Mavila notation

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herman.miller
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Mavila notation

Post by herman.miller »

@cmloegcmluin 's post on the porcupine notation thread got me thinking about the possibility of coming up with some general guidelines for regular temperament notation in general. One basic idea is that you can essentially use the JI notation for them, since each JI interval maps to an interval of the temperament in a regular pattern. The problem with that idea becomes clear when you try applying it to temperaments that are either too complex (such as the luna / hemithirds notation that @Dave Keenan posted about), or too far from JI.

If you want to notate mavila temperament, you can start with the generator mapping [<1 2 1|, <0 -1 3|] and easily find notations for some basic intervals like 5/3 and 5/4. Taking a 9-note chain of generators centered around D, you might end up with this notation: F:/|: 6/5, B:!!/: 8/5, E 9/8, A 3/2, D 1/1, G 4/3, C:||\: 15/8, F:||\: 5/4, B:\!: 5/3. If you keep going, the obvious notation for the next note is E:\!: 10/9. But in mavila, this note is actually higher than the one labeled E 9/8. So you've got a "flat" that raises the pitch and a "sharp" that lowers the pitch! You could "fix" this by writing E:!!/: 16/15 instead of E 9/8, since that :!!/: doesn't change the pitch in mavila.

If you keep going, you start getting pitches that use the accidental :)||(: (25/24). So one option would be to use 25/24 as the "sharp" of mavila notation, and omit the :||\: :!!/: symbols since they don't change anything. You can notate up to 21 notes that way.

B:)!!(: E:)!!(: A:)!!(: D:)!!(: G:)!!(: C:)!!(: F:)!!(: B E A D G C F B:)||(: E:)||(: A:)||(: D:)||(: G:)||(: C:)||(: F:)||(:

But then how do you continue the pattern if you're trying to notate a 23-note mavila scale? A 5:4 above G:)||(: 25/18 is 125/72, but there's not an obvious way to notate that.

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Dave Keenan
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Re: Mavila notation

Post by Dave Keenan »

herman.miller wrote: Tue Feb 23, 2021 2:40 pm If you keep going, you start getting pitches that use the accidental :)||(: (25/24). So one option would be to use 25/24 as the "sharp" of mavila notation, and omit the :||\: :!!/: symbols since they don't change anything. You can notate up to 21 notes that way.

B:)!!(: E:)!!(: A:)!!(: D:)!!(: G:)!!(: C:)!!(: F:)!!(: B E A D G C F B:)||(: E:)||(: A:)||(: D:)||(: G:)||(: C:)||(: F:)||(:

But then how do you continue the pattern if you're trying to notate a 23-note mavila scale? A 5:4 above G:)||(: 25/18 is 125/72, but there's not an obvious way to notate that.
Hi Herman,

That's a question George and I faced many years back — before we decided to give limma-fraction notations for 9, 16 and 23edos, as shown on the recent Periodic Table. We were prompted by Mike Battaglia to create a Mavila-based notation for them. Prior to that we suggested only that they be notated as subsets of 36, 48 and 46 edos respectively.

You can still see the Mavila notation in figure 8 on page 16 of http://sagittal.org/sagittal.pdf, at least until I get around to updating it. It's reassuring that you chose the same symbol we did for 7 generators. It's quite nice that our symbol for 25/24 :)||(: looks a lot like a modified version of our symbol for 2187/2048 :/||\: , the Sagittal sharp. Mike Battaglia praised us for having designed it that way. But we had to admit it was a complete accident — or rather the result of a chain of decisions that had absolutely nothing to do with the fact that 25/24 and 2187/2048 are alternative definitions of the sharp.

We chose :|||): for 14 generators. I don't remember why we chose it. Perhaps you can figure it out. Let me know if you want me to search my emails to see if I can find our rationale.

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herman.miller
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Re: Mavila notation

Post by herman.miller »

I suppose :|||): is as good as anything for just two notes out of mavila[23], so you'd have F:!!!): on one end and B:|||): on the other. Using C:'::\ \!: as a notation for 125/72, you could ignore the schisma accent and write the two notes in question as E:/ /|: and C:\ \!:. But for example if you're writing in the key of G:)||(: you'll want a B:|||): for the major third. Now if you want a mavila[23] notation centered on some other pitch, like C, you might need to go further out.

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herman.miller
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Re: Mavila notation

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Chart of the proposed mavila notation:

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Dave Keenan
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Re: Mavila notation

Post by Dave Keenan »

Thanks for the chart. I took the liberty of making it display as an image in your post. The trick to doing that is to right click on the link in the Attachments tab and choose "Copy link location", then paste that into your post and surround it with [img]...[/img].

I found the following in an email I sent to George on 25-Mar-2012:
At 02:08 PM 25/03/2012, George Secor wrote:
> I agree that the Sagittal native symbols for one, two, and three degrees of alteration for 16 and 23 divisions would be:
> :)||(: :|||): :(X(:

Hi George,

That will make some folks on the Xenharmonic Alliance on Facebook happy. Mike Battaglia suggested using the 25/24 symbol (and I think Herman Miller may have also suggested it years ago) because it corresponds to -7 generators of Mavila. I went looking for symbols with primary commas for -14 and -21 generators and found none, even with an 11-limit mapping, and so chose the unaccented symbols whose secondary meanings include (25/24)^2 and (25/24)^3.
So you can see that we even came up with a symbol for 3 generators. And the 3 symbols can be distinguished purely by number of shafts. I believe the above means that we chose the symbols whose Olympian capture-zones contained (25/24)2 and (25/24)3, and dropped their accents.

We did not include the 3-generator symbol in the updated XH article, because without it the Mavila notation was a Spartan-only notation, :)||(: being the apotome-complement of :/ /|: , and because it was not needed for the specific EDOs being notated.

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