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 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.
EDOs with multiple prime mappings
- Dave Keenan
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Re: EDOs with multiple prime mappings
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.
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".
Another problem is that, in the pure Sagittal, the sequence (where is sharp and 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.
What was the metaphorical "wall" here?cryptic.ruse wrote:Alright, I've banged my head against the wall long enough.
The argument from exhaustion? It doesn't inspire confidence. But I'll do my best to take it seriously.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.
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'd be pleased if you would spell out exactly how you see each of these notations working, with our usual D thru F thing.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 symbols that retain their meanings with respect to the circle of fifths).
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.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.
Another problem is that, in the pure Sagittal, the sequence (where is sharp and 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.
- Dave Keenan
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Re: EDOs with multiple prime mappings
The main topic of this thread is continued here:
viewtopic.php?f=5&t=256
viewtopic.php?f=5&t=256