EDOs with multiple prime mappings

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cryptic.ruse
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Re: EDOs with multiple prime mappings

Postby cryptic.ruse » Sun Oct 30, 2016 12:30 pm

Alright, I've banged my head against the wall long enough.

I'm officially giving up on my endeavor, and recommending the use of Kite's ups and downs for most ETs up to and including 31edo, with the exception of 30edo, and Standard Sagittal as it is for 30edo and everything above 31edo.

I note that with rare exceptions (7edo, 9edo, 11edo, 14edo, 16edo), 33/32 maps to 1 step of every ET in the ups and downs range, and the Sagittal accidentals for that comma conveniently share (simplified) ASCII characters with Kite's ups and downs. 7edo and 9edo don't really need accidentals beyond the normal sharps and flats; 11edo will almost certainly be treated as a subset of 22edo; and in 14edo and 16edo we might just as well say JI is irrelevant and repurpose the :/|\: and :\!/: symbols for "half of 9/8". Since I am skeptical that anyone is going to actually use Kite's ups and downs for anything much larger than 31edo (I suspect that users of larger ETs are more JI-focused and thus will be interested in the JI-related information that Sagittal accidentals convey), I propose altering standard Sagittal for the smaller EDOs so that they all use the :/|\: and :\!/: symbols for one step (in addition to the normal :#: and :b: symbols that retain their meanings with respect to the circle of fifths).

It seems like a win-win in that it a) retains a layer of pertinent JI information in keeping with the spirit of Sagittal, b) reduces the number of symbols needed to notate all the small ETs, and c) reconciles two notational standards in the range of ETs where they would be most likely to conflict, thereby facilitating communication among microtonal musicians using these ETs.

I feel confident that I have sufficiently explored other notational approaches to consider this compromise optimal for the vast majority of use cases.

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Dave Keenan
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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Sun Oct 30, 2016 6:04 pm

I must admit this comes as rather a shock, after having come around to your way of thinking regarding the use of fractional 3-limit notations, at least in the case of EDOs with medium to large errors in their fifths.

cryptic.ruse wrote:Alright, I've banged my head against the wall long enough.

What was the metaphorical "wall" here?

I'm officially giving up on my endeavor, and recommending the use of Kite's ups and downs for most ETs up to and including 31edo, with the exception of 30edo, and Standard Sagittal as it is for 30edo and everything above 31edo.

The argument from exhaustion? It doesn't inspire confidence. ;) But I'll do my best to take it seriously.

Why the complicated description of the transition? 31-edo already uses :/|\: for one step (as do 17, 24 and 38), so why not simply say "up to and including 29".

I note that with rare exceptions (7edo, 9edo, 11edo, 14edo, 16edo), 33/32 maps to 1 step of every ET in the ups and downs range, and the Sagittal accidentals for that comma conveniently share (simplified) ASCII characters with Kite's ups and downs. 7edo and 9edo don't really need accidentals beyond the normal sharps and flats; 11edo will almost certainly be treated as a subset of 22edo; and in 14edo and 16edo we might just as well say JI is irrelevant and repurpose the :/|\: and :\!/: symbols for "half of 9/8". Since I am skeptical that anyone is going to actually use Kite's ups and downs for anything much larger than 31edo (I suspect that users of larger ETs are more JI-focused and thus will be interested in the JI-related information that Sagittal accidentals convey), I propose altering standard Sagittal for the smaller EDOs so that they all use the :/|\: and :\!/: symbols for one step (in addition to the normal :#: and :b: symbols that retain their meanings with respect to the circle of fifths).

I'd be pleased if you would spell out exactly how you see each of these notations working, with our usual D thru F thing.

It seems like a win-win in that it a) retains a layer of pertinent JI information in keeping with the spirit of Sagittal, b) reduces the number of symbols needed to notate all the small ETs, and c) reconciles two notational standards in the range of ETs where they would be most likely to conflict, thereby facilitating communication among microtonal musicians using these ETs.

What about the problem that I pointed out earlier? It doesn't facilitate communication among microtonal musicians using different EDOs having the same nominals, such as 5, 10, 15, 20, 25, 30 or 7, 14, 21, 28, 35. Instead, it obfuscates. Consistent notations for these two sequences, are things we have been asked for in the past, and which fractional 3-limit notations would provide.

Another problem is that, in the pure Sagittal, the sequence :/|\: :/||\: :/|||\: :/X\: (where :/||\: is sharp and :/X\: is double-sharp) strongly suggests (and is intended to suggest) that :/|\: is a semisharp or very nearly so. And until now it has never been used for anything less than 3/8-sharp. With your proposal it would be as small as 1/5-sharp in 18 and 25-edo, 1/4-sharp in 6, 13, 20 and 27-edo, and 1/3-sharp in 8, 15, 22 and 29-edo.

In 22-edo and 29-edo, one step corresponds to the 5-comma 81/80. This is far more salient than the 11-limit meaning of 1 step.

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Dave Keenan
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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Sat Apr 15, 2017 10:12 am

The main topic of this thread is continued here:
http://forum.sagittal.org/viewtopic.php?f=5&t=256


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