Equal Temperament Ruined Harmony (and Why You Should Care)” if you are interested in this subject.
soyyo 2 hours ago [-]
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.
I think you can only be "perfectly" in tune for a single mode so a multi-modal song would become very difficult to play?
deckar01 49 minutes 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.
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.
52-6F-62 2 hours 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.
bob1029 2 hours 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.
f17428d27584 18 minutes ago [-]
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.
criddell 37 minutes ago [-]
Engineers hate it and so they invented the true temperament guitar. It’s like a regular guitar except the frets are a bit funky.
Synaesthesia 2 hours ago [-]
Have you heard of even tempering, on piano?
relaxing 33 minutes ago [-]
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 12 minutes ago [-]
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.
Copyrightest 51 minutes 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.”
RickJWagner 2 hours ago [-]
Interesting.
Advanced banjo players will sometimes use harmonics for a ‘bell’ effect. Here’s a short video from Alison Brown, a great player.
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:
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.
2 days ago [-]
cpursley 2 hours 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.
lillesvin 1 hours 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 1 hours ago [-]
Weird to describe 99%+ of all guitars, including some of the best made guitars in the world, as "poorly made."
yesb 2 hours ago [-]
This article is relevant to a theoretic perfectly designed and built guitar.
rondini 2 hours 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”?
PunchyHamster 2 hours ago [-]
What a load of bollocks
xandrius 2 hours 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 2 hours 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?
bronlund 1 hours 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.
sillysaurusx 1 hours 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 1 hours 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!
Rendered at 17:06:09 GMT+0000 (Coordinated Universal Time) with Vercel.
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
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.
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.
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.
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.
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!
Proof is left as an exercise to the student. ;-)
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).
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.
Without some compensation at the nut, you will never get good tuning.
Disclosure: String player.
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?
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.
https://en.wikipedia.org/wiki/Dynamic_tonality
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.
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/
You can listen to variations here: https://youtu.be/kRui9apjWAY?t=622
Additionally, some songs even change keys, which makes “per-song” not enough of a constraint.
https://en.wikipedia.org/wiki/Just_intonation
https://en.wikipedia.org/wiki/Comma_pump
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
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.
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.
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.
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.
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.
Just because we live with the trade-off doesn’t make it correct in any other sense.
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.
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.”
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/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.
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.
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?
Generosity is worth having by default, though. Filter people out when they burn it explicitly.
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!