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103EDO and 113EDO - The Sagittal forum

103EDO and 113EDO

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cam.taylor
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Joined: Thu Sep 03, 2015 11:55 am

103EDO and 113EDO

Postby cam.taylor » Sun Dec 06, 2015 11:55 am

103EDO and 113EDO have been topics of Scott Dakota's posts over on the XA Math facebook page, and I'm quite interested in exploring them as 103=31+72 and 113=41+72, so they're both Miracle friendly and very compatible with material from 31, 41 and 72EDOs as well as being excellent competitors at high prime limits (I believe Scott's been looking into the 47-limit)

I was thinking of comparing these two with 94, how interval relations work, and how things might "translate" across these moderately fine-grain equal divisions of the octave. It would be wonderful to know what the recommended Sagittal set would be for 103 and 113, as I'd imagine they'd look similar to each other and also 72... any thoughts?

(I have, of course, checked the Sagittal pdf for EDO notations, and neither 103 or 113 is listed, which is why I'm asking)

Thanks in advance!

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Xen-Gedankenwelt
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Re: 103EDO and 113EDO

Postby Xen-Gedankenwelt » Mon Dec 07, 2015 9:53 am


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Dave Keenan
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Re: 103EDO and 113EDO

Postby Dave Keenan » Mon Dec 07, 2015 12:12 pm

I wonder if Scott is has considered the consistency of their JI approximations. When you look at that, neither of those divisions is particularly remarkable, compared to others in the vicinity, such as 94, 111 and 121.
Strictly-speaking 103edo isn't even 1,3,9-consistent, meaning that, as a chain of fifths, C : G : D is not it's best approximation of 1:3:9, although that can be repaired by stretching its octave by 0.2 to 1.9 cents, when its integer consistency limit becomes 15. 113 edo has an integer consistency limit of 14 (which doesn't increase with any stretch or compression of the octave).
See

A notation for 113edo is straightforward: :)|(:=1, :/|:=2, :|):=3, :/ /|:=4, :/|\:=5, :#:=10. An alternative would be :|(:=1.
In the case of 103edo we have: :/|:=1, :|):=3, :/|\:=4, :#:=8. But 2 degrees is difficult.
2 degrees of 103edo could be :|(: or :)|(: but their untempered size is very small, and less than :/|:. 2 degrees of 103edo could also be :/ /|:, which has the opposite problem, but I prefer it for the obviousness of :/|: + :/|: = :/ /|:.

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Xen-Gedankenwelt
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Re: 103EDO and 113EDO

Postby Xen-Gedankenwelt » Mon Dec 07, 2015 6:21 pm



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