Wanting to play in any key and not be locked into a key automatically pushes musicians toward equal temperament, even when playing solo, and even on a violin. Saying no one’s forcing you is technically true but sounds pretty naive, and (forgive the pun) tone deaf to me; there’s no realistic alternative for modern music. Some people do choose to play with other tuning systems on occasion, but there’s a reason why 12 TET is so popular and widespread.
Wanting to change keys freely only pushes fixed-pitch musical instruments toward equal temperament. Since many important instruments are like that, and virtually all instruments that are capable of accurate intonation not relying on ear are like that.
If an ensemble includes instruments that are equal temperament, then the non-fixed-pitched instrumentalists adjust their pitch to sound good with those.
An ensemble consisting only of instruments that can play any interval can change keys by pure intervals.
E.g. switching from the original major key to the relative dominant key can mean changing the root by a pure fifth. In equal temperament, this modulation is done by altering only a single note: sharpening the subdominant. All other notes are from the original scale. If we change key by a pure fifth, that is obviously not so; all notes are detuned off the original scale.
If we change through all the keys along the circle of fifths, perfectly purely, we arrive at the Pythagorean comma: the gap between the destination root and the original.
Another possibility is to progress the roots through the diatonic fifths of the original scale, rather than pure fifths. Like, we start with a pure, just intonated C major, and then change keys through G,D,A,E,B,F#,C#,Ab,Eb,Bb,F back to C using the notes of that pure C major scale, or sharps/flats relative to those. Then we don't run into the Pythagorean comma; but of course all the pure scales we end up using are detuned from C major, and in a different way from following pure fifths.
> 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.
Frets are already on equal temperament on the vast majority of mainstream guitars; you're not getting away from equal temperament unless all you play is open strings, like a koto/harp.
If octaves are perfect with one string in between, the in between string can be slightly detuned from equal temperament to provide a clean fifth, free of beats. Then it also provides a clean fourth up to the octave. That's a useful thing that will make certain chords sound good.
That’s not very helpful. You can only do that one string, and it breaks the perfect octave starting on the detuned string. As soon as you also try to detune the next string up, you break the octave you started from. This is a house of cards idea that falls apart immediately.
Have you actually tried this? What songs work? To me this sounds totally impractical and useless, like it’s a logical technicality for the purposes of this discussion and not something a real musician would ever do. You’re making tuning a pain, breaking the E-E octaves (all barre chords), breaking octaves with 2 strings between, breaking the next-string octaves, breaking a lot of scales and jazz chords, and to top it off it would still only work for certain keys and not others. I’ll pass.
1. Yes; I've been tuning along those lines for nearly four decades. What songs work: anything with power chords that benefit from sounding sharp, free of flutter.
2. The error between the equal temperament perfect fifth and the pure one (3/2) is just less than 2 cents. So the difference I'm talking about is at the same level of accuracy as that of pretty excellent guitar intonation. The corrections are not simply for equal temperament; they are not separable from the condition of the instrument and its intonation. The given instrument is what it is, and to get those 1-5-8 power chords to sound clean you do whatever you have to.
What you’ve described would make all powerchords rooted on the A string audibly worse than standard tuning, with more flutter. Are you avoiding all A string chords?
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.
Indeed. But this is the guitar's design! Fixed temperament. There are many variations and other instruments that explicitly make that aspect of the instrument variable. There are even branches off of Spanish guitar design that use movable frets for that reason.
But fixed temperament and that warble/etc IS guitar.
For the reasons the article explains. You can use “just intonation” a bit on a guitar, but it will only work for certain chords in certain positions. BTW note that just intonation is different from string intonation - I wasn’t talking about making sure the 12th fret is the same note as the 12th fret harmonic on a single string, I was talking about the tuning system called “just intonation” that defines what certain intervals are, and allows for perfect thirds and perfect fifths in some keys. But it won’t work everywhere on a guitar. It’s not possible to get (for example) perfect fifths on all string combinations in all positions, but it is possible to tune the guitar so you have a perfect fifth when crossing 1 string while in 5th position.
The goal of regular guitar intonation and bridge adjustment is to get the guitar as close as possible to 12 tone equal temperament (TET), which is slightly ‘out of tune’ as the article describes. 12 TET is the best you can do if you want something equally close to perfect fifths (or thirds, etc.) in all positions in all keys across all string combinations; that’s what 12 TET is for, it’s designed to minimize the worse case, at the expense of losing the best case.
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.
> 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".
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.
I know some people blame the covid vaccine. I had tinnitus before the vaccine and it got louder when I took the vaccine and then got quieter later. But it gets louder with other medications too. I suspect anything that causes inflammation can increase tinnitus symptoms, and the covid vaccine does temporarily increase inflammation. This could easily push someone who hasn’t noticed their developing tinnitus over the edge and suddenly they notice it and associate it with the vaccine. What they don’t know is that they might have noticed their tinnitus 2 months later if they hadn’t taken the vaccine. Statistically, I would expect there to be lots of people, like maybe as much as one or two percent of the population (which amounts to a few million people in the US) who might legitimately associate their tinnitus with the covid vaccine, even if the vaccine actually had nothing to do with it.
The same explanation goes for ANC - when you cut out all the noise, suddenly it’s way easier to notice the tinnitus you already had.
There might be something with the neck stiffness idea. I do get the feeling my tinnitus lessens when I’m using cervical traction and doing neck stretching regularly.
> Yeah, that's what happens to someone's code when they moves on—becomes someone else's sandbox and they are free to knock down the castle, build another—Chesterton's Fence not withstanding, ha ha.
As someone who references Chesterton’s fence often, I not only agree the code often gets rewritten when someone moves on, I even think it’s often the right thing to do - for medium to small projects where there is one or only a few people who own the code. The reason is because I’ve seen what happens when you don’t rewrite it - the new owner(s) don’t have intimate knowledge of the codebase, and as a result, they work at the speed of molasses regardless of their skill. I have left code behind to people who are better coders than me, and it took years for them to become productive.
To be fair, I have also seen large projects with many people get rewritten and have Chesterton bite back hard, having the projects go late, cost enormous sums of money, and end up as bad as the first time, so rewrites certainly aren’t always called for.
This is all changing dramatically with Claude, BTW, people can now get into a codebase and be productive without rewriting it. They might not understand it, but this is a positive development of some kind at some level.
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