3 ms·

> const r = Math.pow(2.0, 1.0 / 12.0); It looks like the app uses 12-tone equal temperament as the standard for "in tune". For violin it would probably be bet

by elihu 6y ago

> const r = Math.pow(2.0, 1.0 / 12.0); It looks like the app uses 12-tone equal temperament as the standard for "in tune". For violin it would probably be better to use a just intonation scale as the reference rather than ET. (ET major and minor thirds and sixths differ from just by about 15 cents.) Even better would be to be able to toggle between JI and ET. A pretty good 12-tone just scale is to use 1:1, 9:8, 16:15, 6:5, 5:4, 4:3, 45:32, 3:2, 8:5, 5:3, 9:5, 15:9, and 2:1 is the octave. (Multiply the ratio by the frequency of whatever your root note is.) Though notably on a violin you run into a complication with the open E string. If the G string is 1:1 and the strings are all tuned in fifths, they're 1:1, 3:2, 9:4, and 27:8. 27:8 is octave-equivalent to the pythagorean major sixth 27:16 rather than the simpler 5:3 major sixth that goes better with the rest of the scale. So, if you go with a just scale there's a potential for people to be confused about why their open E string seems to be out of tune (and the answer is that unless they're deliberately trying to play a pythagorean major sixth it probably is).

ctrager 6y ago
You might enjoy this article: https://stringsmagazine.com/perfect-fifths-a-few-thoughts-on-tuning-your-viola-violinists-cellists-invited/ https://stringsmagazine.com/perfect-fifths-a-few-thoughts-on...
phkahler 6y ago
I tune my guitar by matching harmonics of adjacent strings. I dont recall which ones, but E-A, then A-D, D-G. Then take the 4x of low E and match open high E to it. Finally use harmonics to match B-E. This can leave G a bit off depending what you're playing. The E-E is a nice way across the gap.
- titzer 6y ago
  That's a good way to tune your ears, too. For G you can use an electric tuner and just memorize the slight dissonance between G and B. I do highly recommend getting a clip-on electronic tuner, because if you want to change tunings quickly or you want to do drop D on a floating bridge, you are gonna need it!
- leetcrew 6y ago
  you might realize this already, but you are not getting equal temperament when you tune a guitar this way.
recursive 6y ago
You'd have to choose a key before it worked then. And depending on the key, some of your open strings would be out of tune then. The good thing about just intonation is that it's always the same. No configuration.
- lmilcin 6y ago
  It doesn't really matter what is convenient but what is in tune as perceived by human ear. Pianos are "out of tune" so that they sound well to humans.
  - recursive 6y ago
    There are plenty of people that care about convenience. Pianos are generally tuned to equal temperament. If that's what you're saying sounds good to humans, why bother with all the fancy stuff?
    - elihu 6y ago
      Well, just intonation generally sounds better to humans. A person playing violin would tend to naturally migrate to JI voicings of intervals whether they're consciously doing it or not. So, a tool that tells you whether you're "in tune" or not should ideally not tell someone they're out-of-tune when if they play in perfect JI. On the other hand, if the goal is to just be in the general ballpark and accuracy of +/- 15 cents or so is just rounding error, then ET is probably fine. (My own violin skills are pretty rudimentary, so ET would be good enough. But if I were better I'd probably want a JI tuner.)
  - abhorrence 6y ago
    It's more that they're equally out of tune in every key. What actually sounds "best" for a given key (though certainly a little strange and unusual given the pervasiveness of equal temperament) would sound quite out of tune in other keys.
    - elihu 6y ago
dr_dshiv 6y ago
The first scientific experiment in history* was on the topic of harmony/tuning. It was conducted by Pythagoreans who forged bronze chimes in different ratios of thickness, in order to demonstrate the generalization of Pythagorean number theory. Yet, modern science still can't measure the harmoniousness of a song at a given point or overall -- we have neither the theory nor the math to do so. It is an active area of scientific research! I find that so cool. * hypothesis-driven empirical test of a mathematical model
- swirepe 6y ago
  >Yet, modern science still can't measure the harmoniousness of a song at a given point or overall -- we have neither the theory nor the math to do so. It is an active area of scientific research! I find that so cool. What about consonance and dissonance? We have both the math and the music theory for those. Wouldn't that be a measure of harmoniousness?
  - dr_dshiv 6y ago
    It's complicated. We can calculate the dissonance (e.g., harmonic entropy) for specific note combinations, but even the best models of consonance and dissonance don't correspond perfectly with human ratings -- nor can be applied to complex sounds. There isn't a meter capable of showing how consonant or dissonant a song is, at any point in time -- or for the song as a whole.

by elihu 6y ago

ctrager 6y ago

You might enjoy this article: https://stringsmagazine.com/perfect-fifths-a-few-thoughts-on-tuning-your-viola-violinists-cellists-invited/ https://stringsmagazine.com/perfect-fifths-a-few-thoughts-on...

phkahler 6y ago

I tune my guitar by matching harmonics of adjacent strings. I dont recall which ones, but E-A, then A-D, D-G. Then take the 4x of low E and match open high E to it. Finally use harmonics to match B-E. This can leave G a bit off depending what you're playing. The E-E is a nice way across the gap.

titzer 6y ago
That's a good way to tune your ears, too. For G you can use an electric tuner and just memorize the slight dissonance between G and B. I do highly recommend getting a clip-on electronic tuner, because if you want to change tunings quickly or you want to do drop D on a floating bridge, you are gonna need it!
leetcrew 6y ago
you might realize this already, but you are not getting equal temperament when you tune a guitar this way.

recursive 6y ago

You'd have to choose a key before it worked then. And depending on the key, some of your open strings would be out of tune then. The good thing about just intonation is that it's always the same. No configuration.

lmilcin 6y ago
It doesn't really matter what is convenient but what is in tune as perceived by human ear. Pianos are "out of tune" so that they sound well to humans.
- recursive 6y ago
  There are plenty of people that care about convenience. Pianos are generally tuned to equal temperament. If that's what you're saying sounds good to humans, why bother with all the fancy stuff?
  - elihu 6y ago
    Well, just intonation generally sounds better to humans. A person playing violin would tend to naturally migrate to JI voicings of intervals whether they're consciously doing it or not. So, a tool that tells you whether you're "in tune" or not should ideally not tell someone they're out-of-tune when if they play in perfect JI. On the other hand, if the goal is to just be in the general ballpark and accuracy of +/- 15 cents or so is just rounding error, then ET is probably fine. (My own violin skills are pretty rudimentary, so ET would be good enough. But if I were better I'd probably want a JI tuner.)
- abhorrence 6y ago
  It's more that they're equally out of tune in every key. What actually sounds "best" for a given key (though certainly a little strange and unusual given the pervasiveness of equal temperament) would sound quite out of tune in other keys.
  - elihu 6y ago

dr_dshiv 6y ago

The first scientific experiment in history* was on the topic of harmony/tuning. It was conducted by Pythagoreans who forged bronze chimes in different ratios of thickness, in order to demonstrate the generalization of Pythagorean number theory. Yet, modern science still can't measure the harmoniousness of a song at a given point or overall -- we have neither the theory nor the math to do so. It is an active area of scientific research! I find that so cool. * hypothesis-driven empirical test of a mathematical model

swirepe 6y ago
>Yet, modern science still can't measure the harmoniousness of a song at a given point or overall -- we have neither the theory nor the math to do so. It is an active area of scientific research! I find that so cool. What about consonance and dissonance? We have both the math and the music theory for those. Wouldn't that be a measure of harmoniousness?
- dr_dshiv 6y ago
  It's complicated. We can calculate the dissonance (e.g., harmonic entropy) for specific note combinations, but even the best models of consonance and dissonance don't correspond perfectly with human ratings -- nor can be applied to complex sounds. There isn't a meter capable of showing how consonant or dissonant a song is, at any point in time -- or for the song as a whole.