Search found 243 matches

by Dave Keenan
Sat Nov 19, 2016 1:25 am
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2705

Re: List of 7-prime limit / 6125-odd limit accidentals

Just to make sure that I understand systematic comma names correctly: 25:28 = +-[4 0 -2 1> (not in Olympian set) would be 7:25MS+A, and 1792:2025 = +-[-8 4 2 -1> (contained in Olympian set) would be c7:25MS+A, correct? Those are absolutely correct. Well done. Some of the ratios in the Olympian set ...
by Dave Keenan
Thu Nov 17, 2016 12:56 pm
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2705

Re: List of 7-prime limit / 6125-odd limit accidentals

Ok, I finished the list of 7-limit ratios (including lower limits) with an exact Olympian representation: 7-limit Olympian set.pdf Nicely done. You could include the proper Sagittal symbols in the PDF, at higher resolution than the forum smilies, if you install the Bravura font. Unfortunately, ther...
by Dave Keenan
Tue Nov 15, 2016 11:52 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4908

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

Proposed apotome-fraction notations (pure Sagittal): Steps 0 1 2 3 4 5 6 7 8 9 10 5-edo :h: :/||\: 10-edo :h: :/|\: :/||\: 8,15-edo :h: :|): :||): :/||\: 6,13,20,27-edo :h: :|): :/|\: :||): :/||\: 18,25,32-edo :h: :/|: :/ /|: :)||(: :||\: :/||\: 30,37-edo :h: :/|: :|): :/|\: :||): :||\: :/||\: 42,4...
by Dave Keenan
Tue Nov 15, 2016 11:34 am
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4908

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

Here are all of the proposed apotome-fraction notations. These are the EDOs whose best fifths are wider than those of 22-edo (> 709.5 c). Those on the same row have the same number of steps per apotome, and differ only in the spacing of their nominals. This spacing can be obtained from the chart at ...
by Dave Keenan
Sun Nov 13, 2016 1:46 pm
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2705

Re: List of 7-prime limit / 6125-odd limit accidentals

Sorry for the late reply! I reread sagittal.pdf and your replies to make sure I understand enough about Sagittal notation with Olympian precision. I think I'm now more or less equal to the task of completing the list of 7-limit accidentals with Olympian precision. Well done. But I have a question: ...
by Dave Keenan
Tue Nov 08, 2016 8:57 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4908

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

All suggestions, questions and criticism of the above will be gratefully received. Here are the proposed limma-fraction notations for 9, 16 and 23-edo. 7n+2-edos: A:B C:D D:E F:G G:A = 1\9, 2\16, 3\23; B:C E:F = 2\9, 3\16, 4\23; # b = -1 (Must use multi-shafts for >2/3-limma. Can't use # or b.) 9-ed...
by Dave Keenan
Tue Nov 08, 2016 7:59 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4908

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

An immediate benefit of the above is that we obtain simple consistent notations for all 5n edos that have the same fifth size, and for all 7n edos that have the same fifth size, in a manner similar to the 12n stack shown in figure 10 on page 19 of http://sagittal.org/sagittal.pdf , as follows: 5n-ed...
by Dave Keenan
Tue Nov 08, 2016 3:19 pm
Forum: Equal Division notations
Topic: A proposal to simplify the notation of EDOs with bad fifths
Replies: 41
Views: 4908

A proposal to simplify the notation of EDOs with bad fifths

The following diagram is very useful for understanding EDO Notations and how they relate to each other. It assumes the nominals are in a chain of the EDO's best fifths. It was prompted by discussions with Cryptic Ruse aka Igliashon Jones . http://forum.sagittal.org/download/file.php?id=37 An apotome...
by Dave Keenan
Tue Nov 08, 2016 1:28 am
Forum: Equal Division notations
Topic: 16 Edo
Replies: 1
Views: 547

Re: 16 Edo

With its best (native) fifth, 16-edo has tone = 2 steps, apotome = -1 step, limma = 3 steps. Because the apotome (a chain of 7 fifths) is negative, we can't use sharps or flats in a native-fifth notation for it. Here are 4 options. [Edit: Updated to include my latest simplified-EDO-notation proposal...
by Dave Keenan
Sun Nov 06, 2016 12:44 am
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2705

Re: List of 7-prime limit / 6125-odd limit accidentals

I see you've been updating the list. Good work. Yes. I badly overstated the difference between commatic and chromatic commas. Most of the same ratios turn up in both applications. The only difference is in their popularity or usefulness rankings in each application. I note that one of the criteria f...