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

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.

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.

Not sure if I’m misunderstanding your claim. A string does vibrate as the sum of the string’s harmonics. That’s how pinch harmonics work, and they wouldn’t work if that wasn’t the case.

You poke a spot where a given harmonic doesn’t vibrate, and that takes energy away from the other harmonics that do need to vibrate at that spot.

If we’re just talking about visually being able to see them, I suppose that’s a different question. Maybe on an incredibly low pitched string, or with a strobe light playing at a synced frequency? But in terms of what the string is doing, it is vibrating as the sum of its harmonics.

>> but you can't see harmonics happening to the string.

But you absolutely can if you rest a finger on a node and pick it, producing primarily the harmonic. You can even see the lesser vibration at the nodes with your eyes.

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.

> If you watch a video like [0], the squiggles aren't real, they're an artifact of a rolling shutter camera.

...is this correct? You can say this about any oscillating phenomenon - that doesn't mean it's not 'real'. The "squiggles" are an artifact of the frequency of the string and the scan rate of the rolling shutter. You'll also see artifacting from a global shutter camera, where the "squiggles" will be an artifact of the string frequency and the frame (rather than scan) rate.

Or do I misunderstand?

I've been playing guitar for 25 years, and it seems to me that I can look at the "squiggles" from a rolling shutter capture of a string and tell you which string it is (and possibly, if I'm having a particularly sharp day, whether it's E or drop-D). I've never tested myself this way - am I certain to fail? :-)

> 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.

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.

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.

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!

I've been doing audio software for 25-30 years. I have no idea what sort of synthesis you'd be doing where the processor clock played any roll at all. Waveform synthesis is normally done in buffers (8 to 8192 samples), and the "clocking" to convert the sample stream into an analog waveform is done by the audio interface/DAC, not the CPU. If you were basically implementing a DAC, then yes, the clock would matter a lot ... is/was that the issue?

> I was born with something not quite like perfect pitch, but when something is even slightly off tune it caused physical discomfort for me.

Define off tune? 12 TET? Just intonation? Bohlen-Pierce (56 TET) ?

The "in tune" notes are as much a function of culture as physics.

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).

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.

Indeed, and another factor is that a fingered note has a different tone quality.

Disclosure: String player.

This sensitivity to intonation is why all the great quartet composers were either deaf, Hungarian, or both.

fretless and continuous instruments are not confined to 12-TET

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.

Yes, people try this. Check out dynamic tonality. It doesn't necessarily need a system. Experienced guitar players often find themselves unconsciously making little microtonal adjustments through bends and other techniques when playing leads. I found myself doing this just because it sounded better to me. I didn't even notice there was a consistent pattern until I eventually learned the math. For example I'd always want to bend minor thirds slightly sharp and bend the neck to slightly detune major thirds.

https://en.wikipedia.org/wiki/Dynamic_tonality

> 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.

Actually Bach's Well Tempered Clavier IS a book written in a single set of tuning system that actually lost/forgotten. We still have discussions about how it's constructed. For more information google "Well Tempered Clavier interpretation"

You can listen to variations here: https://youtu.be/kRui9apjWAY?t=622

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.

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.

I highly recommend the book “How Equal Temperament Ruined Harmony (and Why You Should Care)” if you are interested in this subject.

You may be interested in:

https://en.wikipedia.org/wiki/Just_intonation

https://en.wikipedia.org/wiki/Comma_pump

Logic Pro has Hermode tuning, which does this per chord: https://support.apple.com/guide/logicpro/hermode-tuning-lgcp...

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.

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

I think you can only be "perfectly" in tune for a single mode so a multi-modal song would become very difficult to play?

Not really, because notes do double duty.

You might play a G# note in the context of an E chord (where it's the third), and then you might play it in the context of a C# (where it's the fifth).

These are discernably different pitches, but the same "note", in the same key, in the same song!

True temperament solves for a _different_ issue than what OP's post talks about. From the strandberg true temperament page:

> Let’s begin by describing the issue with standard equal tempered frets; standard fret spacing is calculated from one single piece of information about the guitar, the scale length. This principle ignores that the frequency of a vibrating string is calculated by three factors: the mass of the string, the tension applied and the speaking length. All three of these factors are affected to different degrees each time a string is pressed down on a fret. The only way to correctly compensate for all three of these parameters is to adjust each string-to-fret connection point independently, until each note plays the correct frequency. This issue, which is impossible to solve with standard tempered frets, is what True Temperament solves.

So the true temperament system is compensating for the fact that a thicker string behaves differently when fretted than a thinner string. It still provides a 12 TET system however.

What you are probably thinking of, is a _just intonation_ fretboard, which exists and looks very different: https://projectionsliberantes.ca/en/guitars-tuning-system/

You can see that rather than squiggles, different strings have frets in completely different places.

Here's the YouTube link without that tracking code for those of us on mobile:

https://youtu.be/EZC69A8TsJ8

(I wish Firefox on iOS had a "open clean link" option, but I'd wish Mozilla would fix other more important stuff first, like letting me search/open bookmarks from a private tab.)

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.

> You can, for instance, tune instead to get pure fretted fifths between adjacent strings, and fretted octaves between strings one removed.

No, you can’t. If you tune so that octaves with one string between are correct everywhere on the neck, that will force the tuning to be 12 tone equal temperament, and a fifth in 12 TET cannot be a perfect fifth.

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

Steve Hackett takes advantage of guitar harmonics in a piece inspired by Bach's prelude to the first suite for solo violincello:

https://www.youtube.com/watch?v=ubadQ1jcWOM

And the late Jaco Pastorius with the bass harmonics song that would have broken the Internet if we had had the internet when he released his first solo album:

https://www.youtube.com/watch?v=nsZ_1mPOuyk

Speaking as a person who owns basses... I like the sound of harmonics on a bass better. I think it's something to do with the longer strings giving more play to the overtones.

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 :(

Can you elaborate? Just to make your comment less of a useless knee-jerk reaction but rather a discussion started for someone else.

> 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.

Many musicians can readily confirm that the difference between temperaments can be felt and heard by trained ears. A guitar tuned to equal temperament has major thirds that warble audibly. It feels different when you use just intonation, which isn’t generally possible on a guitar.

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.

Have you heard of even tempering, on piano?

Engineers hate it and so they invented the true temperament guitar. It’s like a regular guitar except the frets are a bit funky.

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.

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–

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.”

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.

Weird to describe 99%+ of all guitars, including some of the best made guitars in the world, as "poorly made."

This article is relevant to a theoretic perfectly designed and built guitar.

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”?