User:Lhearne/Extra-Diatonic Intervals: Difference between revisions
Mostly added sections on Miracle, 11edo and 21edo; and 6edo |
m Added Machine |
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Slendric[11] 5|5: P1 S1 SM2 sm3 s4 P4 P5 S5 SM6 sm7 s8 P8 | Slendric[11] 5|5: P1 S1 SM2 sm3 s4 P4 P5 S5 SM6 sm7 s8 P8 | ||
We may also write temperaments with a 9/8 but no 3/2. The most well known of these is Machine: | |||
Machine[5] 2|2: P1 M2 M3 m6 m7 P8 | |||
Machine[6] 3|2: P1 M2 M3 A4 m6 m7 P8 | |||
Machine[11] 5|5: P1 d3 M2 d4 M3 d5 A4 m6 A5 m7 A6 P8 | |||
=== Further application in edos === | === Further application in edos === | ||
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P1 Sm2 Sm3 N3 sM3 P4 P5 Sm6 N6 sM6 sM7 P8 as a well-ordered interval name set. | P1 Sm2 Sm3 N3 sM3 P4 P5 Sm6 N6 sM6 sM7 P8 as a well-ordered interval name set. | ||
We should not expect our Machine[11] scale to be represented in this spelling of 11edo: A spelling of 11edo that shows that it supports Machine uses a different mapping, using the 9/8 from two 22edo P5s. We could spell 11edo as every other note of 22edo if we wish to see how it supports Machine. | |||
21edo can be written as three 7edos as it's best fifth is that of 7edo. Since 81/80 is -1 steps in 21edo, we use 64/63 alterations: | 21edo can be written as three 7edos as it's best fifth is that of 7edo. Since 81/80 is -1 steps in 21edo, we use 64/63 alterations: | ||
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This tells us that in 6edo 81/80 is mapped to -2 steps of 6edo. This is not a problem, as we can use alterations of 64/63, mapped to 1 step, though I don't see why anyone would want to think of 6edo in this way. | This tells us that in 6edo 81/80 is mapped to -2 steps of 6edo. This is not a problem, as we can use alterations of 64/63, mapped to 1 step, though I don't see why anyone would want to think of 6edo in this way. | ||
Similarly to Machine in 11edo, Machine in 6edo uses a different (much better) mapping of 9/8: That of 12edo. 6edo is much better spelled as a subset of 12edo, where we can see if supports Machine. | |||
The primary interval names for the remaining trivial edos are trivially derived and are given along with all those described so far in the section below. | The primary interval names for the remaining trivial edos are trivially derived and are given along with all those described so far in the section below. | ||
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Injera[14] 3|3 (2): P1 sm2 M2 sm3 m3 SM3 P4 4-5 P5 sm6 M6 SM6 m7 SM7 P8 | Injera[14] 3|3 (2): P1 sm2 M2 sm3 m3 SM3 P4 4-5 P5 sm6 M6 SM6 m7 SM7 P8 | ||
Machine[5] 2|2: P1 M2 M3 m6 m7 P8 | |||
Machine[6] 3|2: P1 M2 M3 A4 m6 m7 P8 | |||
Machine[11] 5|5: P1 d3 M2 d4 M3 d5 A4 m6 A5 m7 A6 P8 | |||
Mavila[7] 3|3: P1 M2 m3 P4 P5 M6 m7 P8 | Mavila[7] 3|3: P1 M2 m3 P4 P5 M6 m7 P8 | ||