5n edos

William Lynch
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5n edos

Postby William Lynch » Mon Apr 18, 2016 11:40 pm

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.

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Dave Keenan
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Re: 5n edos

Postby Dave Keenan » Mon Apr 18, 2016 11:59 pm

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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Re: 5n edos

Postby William Lynch » Tue Apr 19, 2016 2:14 pm

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

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Re: 5n edos

Postby Dave Keenan » Tue Apr 19, 2016 6:11 pm

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.

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Re: 5n edos

Postby Dave Keenan » Tue Apr 19, 2016 7:29 pm

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.

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Re: 5n edos

Postby Dave Keenan » Tue Apr 19, 2016 8:57 pm

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
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Re: 5n edos

Postby William Lynch » Tue Apr 19, 2016 11:05 pm

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?

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Dave Keenan
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Re: 5n edos

Postby Dave Keenan » Wed Apr 20, 2016 12:12 am

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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Re: 5n edos

Postby William Lynch » Wed Apr 20, 2016 12:22 am

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?

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Dave Keenan
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Re: 5n edos

Postby Dave Keenan » Wed Apr 20, 2016 12:32 am

For Windows users, it would be possible to use the Microsoft Keyboard Layout Creator to make a keyboard layout that lets you type the Greek equivalent of a Latin letter by holding the AltGr or right Alt key (or Ctrl and Alt) while typing the letter. I thought someone might have already done this and made it available, but if so, I can't find it. If someone out there is willing to do it, I recomemnd the keyboard mapping implied by the "Symbol" font. [Edit: I did it. See below]
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