User:Kaiveran/Scrapbook

My own takes on heptatonic categories for a future Color-inspired notation, if it is determined to be useful

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On Essentially Tempered Chords

• "Finding essentially tempered chords in as efficient a manner as possible is topic of value to me, as it is information I want to know as fast as possible when examining prospective tempering or analogy approaches. This depends on how many commas one is juggling for the set of dyadic essentially tempered chords. If one comma, and if 2/1 is the equave, then write all numerators in one row, then write all the denominators in a a lower row, then do combination permutations of all the dyad ratio combinations that make chords across 2/1. Do these up through whatever odd limit one considers acoustically pertinent."
  • Scott Dakota

Ditto for a pentatonic framework, using the pseudo-7s of a quarter-fifth genchain.

Random Tetrachords

• Sanasiwa Diatonic – 1/1, 61/57, 68/57, 4/3
  • 61/57 - 68/61 - 19/17
• Yasa Chromatic – 1/1, 16/15, 17/15, 4/3
  • 16/15 - 17/16 - 20/17
• Nathisa Enharmonic – 1/1, 37/36, 19/18, 4/3
  • 37/36 - 38/37 - 24/19
• Yazala Hyperenharmonic – 1/1, 55/54, 28/27, 4/3
  • 55/54 - 56/55 - 9/7
• Yathafitwena Hyperenharmonic – 1/1, 79/78, 40/39, 4/3
  • 79/78 - 80/79 - 13/10

Template Messings

Intervals of 5edo (as a 2.3.7 subgroup temperament)

Degree	Cents	Approximated JI intervals
		2-limit	3-limit	7-limit
0	0.000	1/1
1	240.000		9/8 32/27	7/6 8/7
2	480.000		4/3	9/7 21/16 64/49
3	720.000		3/2	14/9 32/21 49/32
4	960.000		16/9 27/16	7/4 12/7
5	1200.000	2/1