7L 3s: Difference between revisions
m →Scale tree: reimplement the correction |
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Note: In TAMNAMS, a k-step interval class in dicotonic may be called a "k-step", "k-mosstep", or "k-dicostep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses. | Note: In TAMNAMS, a k-step interval class in dicotonic may be called a "k-step", "k-mosstep", or "k-dicostep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses. | ||
{| class="wikitable" | |||
!# generators up | |||
!Notation (1/1 = 0) | |||
! name | |||
!In L's and s's | |||
!# generators up | |||
! Notation of 2/1 inverse | |||
! name | |||
! In L's and s's | |||
|- | |||
| colspan="8" style="text-align:center" |The 10-note MOS has the following intervals (from some root): | |||
|- | |||
| 0 | |||
|0 | |||
|perfect unison | |||
|0 | |||
|0 | |||
|0 | |||
|perfect 10-step | |||
|7L+3s | |||
|- | |||
| 1 | |||
| 7 | |||
|perfect 7-step | |||
|5L+2s | |||
| -1 | |||
|3 | |||
|perfect 3-step | |||
|2L+1s | |||
|- | |||
|2 | |||
|4 | |||
|major 4-step | |||
|3L+1s | |||
| -2 | |||
|6 | |||
|minor 6-step | |||
|4L+2s | |||
|- | |||
|3 | |||
|1 | |||
|major (1-)step | |||
| 1L | |||
| -3 | |||
|9v | |||
| minor 9-step | |||
|6L+3s | |||
|- | |||
|4 | |||
|8 | |||
|major 8-step | |||
| 6L+2s | |||
| -4 | |||
|2v | |||
|minor 2-step | |||
|1L+1s | |||
|- | |||
|5 | |||
|5 | |||
|major 5-step | |||
|4L+1s | |||
| -5 | |||
|5v | |||
| minor 5-step | |||
| 3L+2s | |||
|- | |||
|6 | |||
|2 | |||
| major 2-step | |||
|2L | |||
| -6 | |||
|8v | |||
|minor 8-step | |||
|5L+3s | |||
|- | |||
|7 | |||
|9 | |||
|major 9-step | |||
| 7L+2s | |||
| -7 | |||
|1v | |||
| minor (1-)step | |||
|1s | |||
|- | |||
|8 | |||
|6^ | |||
|major 6-step | |||
| 5L+1s | |||
| -8 | |||
|4v | |||
|minor 4-step | |||
| 2L+2s | |||
|- | |||
|9 | |||
|3^ | |||
| augmented 3-step | |||
|3L | |||
| -9 | |||
|7v | |||
|diminished 7-step | |||
|4L+3s | |||
|- | |||
|10 | |||
|0^ | |||
| augmented unison | |||
|1L-1s | |||
| -10 | |||
|0v | |||
|diminished 10-step | |||
|6L+4s | |||
|- | |||
|11 | |||
|7^ | |||
| augmented 7-step | |||
|6L+1s | |||
| -11 | |||
|3v | |||
|diminished 3-step | |||
|1L+2s | |||
|- | |||
| colspan="8" style="text-align:center" |The chromatic 17-note MOS (either [[7L 10s]], [[10L 7s]], or [[17edo]]) also has the following intervals (from some root): | |||
|- | |||
|12 | |||
|4^ | |||
| augmented 4-step | |||
|4L | |||
| -12 | |||
| 6v | |||
|diminished 6-step | |||
|3L+3s | |||
|- | |||
|13 | |||
|1^ | |||
|augmented (1-)step | |||
|2L-1s | |||
| -13 | |||
| 9w | |||
|diminished 9-step | |||
|5L+4s | |||
|- | |||
|14 | |||
|8^ | |||
|augmented 8-step | |||
|8L+1s | |||
| -14 | |||
|2w | |||
|diminished 2-step | |||
|2s | |||
|- | |||
|15 | |||
|5^ | |||
|augmented 5-step | |||
| 5L | |||
| -15 | |||
|5w | |||
| diminished 5-step | |||
|2L+3s | |||
|- | |||
|16 | |||
|2^ | |||
| augmented 2-step | |||
|3L-1s | |||
| -16 | |||
|8w | |||
|diminished 8-step | |||
|4L+4s | |||
|} | |||
== 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 edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 – five degrees of [[17edo]]: | 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 edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 – five degrees of [[17edo]]: | ||