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User:Moremajorthanmajor/7L 3s (perfect eleventh-equivalent): Difference between revisions

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| -13
| -13
|9w
|9w
|diminished ninth
|diminished tenth
|5L+4s
|5L+4s
|-
|-
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|8^
|8^
|augmented ninth
|augmented ninth
|8L+1s
|7L+1s
| -14
| -14
|2w
|2w
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|diminished ninth
|diminished ninth
|4L+4s
|4L+4s
|}
{| class="wikitable"
!# generators up
!Notation (1/1 = G ut, ~8/3 = C sol fa ut)
!name
!In L's and s's
!# generators up
!Notation of twenty-first inverse
!name
!In L's and s's
|-
| colspan="8" style="text-align:center" |The 20-note MOS has the following intervals (from some root):
|-
|0
|G ut, C sol fa ut
|perfect unison, perfect eleventh
|0, 7L+3s
|0
|G ut, C sol fa ut
|perfect eleventh, “perfect” minor twenty-first
|7L+3s, 14L+6s
|-
|1
|G sol fa re ut, C fa
|perfect octave, perfect eighteenth
|5L+2s, 12L+5s
|  -1
|C fa ut, F fa ut
|perfect fourth, minor fourteenth
|2L+1s, 9L+4s
|-
|2
|D sol re ut, G sol fa ut
|just fifth, perfect fifteenth
|3L+1s, 10L+4s
|  -2
|F fa ut, B fa
|minor seventh, minor seventeenth
|4L+2s, 11L+5s
|-
|3
|A re, D sol la re ut
|major second, perfect twelfth
|1L, 8L+3s
|  -3
|B fab, E lab
|minor tenth, minor twentieth
|6L+3s, 13L+6s
|-
|4
|A la sol re mi, D sol
|major ninth, perfect nineteenth
|6L+2s, 13L+5s
|  -4
|B mib, E la mi reb
|minor third, minor thirteenth
|1L+1s, 8L+4s
|-
|5
|E la mi re, A la sol re
|major sixth, major sixteenth
|4L+1s, 11L+4s
|  -5
|E la mi reb, A la mi reb
|minor sixth, minor sixteenth
|3L+2s, 10L+5s
|-
|6
|B mi, E la mi re si
|major third, major thirteenth
|2L, 9L+3s
|  -6
|A la sol reb, D  solb
|minor ninth, diminished nineteenth
|5L+3s, 12L+6s
|-
|7
|B si la mi, E la
|major tenth, major twentieth
|7L+2s, 14L+5s
|  -7
|A reb, D sol la reb
|minor second, diminished twelfth
|1s, 7L+4s
|-
|8
|F si mi, B si la mi
|major seventh, major seventeenth
|5L+1s, 12L+4s
|  -8
|D sol re utb, G sol fa utb
|diminished fifth, diminished fifteenth
|2L+2s, 9L+5s
|-
|9
|C si, F si mi
|augmented fourth, major fourteenth
|3L, 10L+3s
|  -9
|G sol fa utb, C fab
|diminished octave, diminished eighteenth
|4L+3s, 11L+6s
|-
|10
|G ut#, C si
|augmented unison, augmented eleventh
|1L-1s, 8L+2s
|  -10
|G utb, C fa utb
|diminished eleventh, diminished twenty-first
|6L+4s, 13L+7s
|-
| colspan="8" style="text-align:center" |The chromatic 17-note MOS (either [[7L 10s (perfect eleventh equivalent)|14L 20s]], [[10L 7s (perfect eleventh equivalent)|20L 14s]], or [[34edXXI]]) also has the following intervals (from some root):
|-
|11
|G sol re ut#, C si
|augmented octave, augmented eighteenth
|6L+1s, 13L+4s
|  -11
|C fa utb, F fa utb
|diminished fourth, diminished fourteenth
|1L+2s,
8L+5s
|-
|12
|D sol re ut#, G sol fa ut#
|augmented fifth, augmented fifteenth
|4L, 11L+3s
|  -12
|F fa utb, B fab
|diminished seventh, diminished seventeeth
|3L+3s, 10L+6s
|-
|13
|A re#, D sol re ut#
|augmented second, augmented twelfth
|2L-1s, 9L+2s
|  -13
|B fab, E labb
|diminished tenth, diminished twentieth
|5L+4s, 12L+7s
|-
|14
|A la sol re mi#, D sol#
|augmented ninth, augmented nineteenth
|7L+1s, 14L+4s
|  -14
|B mibb, E la mi re sibb
|diminished third, diminished thirteenth
|2s, 7L+5s
|-
|15
|E la mi re#, A la sol re#
|augmented sixth, augmented sixteenth
|5L, 12L 3s
|  -15
|E la mi rebb, A la sol rebb
|diminished sixth, diminished sixteenth
|2L+3s, 9L+6s
|-
|16
|B mi#, E la mi re si#
|augmented third, augmented thirteenth
|3L-1s,
10L+2s
|  -16
|A sol la mi rebb, D la solbb
|diminished ninth, doubly diminished nineteenth
|4L+4s, 11L+7s
|}
|}
==Scale tree==
==Scale tree==
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[[Mapping]]: [{{val|1 0 -3}}, {{val|0 1 6}}]
[[Mapping]]: [{{val|1 0 -3}}, {{val|0 1 6}}]


[[Optimal ET sequence]]: ~[[17ed8/3]], ~[[27ed8/3]], ~[[44ed8/3]]
[[Optimal ET sequence]]: [[17ed8/3]], [[27ed8/3]], [[44ed8/3]]
==='''Bolivar-Superpyth'''===
==='''Bolivar-Superpyth'''===
[[Subgroup]]: 8/3.2.7/6
[[Subgroup]]: 8/3.2.7/6
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[[Mapping]]:  [{{val|1 0 2}}, {{val|0 1 -4}}]
[[Mapping]]:  [{{val|1 0 2}}, {{val|0 1 -4}}]


[[Optimal ET sequence]]: ~[[17ed8/3]], ~[[24ed8/3]], ~[[31ed8/3]], ~[[38ed8/3]]
[[Optimal ET sequence]]: [[17ed8/3]], [[24ed8/3]], [[31ed8/3]], [[38ed8/3]]
==7-note subsets==
==7-note subsets==
If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)|3L 4s]]:
If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)|3L 4s]]:
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