- 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:
**3526**

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 nat...

- 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:
**3526**

<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...

- 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:
**3526**

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...

- 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:
**3526**

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...

- 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:
**3526**

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...

- Mon Jul 16, 2018 3:52 pm
- Forum: Equal Division notations
- Topic: A proposal to simplify the notation of EDOs with bad fifths
- Replies:
**41** - Views:
**3526**

Here's another way of looking at the small-EDO notation problem. I've added lines of constant fifth-size. A JI-based notation can also be an apotome-fraction notation that's designed for fifths of a specific size (or a small range of sizes), so there's no real distinction between apotome-fraction an...

- Fri Jun 22, 2018 9:15 pm
- Forum: Just Intonation notations
- Topic: 13-limit JI
- Replies:
**51** - Views:
**7374**

I just received the following welcome email from Daniel Spreadbury of Steinberg: Hi Dave, George, It’s been a while! I hope the two of you are keeping well. I just wanted to drop you a line to let you know that Dorico Pro 2 came out just over three weeks ago, and has an initial implementation of pla...

- Thu Sep 07, 2017 9:09 am
- Forum: Equal Division notations
- Topic: A proposal to simplify the notation of EDOs with bad fifths
- Replies:
**41** - Views:
**3526**

Well George, we've slept on it for 9 months now, and there has recently been a request on one of the facebook groups, for someone to add the corresponding Sagittal notation(s) to every EDO entry in the Xenharmonic Wiki. So we really ought to decide whether these will become the new standard notation...

- Tue Sep 05, 2017 12:46 pm
- Forum: Equal Division notations
- Topic: A proposal to simplify the notation of EDOs with bad fifths
- Replies:
**41** - Views:
**3526**

Relative to the notations given in http://sagittal.org/sagittal.pdf at the time of writing, this proposal will add native-fifth notations for the following seventeen EDOs: 6, 8, 11, 13, 18, 20, 25, 28, 30, 32, 35, 37, 42, 52, 54, 59, 71. And it will change the existing native-fifth notations for the...

- Tue Sep 05, 2017 9:59 am
- Forum: Equal Division notations
- Topic: A proposal to simplify the notation of EDOs with bad fifths
- Replies:
**41** - Views:
**3526**

Here's is the final version, which George and I agree on, of all the EDO native-fifth notations resulting from this proposal. First we show all of the proposed apotome-fraction notations. These are for the EDOs whose best fifths are more than 7.5 c wider than just (> 709.5 c) (wider than those of 22...