Rastmic chords: Difference between revisions
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A ''rastmic chord'' is an [[Dyadic_chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the rastma, 243/242, in the 2.3.11 subgroup in the 11 odd limit | A ''rastmic chord'' is an [[Dyadic_chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the rastma, 243/242, in the 2.3.11 subgroup in the 11 odd limit. | ||
The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16: | |||
* There are three ''rastmic triads'': the classic neutral triad 1-11/9-3/2 with steps 11/9-11/9-4/3, and an inversely related pair of triads, 1-9/8-11/6 with steps 9/8-18/11-12/11 and 1-9/8-11/9 with steps 9/8-12/11-18/11. | |||
Equal divisions with rastmic chords include 10, 17, 24, 31 ,41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be, 1318be. | * ''Rastmic tetrads'' are seven in number: the palindromic classic [[neutral tetrad]] 1-11/9-3/2-11/6 with steps 11/9-11/9-11/9-12/11; the palindromic 1-3/2-18/11-11/6 with steps 3/2-12/11-9/8-12/11; the palindromic 1-9/8-11/9-11/8 with steps 9/8-12/11-9/8-16/11; the inverse pair 1-11/9-11/8-3/2 with steps 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps 12/11-9/8-11/9-4/3; and the inverse pair 1-9/8-11/9-3/2 with steps 9/8-12/11-11/9-4/3 and 1-9/8-3/2-11/6 with steps 9/8-4/3-11/9-12/11. | ||
* There are five ''rastmic pentads'': the palindromic pentad 1-9/8-11/9-3/2-11/6 with steps 9/8-12/11-11/9-11/9-12/11; the pair 1-9/8-11/8-3/2-11/6 with steps 9/8-11/9-12/11-11/9-12/11 and 1-11/9-11/8-3/2-11/6 with steps 11/9-9/8-12/11-11/9-12/11; and the pair 1-9/8-11/9-11/8-3/2 with steps 9/8-12/11-9/8-12/11-4/3 and 1-9/8-3/2-18/11-11/6 with steps 9/8-4/3-12/11-9/8-12/11. | |||
* There is also a ''rastmic hexad'': 1-9/8-11/9-11/8-3/2-11/6, with steps 9/8-12/11-9/8-12/11-11/9-12/11. This can be extended to the neutral diatonic scale, LsLsLss, which is [[Chromatic_pairs#Neutral|Neutral[7]]]. In neutral, with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give [[neutral7]], which therefore has two rastmic hexads and of course many more smaller rastmic chords. | |||
Equal divisions of the octave with rastmic chords include 10, 17, 24, 31, 41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be, 1318be. | |||
{| class="wikitable" | |||
|- | |||
! chord by pitches | |||
! chord by intervals | |||
|- | |||
| 1 - 11/9 - 3/2 | |||
| 11/9 - 11/9 - 4/3 | |||
|- | |||
| 1 - 9/8 - 11/6 | |||
| 9/8 - 18/11 - 12/11 | |||
|- | |||
| 1 - 9/8 - 11/9 | |||
| 9/8 - 12/11 - 18/11 | |||
|- | |||
| 1 - 11/9 - 3/2 - 11/6 | |||
| 11/9 - 11/9 - 11/9 - 12/11 | |||
|- | |||
| 1 - 3/2 - 18/11 - 11/6 | |||
| 3/2 - 12/11 - 9/8 - 12/11 | |||
|- | |||
| 1 - 9/8 - 11/9 - 11/8 | |||
| 9/8 - 12/11 - 9/8 - 16/11 | |||
|- | |||
| 1 - 11/9 - 11/8 - 3/2 | |||
| 11/9 - 9/8 - 12/11 - 4/3 | |||
|- | |||
| 1 - 12/11 - 11/9 - 3/2 | |||
| 12/11 - 9/8 - 11/9 - 4/3 | |||
|- | |||
| 1 - 9/8 - 11/9 - 3/2 | |||
| 9/8 - 12/11 - 11/9 - 4/3 | |||
|- | |||
| 1 - 9/8 - 3/2 - 11/6 | |||
| 9/8 - 4/3 - 11/9 - 12/11 | |||
|- | |||
| 1 - 9/8 - 11/9 - 3/2 - 11/6 | |||
| 9/8 - 12/11 - 11/9 - 11/9 - 12/11 | |||
|- | |||
| 1 - 9/8 - 11/8 - 3/2 - 11/6 | |||
| 9/8 - 11/9 - 12/11 - 11/9 - 12/11 | |||
|- | |||
| 1 - 11/9 - 11/8 - 3/2 - 11/6 | |||
| 11/9 - 9/8 - 12/11 - 11/9 - 12/11 | |||
|- | |||
| 1 - 9/8 - 11/9 - 11/8 - 3/2 | |||
| 9/8 - 12/11 - 9/8 - 12/11 - 4/3 | |||
|- | |||
| 1 - 9/8 - 3/2 - 18/11 - 11/6 | |||
| 9/8 - 4/3 - 12/11 - 9/8 - 12/11 | |||
|- | |||
| 1 - 9/8 - 11/9 - 11/8 - 3/2 - 11/6 | |||
| 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11 | |||
|} | |||