Interval arithmetic: Difference between revisions
→Unconventional notations: Fix error in pentatonic fifthchain |
Undo revision 172778 by Fredg999 (talk) When we stack 5ths, the ratios in the fifthchain go 3/2, 9/8 (not 9/4), 27/16 (not 27/32), etc. We sometimes add 5ths and sometimes subtract 4ths, whichever one keeps everything between 1/1 and 2/1. The diminished penta-1sn is 243/256. We want the dim penta-hexave 243/128. Just like heptatonically we'd want the major 7th. BTW originally I wrote d8 when I meant d6. Thx for helping me find my typo! :) Tag: Undo |
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A notation of N notes will usually have 3 perfect intervals, N-3 major ones, N-3 minor ones, and N of everything else, distributed symmetrically around P1. For example, the pentatonic fifthchain is: | A notation of N notes will usually have 3 perfect intervals, N-3 major ones, N-3 minor ones, and N of everything else, distributed symmetrically around P1. For example, the pentatonic fifthchain is: | ||
...A3 A1 A4 M2 M5 P3 '''P1''' P4 m2 m5 d3 | ...A3 A1 A4 M2 M5 P3 '''P1''' P4 m2 m5 d3 d6 d4 d2… | ||
The minor penta-2nd has a fifthspan of +2, and is 9/8. The major penta-2nd (fifthspan -3) is 32/27. The latter is major not minor simply because it is larger than 9/8 (the original meaning of major). | The minor penta-2nd has a fifthspan of +2, and is 9/8. The major penta-2nd (fifthspan -3) is 32/27. The latter is major not minor simply because it is larger than 9/8 (the original meaning of major). | ||