5n edos

William Lynch
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Joined: Mon Sep 21, 2015 9:27 pm

5n edos

My idea is to notate 5n edos by mapping 10 edo to the staff as chains of fifths. Thus 5 edo is either lines or spaces. 15 edo would require accidentals for two out of three chains. 20 edo would just be a sort of quarter tone accidentals, sagittal of course.

Dave Keenan
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Re: 5n edos

So your 10 nominals would be in two chains of 720 cent fifths a half octave apart. We could call them CGDAE and γδαεβ (gamma delta alpha epsilon beta) in the manner of Erv Wilson, as in the recent discussion of Pajara[10] nominals. The Greek letters are like flattened versions of their Latin transliterals. Alpha would be a half-octave from D. Then to notate 15 and 20edo we'd need accidentals for 2 and 3 degrees of 60edo, notated relative to the 720 cent fifth (instead of the usual 700 cent fifth).

You'd get a notation for 30 edo out of that for free. But you wouldn't get a notation for 25 edo. Would that matter?

William Lynch
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Joined: Mon Sep 21, 2015 9:27 pm

Re: 5n edos

Ok I'm convinced. How should 15 EDO and other 5n edos be notated in sagittal?

Dave Keenan
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Re: 5n edos

The notations for 10edo and 15edo in Figure 8 on page 16 of http://sagittal.org/sagittal.pdf effectively give us accidentals for 4, 6, 8 and 12 degrees of 60edo notated relative to the 5edo fifth (720 cents). These are , , (or #) and (or #)
The best I can come up with for 2 and 3 degrees of 60edo notated relative to the 5edo fifth are and . So these are 1 degree of 30edo and 1 degree of 20 edo.

You didn't answer my question as to whether you want 25edo in this system. And I'm unclear whether you want a 5 nominal or a 10 nominal notation for 5, 10, 15. 20, 30 edos. 10 nominals is easier.

Dave Keenan
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Re: 5n edos

On second thoughts, 5 nominals is no more difficult than 10 nominals.

5 nominals
5edo: C D E G A
10edo: C D D E E G G A A C
15edo: C C D D D E E G G G A A A C
20edo: C C D D D D E E E E G G G G A A A A C C
25edo: C C C D D D D D E E E E E G G G G G A A A A A C C
30edo: C C C D D D D D D E E E E E E G G G G G G A A A A A A C C C

10 nominals
5edo: C D E G A
10edo: C δ D ε E γ G α A χ
15edo: C δ δ D ε ε E γ γ G α α A χ χ
20edo: C C δ δ D D ε ε E E γ γ G G α α A A χ χ
25edo: C C δ δ D D D ε ε E E E γ γ G G G α α A A A χ χ C
30edo: C C δ δ δ D D D ε ε ε E E E γ γ γ G G G α α α A A A χ χ χ C

Sorry about the spaces between the lowercase Greek letters and their accidentals. I have to do that to get the Sagittal smilie codes to be interpreted properly. The forum isn't set up to treat Greek letters as nominals, although that's something I could make it do in future.

Dave Keenan
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Re: 5n edos

I note that the 25edo notations are a bit of a hodge-podge. They use a mix of accidentals from the 20edo and 30edo notations.

is primarily used for 1\30 but is also used for 0.5\25 in the 10 nominal notation only.
is primarily used for 1\20 but is also used for 1\25.
is primarily used for 1\15 or 2\30 but is also used for 2\25 in the 5 nominal notation only.

ASCII versions are
= )~| = 1\30
= ~~| = 1\20
= /| = 1\15 2\30
= /|) = 1\10 2\20 3\30

William Lynch
Posts: 45
Joined: Mon Sep 21, 2015 9:27 pm

Re: 5n edos

Thanks so much, that makes sense now. I kind of am getting a bit into the whole descriptor thing of sagittal so that we can see what happens across tunings. I quite like the 5 nominal system and I feel like a 10 nominal may be just too complicated for no gain as A. the letters do not blend with the sagittal and B greek letters are a pain to type quickly since there is no magic greek key on a keyboard and you have to manually switch.

I may decide to use J K L M N though instead but perhaps not.

So then this doesn't differentiate 720 as a different interval since it's just treated like a fifth?

Dave Keenan
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Re: 5n edos

William Lynch wrote:So then this doesn't differentiate 720 as a different interval since it's just treated like a fifth?
That's correct. One should tell the reader, in some way, at the start of the score, what the overall tuning is, what size of fifth the nominals are based on, and maybe a legend for how many degrees each accidental corresponds to.

William Lynch
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Joined: Mon Sep 21, 2015 9:27 pm

Re: 5n edos

Ok, I'm trying to get this to all work in MUS2 with Bravura font but I cannot seem to find Shai and Shao. Am I supposed to combine something? I'm using the mixed sagittal btw, is it like a Gao Flat or something?

Dave Keenan