User:Inthar/4L 3s: Difference between revisions
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! [[18edo]] value | ! [[18edo]] value | ||
! class="unsortable"| Note name on J | ! class="unsortable"| Note name on J | ||
! #Gens up | ! #Gens up | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 0\18, 0.0 | | 0\18, 0.0 | ||
| J | | J | ||
| 0 | | 0 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 1\18, 66.7 | | 1\18, 66.7 | ||
| J& | | J& | ||
| -7 | | -7 | ||
|- | |- | ||
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| 1\18, 66.7 | | 1\18, 66.7 | ||
| K@@ | | K@@ | ||
| +11 | | +11 | ||
|- | |- | ||
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| 2\18, 133.3 | | 2\18, 133.3 | ||
| K@ | | K@ | ||
| +4 | | +4 | ||
|- | |- | ||
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| 3\18, 200.0 | | 3\18, 200.0 | ||
| K | | K | ||
| -3 | | -3 | ||
|- | |- | ||
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| 4\18, 266.7 | | 4\18, 266.7 | ||
| K& | | K& | ||
| -10 | | -10 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 4\18, 266.7 | | 4\18, 266.7 | ||
| L@ | | L@ | ||
| +8 | | +8 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 5\18, 333.3 | | 5\18, 333.3 | ||
| L | | L | ||
| +1 | | +1 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 6\18, 400.0 | | 6\18, 400.0 | ||
| L& | | L& | ||
| -6 | | -6 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 7\18, 466.7 | | 7\18, 466.7 | ||
| L&& | | L&& | ||
| -13 | | -13 | ||
|- | |- | ||
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| 6\18, 400.0 | | 6\18, 400.0 | ||
| M@@ | | M@@ | ||
| +12 | | +12 | ||
|- | |- | ||
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| 7\18, 466.7 | | 7\18, 466.7 | ||
| M@ | | M@ | ||
| +5 | | +5 | ||
|- | |- | ||
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| 8\18, 533.3 | | 8\18, 533.3 | ||
| M | | M | ||
| -2 | | -2 | ||
|- | |- | ||
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| 9\18, 600.0 | | 9\18, 600.0 | ||
| M& | | M& | ||
| -9 | | -9 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 9\18, 600.0 | | 9\18, 600.0 | ||
| N@ | | N@ | ||
| +9 | | +9 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 10\18, 666.7 | | 10\18, 666.7 | ||
| N | | N | ||
| +2 | | +2 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 11\18, 733.3 | | 11\18, 733.3 | ||
| N& | | N& | ||
| -5 | | -5 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 12\18, 800.0 | | 12\18, 800.0 | ||
| N&& | | N&& | ||
| -12 | | -12 | ||
|- | |- | ||
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| 11\18, 733.3 | | 11\18, 733.3 | ||
| O@@ | | O@@ | ||
| +13 | | +13 | ||
|- | |- | ||
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| 12\18, 800.0 | | 12\18, 800.0 | ||
| O@ | | O@ | ||
| +6 | | +6 | ||
|- | |- | ||
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| 13\18, 866.7 | | 13\18, 866.7 | ||
| O | | O | ||
| -1 | | -1 | ||
|- | |- | ||
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| 14\18, 933.3 | | 14\18, 933.3 | ||
| O& | | O& | ||
| -8 | | -8 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 14\18, 933.3 | | 14\18, 933.3 | ||
| P@ | | P@ | ||
| +10 | | +10 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 15\18, 1000.0 | | 15\18, 1000.0 | ||
| P | | P | ||
| +3 | | +3 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 16\18, 1066.7 | | 16\18, 1066.7 | ||
| P& | | P& | ||
| -4 | | -4 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
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| 17\18, 1133.3 | | 17\18, 1133.3 | ||
| P& | | P& | ||
| -11 | | -11 | ||
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| 17\18, 1133.3 | | 17\18, 1133.3 | ||
| J@ | | J@ | ||
| +7 | | +7 | ||
|} | |} | ||
Revision as of 00:59, 30 April 2021
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 |
Assuming the symmetric 2121212 mode, the 1-4-7 chord is:
- 8:11:14 on degrees 1 and 6
- 8:11:15 on degrees 3, 5, and 7
- something complex on degrees 2 and 4
Modal harmony
The seven modes are, from brightest to darkest:
| Nerevarine mode | LLSLSLS |
| Vivecan mode | LSLLSLS |
| Lorkhanic mode | LSLSLLS |
| Sothic mode | LSLSLSL |
| Kagrenacan mode | SLLSLSL |
| Almalexian mode | SLSLLSL |
| Dagothic mode | 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.
In orgone, these scale degrees appear in the most consonant triads and tetrads of 11edo orgone, namely 8:9:11:15, 8:9:11:14 and 16:17:22:28. Those chords are therefore crucial for Orgone[7] modal harmony.
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
MODMOSes and chroma modification become more important. Use MODMOSes with SS = diminished mos3rd = 266.67¢. For example, rotations of LLLSLSS.
or 5L 1M 1S: LLMLLLS or LLSLLLM
Treat it as neutralized mavila antidiatonic?