A lot of people suggest that piano timbre is somehow optimized for 12edo (and shallow well-temperaments etc.). The author of How Equal Temperament Ruined Harmony said that 1/4 comma meantone's 5ths on a piano sound like a goose honking or something like that, and favoured 55edo for that reason. My 31edo Musescore pieces that sound fine voiced with sine, square or saw waves often sound off on piano.
Thanks for you response, that's exactly what I thought. Is there any study about calculating terrific timbre for n-edo? Maybe that would be more matter, I don't like 12edo from acostic guitar but from piano it sounds interestingly good.
I mean, there are 53 kinds of perfect fifth(0-31, 1-32, 2-33, ... 51-29, 52-30) but one is slightly out of tuned perfect fifth. I'm asking whether people can sense this easily or not.
Neutral third is 9:11 and perfect fifth is 2:3 So neutral triad is 9:11:13.5 but we don't want a decimal there so multiplys 2 and 18:22:27 has made. That doesn't mean neutral triad is not 11th harmonic. If is, than minor triad 10:12:15 would be not a 5th harmonic.
Just to make sure I understand you: you are dividing 3/1 into 12 equal parts, with a step size of roughly 158.5 cents, which also happens to be roughly half of a Just 5-limit minor 3rd (6/5 ratio)?
Oops I just miswrited.😓 You understood right. And yes, if you stack 31/12=158.5cent only 15edo and 53edo are well-approximated. And with stacking 31/6=317cent 19edo and 34edo are also well approximated.
How used are you to near-perfect triads? The 53 edo 9 step major second is off by only -0.14 cents, which is basically perfect to human ears. It's higher than the 12 edo error of -3. 9 cents, but even that is pretty good and a difference of -3.8 cents in the correct direction shouldn't be an issue. What might be bothering you is the melodic step from E, which is now only 8 steps instead of the *just* under 9 you're expecting.
A lot of people suggest that piano timbre is somehow optimized for 12edo (and shallow well-temperaments etc.). The author of How Equal Temperament Ruined Harmony said that 1/4 comma meantone's 5ths on a piano sound like a goose honking or something like that, and favoured 55edo for that reason. My 31edo Musescore pieces that sound fine voiced with sine, square or saw waves often sound off on piano.
Thanks for you response, that's exactly what I thought. Is there any study about calculating terrific timbre for n-edo? Maybe that would be more matter, I don't like 12edo from acostic guitar but from piano it sounds interestingly good.
Thank you so much😀😀
if you're starting from 1, then 32 would be the fifth. honestly i'm not really sure what you're asking.
I mean, there are 53 kinds of perfect fifth(0-31, 1-32, 2-33, ... 51-29, 52-30) but one is slightly out of tuned perfect fifth. I'm asking whether people can sense this easily or not.
You don’t like the just minor 7 chord 10:12:15:18? That’s quite a random bias IMO.
It sounds pretty by itself, but compared to pythagorean minor 7th it doesn't sounds like depressing or subdominant, for me.
12:14:18:21 is even more minor
Yeah I'm kinda fan of subminor chord but as supermajor sounds terrible i can't make a chord progression of subminor chords🤔
Neutral third is 9:11 and perfect fifth is 2:3 So neutral triad is 9:11:13.5 but we don't want a decimal there so multiplys 2 and 18:22:27 has made. That doesn't mean neutral triad is not 11th harmonic. If is, than minor triad 10:12:15 would be not a 5th harmonic.
There's 22
Just to make sure I understand you: you are dividing 3/1 into 12 equal parts, with a step size of roughly 158.5 cents, which also happens to be roughly half of a Just 5-limit minor 3rd (6/5 ratio)?
Oops I just miswrited.😓 You understood right. And yes, if you stack 31/12=158.5cent only 15edo and 53edo are well-approximated. And with stacking 31/6=317cent 19edo and 34edo are also well approximated.
Here's a pump of the kleisma in 53edo, in the Hanson[19] scale, a stack of 19 notes with a minor third between each.
I heard 1 4 7 15 18 21 29 32 35 43 46, am I right?
How used are you to near-perfect triads? The 53 edo 9 step major second is off by only -0.14 cents, which is basically perfect to human ears. It's higher than the 12 edo error of -3. 9 cents, but even that is pretty good and a difference of -3.8 cents in the correct direction shouldn't be an issue. What might be bothering you is the melodic step from E, which is now only 8 steps instead of the *just* under 9 you're expecting.
Thank you for your information.