User:Inthar/4L 3s
Modal harmony
The seven modes are, from brightest to darkest:
| Nerevarine mode | 6|0 | LLSLSLS |
| Vivecan mode | 5|1 | LSLLSLS |
| Lorkhanic mode | 4|2 | LSLSLLS |
| Sothic mode | 3|3 | LSLSLSL |
| Kagrenacan mode | 2|4 | SLLSLSL |
| Almalexian mode | 1|5 | SLSLLSL |
| Dagothic mode | 0|6 | SLSLSLL |
Modally, the highest to lowest entropy scale degrees (unison = 1) are:
- 2 and 7 (equally): .99 bits
- 4 and 5 (equally): .86 bits
- 3 and 6 (equally): .59 bits
If a scale degree is high entropy it tends to be the most informative on average; the modes that have this interval as major and minor respectively are roughly a 50-50 split. This tells us that unlike in the diatonic scale, thirds and sixths are the least informative in distinguishing smitonic modes. On the other hand, seconds, fourths and sevenths are highly informative.
11edo smitonic
The intervals of the symmetric LsLsLsL mode (harmonics in bold): Sortable table of major and minor intervals in hypohard smitonic tunings:
| Degree | 11edo value | Note name on J | #Gens up |
|---|---|---|---|
| unison | 0\11, 0.0 | J | 0 |
| minor mos2nd | 1\11, 109.1 | K@ | +4 |
| major mos2nd | 2\11, 218.2 | K | -3 |
| perf. mos3rd | 3\11, 327.3 | L | +1 |
| aug. mos3rd | 4\11, 436.4 | L& | -6 |
| minor mos4th | 4\11, 436.4 | M@ | +5 |
| major mos4th | 5\11, 545.5 | M | -2 |
| minor mos5th | 6\11, 656.6 | N | +2 |
| major mos5th | 7\11, 763.6 | N& | -5 |
| dim. mos6th | 7\11, 763.6 | O@ | +6 |
| perf. mos6th | 8\11, 872.7 | O | -1 |
| minor mos7th | 9\11, 981.8 | P | +3 |
| major mos7th | 10\11, 1090.9 | P& | -4 |
- consonances: major 2nd, minor 3rd, sharp fourth, the minor seventh
- dissonances: minor 2nd, major 3nd, flat fifth, minor 6th, major seventh
18edo smitonic
| Degree | 18edo value | Note name on J | #Gens up |
|---|---|---|---|
| unison | 0\18, 0.0 | J | 0 |
| chroma | 1\18, 66.7 | J& | -7 |
| dim. mos2nd | 1\18, 66.7 | K@@ | +11 |
| minor mos2nd | 2\18, 133.3 | K@ | +4 |
| major mos2nd | 3\18, 200.0 | K | -3 |
| aug. mos2nd | 4\18, 266.7 | K& | -10 |
| dim. mos3rd | 4\18, 266.7 | L@ | +8 |
| perf. mos3rd | 5\18, 333.3 | L | +1 |
| aug. mos3rd | 6\18, 400.0 | L& | -6 |
| doubly aug. mos3rd | 7\18, 466.7 | L&& | -13 |
| dim. mos4th | 6\18, 400.0 | M@@ | +12 |
| minor mos4th | 7\18, 466.7 | M@ | +5 |
| major mos4th | 8\18, 533.3 | M | -2 |
| aug. mos4th | 9\18, 600.0 | M& | -9 |
| dim. mos5th | 9\18, 600.0 | N@ | +9 |
| minor mos5th | 10\18, 666.7 | N | +2 |
| major mos5th | 11\18, 733.3 | N& | -5 |
| aug. mos5th | 12\18, 800.0 | N&& | -12 |
| doubly dim. mos6th | 11\18, 733.3 | O@@ | +13 |
| dim. mos6th | 12\18, 800.0 | O@ | +6 |
| perf. mos6th | 13\18, 866.7 | O | -1 |
| aug. mos6th | 14\18, 933.3 | O& | -8 |
| dim. mos7th | 14\18, 933.3 | P@ | +10 |
| minor mos7th | 15\18, 1000.0 | P | +3 |
| major mos7th | 16\18, 1066.7 | P& | -4 |
| aug. mos7th | 17\18, 1133.3 | P& | -11 |
| dim. mosoctave | 17\18, 1133.3 | J@ | +7 |
Modal harmony
I find 6|0, 5|1 and 0|6 to be the most stable modes. (However, the modmos 0|6 &3 &4 &5 is a more desirable Freygish than the native Dagothic mode.) In 18edo, sharpening the flat fifth to a sharp fifth in the smitonic modes 4|2, 3|3, and 2|4 is desirable. The flat fifth should be used as a functional degree to modulate to (so you get the original tonic as a superfourth on it), rather than as a chord note. The leading tone could also be sharpened too, particularly in the 7|0 and 6|1 modes.
See also: Mother chords for smitonic modes (xenpaper link).
Chords
The 533c (8\18) superfourth is perhaps the most important non-LCJI consonance in 18edo smitonic. Not only can it be used as a basic consonance in chords such as 0c-200c-533c, it also helps stabilize more unstable chords such as those with sharp and flat fifths especially when voiced as 1733c. Movements down superfourths (or supraminor thirds) are also convincing.
no fifth
Given in 18edo steps
- 0 5 8 13 16
- 0 3 16
- 0 3 8
- 0 3 8 16
- 0 3 8 13
- 0 3 8 13 16
- 0 5 8
- 0 5 8 13
- 0 5 8 16
- 0 5 8 13 16
- 0 5 8 13 16 21
- 0 5 8 13 16 21 28
- 0 5 13 16 26
- 0 5 14 17 26
flat fifth
- 0 10 26
- 0 5 10 15
- 0 5 10 15 26: stabilized 0 5 10 15
sharp fifth
Nejis
Inthar-approved smitonic nejis.
- 28:32:34:38:41:46:52:56 Septimal Lorkhanic
- 28:32:34:38:41:46:50:56 Septimal Sothic
- 28:30:34:38:41:46:50:56 Septimal Kagrenacan
- 28:30:34:37:41:46:50:56 Septimal Almalexian
- 28:30:34:37:41:44:50:56 Septimal Dagothic
Non-puristic smitonic nejis
- 14:16:18:19:21:23:26:28 Septimal Nerevarine with 3/2 Fifth
- 14:16:17:19:21:23:26:28 Septimal Lorkhanic with 3/2 Fifth
- 14:16:17:19:21:23:25:28 Septimal Sothic with 3/2 Fifth
- 14:15:17:19:21:23:25:28 Septimal Kagrenacan with 3/2 Fifth
- 14:15:17:19:21:22:25:28 Septimal Kagrenacan @6 with 3/2 Fifth
- 28:30:34:37:42:46:50:56 Septimal Almalexian with 3/2 Fifth
- 28:30:34:37:42:44:50:56 Septimal Dagothic with 3/2 Fifth