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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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|4L+4s
|4L+4s
|}
|}
==Scale tree==
{| 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 re ut, C sol fa
|perfect octave, perfect eighteenth
|5L+2s, 12L+5s
|  -1
|C fa ut, F fa
|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, B la mib
|minor seventh, minor seventeenth
|4L+2s, 11L+5s
|-
|3
|A re, D sol re
|major second, perfect twelfth
|1L, 8L+3s
|  -3
|B la mib, E lab
|minor tenth, minor twentieth
|6L+3s, 13L+6s
|-
|4
|A la mi re, D la sol
|major ninth, perfect nineteenth
|6L+2s, 13L+5s
|  -4
|B mib, E la mib
|minor third, minor thirteenth
|1L+1s, 8L+4s
|-
|5
|E la mi re, A la mi 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, D la mi
|major third, major thirteenth
|2L, 9L+3s
|  -6
|A la mi reb, D la solb
|minor ninth, diminished nineteenth
|5L+3s, 12L+6s
|-
|7
|B la mi, E la
|major tenth, major twentieth
|7L+2s, 14L+5s
|  -7
|A reb, D sol reb
|minor second, diminished twelfth
|1s, 7L+4s
|-
|8
|F mi, B 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 fa ut#, F mi
|augmented fourth, major fourteenth
|3L, 10L+3s
|  -9
|G sol re utb, C sol fab
|diminished octave, diminished eighteenth
|4L+3s, 11L+6s
|-
|10
|G ut, C sol fa ut
|augmented unison, augmented eleventh
|1L-1s, 8L+2s
|  -10
|G utb, C sol 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 sol fa#
|augmented octave, augmented eighteenth
|6L+1s, 13L+4s
|  -11
|C fa utb, F fab
|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 fab, B la mibb
|diminished seventh, diminished seventeeth
|3L+3s, 10L+6s
|-
|13
|A re#, D sol re#
|augmented second, augmented twelfth
|2L-1s, 9L+2s
|  -13
|B la mibb, E labb
|diminished tenth, diminished twentieth
|5L+4s, 12L+7s
|-
|14
|A la mi re#, D la sol#
|augmented ninth, augmented nineteenth
|7L+1s, 14L+4s
|  -14
|B mibb, D la mibb
|diminished third, diminished thirteenth
|2s
|-
|15
|E la mi re#, A la mi re#
|augmented sixth, augmented sixteenth
|5L, 12L 3s
|  -15
|E la mi rebb, A la mi rebb
|diminished sixth, diminished sixteenth
|2L+3s, 9L+6s
|-
|16
|B mi#, D la mi#
|augmented third, augmented thirteenth
|3L-1s,
10L+2s
|  -16
|A la mi rebb, D la solbb
|diminished ninth, doubly diminished nineteenth
|4L+4s, 11L+7s
|}
==And Scale tree==
The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible ~ed8/3s, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between ~ed8/3 would be (3+2)\(10+7) = 5\17 – five degrees of [[17edXI]]:
The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible ~ed8/3s, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between ~ed8/3 would be (3+2)\(10+7) = 5\17 – five degrees of [[17edXI]]:
{| class="wikitable center-all"
{| class="wikitable center-all"
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