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EDOs with multiple prime mappings - Page 4 - The Sagittal forum

EDOs with multiple prime mappings

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Dave Keenan
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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Thu Oct 13, 2016 2:57 pm

Here's my latest proposal for standard Sagittal EDO notation classes. As well as notating all sub-meantones as limma-fractions, I've corrected where I mistakenly showed 66-edo notated as apotome-fractions.

EdoNotationClasses2.gif

The boundaries are at fifth errors of +-7.5 cents. Superpythagoreans and Meantones are just on the blue side of these boundaries. I suggest that if you want a fractional-3-limit notation for any of the EDOs in the blue area (a non-standard notation for them), they should be notated as apotome-fractions. i.e. You can imagine the amber underlaying the blue, like sand under water. But the red is fire, and stops at the water's edge.

Many thanks to Cryptic Ruse for promoting fractional-3-limit notations for EDOs below 72, and for showing that it is possible to do it with a small number of accidental symbols.

Here's my proposed mixed-Sagittal symbol set for fractional-3-limit notations (originally posted here: ). I've only shown the upward symbols, but of course there are matching downward symbols too.

I note that all of these symbols contain a left-scroll (to indicate that this is a fractional-3-limit notation and not a JI-based notation), and most of them are Spartan symbols with a left-scroll added. The left-scroll adds an "r" or "l" to the symbol's name.

Notice how the width of the Sagittals increases steadily with the size of their alteration.

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Re: EDOs with multiple prime mappings

Postby cryptic.ruse » Thu Oct 13, 2016 3:34 pm


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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Thu Oct 13, 2016 8:33 pm


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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Thu Oct 13, 2016 11:32 pm

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EdoNotationClasses3.gif

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Dave Keenan
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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Sat Oct 15, 2016 12:25 am

Having done apotome-fraction notations for EDOs with negative limmas, let's see what limma-fraction notations for EDOs with negative apotomes look like.


They look OK to me.

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cryptic.ruse
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Re: EDOs with multiple prime mappings

Postby cryptic.ruse » Sat Oct 15, 2016 10:14 am


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cryptic.ruse
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Re: EDOs with multiple prime mappings

Postby cryptic.ruse » Sat Oct 15, 2016 4:55 pm


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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Sun Oct 16, 2016 12:36 am


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Re: EDOs with multiple prime mappings

Postby cryptic.ruse » Wed Oct 19, 2016 10:57 am

So, after spending some time on this, I have indeed discovered that by dividing 9/8 (the one consistent with the best 3/2, provided the best 3/2 is no sharper than 720¢) instead of the limma and apotome, I can accomplish exactly the same results as my original proposal with one fewer symbol pair, and in fact the result is even more effective: since we are deriving accidentals from divisions of 9/8, we can have meaningful single-symbol accidentals in 11edo, 13edo, and 18edo that exist independently of the apotome or limma (if we desire such things, anyway).

One thing I am currently trying to figure out (and you may already have figured it out, I need to re-read your replies about repurposing symbols), is what is the best way to repurpose symbols across ETs whose whole-tones do not share the same GCD. I.e., since I now only "need" three symbol pairs (plus the apotome), so if I am ok with having a total of six symbol pairs (including the apotome), what is the most effective way to assign multiple meanings to the five non-apotome symbol pairs to cut down the overall amount of symbols on the page?

I'm not entirely sure if this approach is more fruitful than the original premise of dividing the two pythagorean semitones, nor am I sure it wouldn't be better to divide the best 9/8 independent of 3/2 (incidentally, of ETs in this size range, almost exactly half are 1-3-9 inconsistent, in a sort of alternating pattern...I never realized that!). But I want to hack my way through this before moving onward.

I'll be back with a more in-depth reply in the next week, I think.

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Re: EDOs with multiple prime mappings

Postby Dave Keenan » Thu Oct 20, 2016 2:05 pm



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