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Old 8th April 2013, 12:54 PM   #98
calebprime
Penultimate Amazing
 
Join Date: Jul 2006
Posts: 13,001
Originally Posted by calebprime View Post
...
So, for me, 171EDO is in the sweet zone (The Goldilocks zone) between not too big and not too inaccurate, and does ratios of 3,5,7 and 15 very well, and 11s and 13s ok.

The approximation of a 3/2 in 171EDO is 701.754 cents. That is exactly 100 steps in 171EDO, so that's convenient.

It sounds a little brighter and a lot more accurate than the familiar "5th" or 3/2 approximation of 12 or 72edo at 700 cents. I like that.

171 is divisible by 3, so that means that a system of 171 pitches will have increments at exactly 400 and 800 cents -- an equal-tempered "augmented" triad with 1/1. That's a sound and a way of thinking that I like.

What I hear is that I can barely tell it from 13-limit Just Intonation, but it still simplifies things considerably, and brings all those ratios into a closed, additive system.

In the 11 ratios, it's as much as 4 cents off, but I can live with that.

It was very hard to choose. 224EDO is the most accurate. 159EDO (3x53) is excellent and is used by tuning expert Ozan Yarman. 89 is a good smaller system. 87 is good but for the wide 5ths.

72EDO is the choice of some of the Boston Microtonalists. I don't make the same assumptions they do, or have the same goals.

94EDO is an excellent all-around master system.

130EDO shows up on every list. I forget as I write this why I didn't choose it. (Maybe the harmonic 7ths weren't so good?)

But 171 is my choice for the next few years.
130 would have been an equally good choice.

130 has fewer notes, but both 130 and 171 are in a zone where they are master tuning resolutions, not actual pitches assigned to some giant keyboard!

171 is divisible by 3, good, but 130 is divisible by 2, which is equally good. Neither are divisible by 6 -- or both 2 and 3.

For most of my 36-note keyboard tunings, they are virtually the same.

130 has slightly better 11-ratios.

171 has ever-so-slightly better relation between 16/15 and the lower 135/128 I sometimes use.

171 has ever-so-slightly better 5 and 7 ratios, but not by much. Ever so slightly better chain of 3/2's, but again, it's very close.

171 has an ever-so-slightly more copacetic relation of step-size to 3/2 approximation (100 steps to the "fifth".)

So 130 would have been fine, but 171 has a slight edge for what I do.

I reflect that we accept the complexity of our many systems of reckoning time: seconds, minutes, hours, days, weeks, months, years.

So it's not entirely unreasonable or inconceivable to have 6,7, or 8-note scales inside an implicit 12-tone framework inside a 36-note keyboard setup inside a 171-note master scale inside a 1200-cent system.

Last edited by calebprime; 8th April 2013 at 12:55 PM.
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