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

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|-
|-
|1
|1
|G sol re ut, C sol fa  
|G sol fa re ut, C fa
|perfect octave, perfect eighteenth  
|perfect octave, perfect eighteenth  
|5L+2s, 12L+5s
|5L+2s, 12L+5s
|  -1
|  -1
|C fa ut, F fa  
|C fa ut, F fa ut
|perfect fourth, minor fourteenth  
|perfect fourth, minor fourteenth  
|2L+1s, 9L+4s
|2L+1s, 9L+4s
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|3L+1s, 10L+4s
|3L+1s, 10L+4s
|  -2
|  -2
|F fa, B la mib
|F fa ut, B fa
|minor seventh, minor seventeenth
|minor seventh, minor seventeenth
|4L+2s, 11L+5s
|4L+2s, 11L+5s
|-
|-
|3
|3
|A re, D sol re
|A re, D sol la re ut
|major second, perfect twelfth
|major second, perfect twelfth
|1L, 8L+3s
|1L, 8L+3s
|  -3
|  -3
|B la mib, E lab
|B fab, E lab
|minor tenth, minor twentieth  
|minor tenth, minor twentieth  
|6L+3s, 13L+6s
|6L+3s, 13L+6s
|-
|-
|4
|4
|A la mi re, D la sol
|A la sol re mi, D sol
|major ninth, perfect nineteenth  
|major ninth, perfect nineteenth  
|6L+2s, 13L+5s
|6L+2s, 13L+5s
|  -4
|  -4
|B mib, E la mib
|B mib, E la mi reb
|minor third, minor thirteenth  
|minor third, minor thirteenth  
|1L+1s, 8L+4s
|1L+1s, 8L+4s
|-
|-
|5
|5
|E la mi re, A la mi re
|E la mi re, A la sol re
|major sixth, major sixteenth  
|major sixth, major sixteenth  
|4L+1s, 11L+4s
|4L+1s, 11L+4s
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|-
|-
|6
|6
|B mi, D la mi
|B mi, E la mi re si
|major third, major thirteenth  
|major third, major thirteenth  
|2L, 9L+3s
|2L, 9L+3s
|  -6
|  -6
|A la mi reb, D la solb
|A la sol reb, D solb
|minor ninth, diminished nineteenth  
|minor ninth, diminished nineteenth  
|5L+3s, 12L+6s
|5L+3s, 12L+6s
|-
|-
|7
|7
|B la mi, E la
|B si la mi, E la
|major tenth, major twentieth  
|major tenth, major twentieth  
|7L+2s, 14L+5s
|7L+2s, 14L+5s
|  -7
|  -7
|A reb, D sol reb  
|A reb, D sol la reb
|minor second, diminished twelfth  
|minor second, diminished twelfth  
|1s, 7L+4s
|1s, 7L+4s
|-
|-
|8
|8
|F mi, B la mi
|F si mi, B si la mi
|major seventh, major seventeenth
|major seventh, major seventeenth
|5L+1s, 12L+4s
|5L+1s, 12L+4s
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|-
|-
|9
|9
|C fa ut#, F mi
|C si, F si mi
|augmented fourth, major fourteenth  
|augmented fourth, major fourteenth  
|3L, 10L+3s
|3L, 10L+3s
|  -9
|  -9
|G sol re utb, C sol fab
|G sol fa utb, C fab
|diminished octave, diminished eighteenth  
|diminished octave, diminished eighteenth  
|4L+3s, 11L+6s
|4L+3s, 11L+6s
|-
|-
|10
|10
|G ut, C sol fa ut
|G ut#, C si
|augmented unison, augmented eleventh  
|augmented unison, augmented eleventh  
|1L-1s, 8L+2s
|1L-1s, 8L+2s
|  -10
|  -10
|G utb, C sol fa utb
|G utb, C fa utb
|diminished eleventh, diminished twenty-first
|diminished eleventh, diminished twenty-first
|6L+4s, 13L+7s
|6L+4s, 13L+7s
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|-
|-
|11
|11
|G sol re ut#, C sol fa#
|G sol re ut#, C si
|augmented octave, augmented eighteenth  
|augmented octave, augmented eighteenth  
|6L+1s, 13L+4s
|6L+1s, 13L+4s
|  -11
|  -11
|C fa utb, F fab
|C fa utb, F fa utb
|diminished fourth, diminished fourteenth  
|diminished fourth, diminished fourteenth  
|1L+2s,
|1L+2s,
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|4L, 11L+3s
|4L, 11L+3s
|  -12
|  -12
|F fab, B la mibb
|F fa utb, B fab
|diminished seventh, diminished seventeeth
|diminished seventh, diminished seventeeth
|3L+3s, 10L+6s
|3L+3s, 10L+6s
|-
|-
|13
|13
|A re#, D sol re#
|A re#, D sol re ut#
|augmented second, augmented twelfth  
|augmented second, augmented twelfth  
|2L-1s, 9L+2s
|2L-1s, 9L+2s
|  -13
|  -13
|B la mibb, E labb
|B fab, E labb
|diminished tenth, diminished twentieth  
|diminished tenth, diminished twentieth  
|5L+4s, 12L+7s
|5L+4s, 12L+7s
|-
|-
|14
|14
|A la mi re#, D la sol#
|A la sol re mi#, D sol#
|augmented ninth, augmented nineteenth  
|augmented ninth, augmented nineteenth  
|7L+1s, 14L+4s
|7L+1s, 14L+4s
|  -14
|  -14
|B mibb, D la mibb
|B mibb, E la mi re sibb
|diminished third, diminished thirteenth  
|diminished third, diminished thirteenth  
|2s
|2s, 7L+5s
|-
|-
|15
|15
|E la mi re#, A la mi re#
|E la mi re#, A la sol re#
|augmented sixth, augmented sixteenth  
|augmented sixth, augmented sixteenth  
|5L, 12L 3s
|5L, 12L 3s
|  -15
|  -15
|E la mi rebb, A la mi rebb
|E la mi rebb, A la sol rebb
|diminished sixth, diminished sixteenth  
|diminished sixth, diminished sixteenth  
|2L+3s, 9L+6s
|2L+3s, 9L+6s
|-
|-
|16
|16
|B mi#, D la mi#
|B mi#, E la mi re si#
|augmented third, augmented thirteenth  
|augmented third, augmented thirteenth  
|3L-1s,
|3L-1s,
10L+2s
10L+2s
|  -16
|  -16
|A la mi rebb, D la solbb
|A sol la mi rebb, D la solbb
|diminished ninth, doubly diminished nineteenth  
|diminished ninth, doubly diminished nineteenth  
|4L+4s, 11L+7s
|4L+4s, 11L+7s
|}
|}
==And Scale tree==
==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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