Search found 238 matches

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: 3245

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 ...
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: 3245

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: 3245

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: 423

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: 2073

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...
by Dave Keenan
Sun Nov 06, 2016 12:17 am
Forum: Glyph design and Handwriting
Topic: New Olympian diacritics
Replies: 0
Views: 736

New Olympian diacritics

Many thanks to Xen-Gedankenwelt for helping to get the full set of Sagittal symbols up as "smilies" on this forum. View more smilies None of the recently uploaded symbols will be of any interest to those of you using the "mixed" Sagittal notation, as this only requires the single...
by Dave Keenan
Sat Nov 05, 2016 6:04 pm
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2073

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

Xen, Thank you so much for doing that tedious job. I've finally got the rest of the information together and put them up on the forum, tested them and hopefully fixed all my naming and encoding errors. Your work was flawless. So we finally have the full set of Sagittal symbols available on the forum...
by Dave Keenan
Thu Nov 03, 2016 7:06 pm
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2073

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

I think your asterisk note above should say "* ambiguous, usually refers to a different comma" rather than "... different accidental". The ratios are a mixed collection from personal experience, my own comma lists, commas from popular temperaments, or commas / ratios from the fol...
by Dave Keenan
Wed Nov 02, 2016 7:24 pm
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2073

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

One accidental pair which I'd be interested in is for 256:245, the difference between 8/7 and 35/32. 245:256 is :.::~~||: which is the apotome-complement of :'::~|): i.e. :.::~~||: = :.::~!)::#: 9:10 is :.::)X(: = :.::\ \!::x: You should be able to get the rest from George's spreadsheet, using figu...
by Dave Keenan
Wed Nov 02, 2016 5:21 pm
Forum: Linear Temperament notations
Topic: List of 7-prime limit accidentals
Replies: 13
Views: 2073

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

That's marvelous work, Xen. For Moments of Symmetry based on pentatonic scales, it would be very useful to have accidentals for 16:15 and 256:243. 15:16 is :.::/||\: 256:243, the limma, is :.::||\: I think I'd prefer to use two accidentals for neutral or major second-sized ratios like 160/147 or 9/8...

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