Search found 243 matches

by Dave Keenan
Mon Jul 23, 2018 6:40 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

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.   Steps per limma B:C E:F (diatonic semitone) -2 -1 0 1 2 3 4 5 6 7 Steps per apotome :b: :#: -2 (chromatic semitone) Subset 11 notation 22s s Add them to get -1 steps per whole...
by Dave Keenan
Mon Jul 23, 2018 5:00 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

Here is that diagram showing only my preferred notation types, with each type coloured differently.   Steps per limma B:C E:F (diatonic semitone) -2 -1 0 1 2 3 4 5 6 7 Steps per apotome :b: :#: -2 (chromatic semitone) Subset 11 notation SS Add them to get -1 steps per whole-tone 9 16 23 C:D D:E F:G ...
by Dave Keenan
Mon Jul 23, 2018 3:52 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

Here's a diagram you can copy and make changes to (preferably highlighting the changes with some colour). It shows what notation types I think we should give (in sagittal.pdf and sag_et.par) for each EDO from 5 to 72, and the order in which I prefer the types. We already have all these notations, of...
by Dave Keenan
Mon Jul 23, 2018 3:05 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

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 referring to...
by Dave Keenan
Sat Jul 21, 2018 5:51 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

72 is as good a cutoff as any. As I said before, I don't think anyone is going to refret a guitar to any division this complex. I agree. But I don't understand why this is relevant to whether or not a division should have a native fifth notation. There are many other things people may want to do wi...
by Dave Keenan
Sat Jul 21, 2018 11:31 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

I agree that 1:3:9 inconsistency (or equivalently: more than 25% relative error in the fifth) is another kind of "bad fifth", and such divisions do not require a native fifth notation. They can make do with a subset notation. But we would like to give, at least the low numbered ones, a native fifth ...
by Dave Keenan
Sat Jul 21, 2018 9:13 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

<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 20) 1:3:9...
by Dave Keenan
Sat Jul 21, 2018 12:07 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

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 nota...
by Dave Keenan
Fri Jul 20, 2018 12:05 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

54-edo is far more difficult to find a JI-based notation for. It is 1:3:7:11:13:17 consistent, but, as you say, the 7-comma is zero degrees and so is notationally-useless. So are the 17-comma and 17-kleisma, as they are the same size as the 11-diesis (3 degrees). At least the 13L-diesis is 4 degrees...
by Dave Keenan
Thu Jul 19, 2018 8:17 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4945

Re: A proposal to simplify the notation of EDOs with bad fifths

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 checked...