The Sagittal forum

Dave Keenan wrote: ↑Mon Jul 23, 2018 6:40 pm Here is the diagram showing my preferred notations for EDOs from 5 to 72, with symbols up to the 1/2-apotome or 3/4-limma.

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This should be:
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Here is the diagram showing my preferred notations for EDOs from 5 to 72, with symbols up to the 1/2-apotome or 3/4-limma.   45 :/|): I am submitting the following counter-proposal. 45-edo is 7-limit consistent (prime 3 has -8.622 cents or -32.33% error) and has a valid apotome of 2 degrees. I reco...

I previously wrote: 54 is 5-limit inconsistent (prime 3 has 9.156 cents or 41.20% error); the 7-comma vanishes, and the 5-comma and 11M-diesis are both 3 degrees. It does not appear that the bad-5ths proposal can be simplified. 54: :)|: :)~|: :/|: :/|): :||\: :~||\: :(||~: :/||\: (bad-5ths proposal)...

Dave Keenan wrote: I suggest that, to reduce the total number of symbols required to cover all the EDOs up to 72, we adopt the alternative notation for 58-edo described in the note at the bottom of page 15 of the XH article. i.e. Change it from 58: :/|: :(|(: :/|\: to 58: :/|: :|\: :/|\: My reply: I...

I have responded to your recent proposals for new JI-based notations for some divisions—in most cases accepting them. I'd appreciate if you would address those I have not (yet) accepted, and address my recent JI notation proposals, including changing :/|): to :(|\: everywhere that it is used as a h...

I checked those possible 61-edo notations I flagged, and I find that the 54-edo AF notation is not valid for 61, because the 5-comma :/|: is 2 degrees, not 3. But the 68-edo notation is valid for 61. And yes, 61 is 1:3:5:11:13 consistent. 61: :|\: :/|: :/|\: :(|\: :(|): :||\:  :/||: :/||\: JB (same...

On second thoughts: There are two reasons for making [44] a subset of 176-EDO: 1) 176 is a much better division than 132; and 2) The notation for 88-EDO is as a subset of 176, so the tones common to 44 and 88 would be notated alike. When you say 176 is "better" than 132, I assume you're r...

<Groan> Please excuse me if I let off some steam at this point, because I had the impression that we already had native-5th notations for all (or nearly all) of the divisions not identified as "bad-5th". Instead, I see that we have very few (if any) native-5th notations for the (more than...

Thanks George. I note for other readers, that although we are summarising these notations using multi-shaft sagittals, each such symbol can be replaced by an equivalent combination of conventional sharps and flats with a single-shaft sagittal. Before I look into examining the merits of JI-based not...

So, to summarise: Of all those EDOs having fifths more than 7.5c wide, and therefore able to be notated using the above apotome-fraction notation, you find that 27 and 49 are not simplified thereby, and so should retain, as their preferred notation, their existing* JI-based notations. I have checke...