User:Inthar/4L 3s: Difference between revisions
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{{breadcrumb|4L 3s}} | |||
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==Modal harmony== | |||
{{main|Smitonic}} | {{main|Smitonic}} | ||
The seven modes are, from brightest to darkest: | The seven modes are, from brightest to darkest: | ||
| Line 63: | Line 7: | ||
|- | |- | ||
| Nerevarine mode | | Nerevarine mode | ||
| <nowiki>6|0</nowiki> | |||
| LLSLSLS | | LLSLSLS | ||
|- | |- | ||
| Vivecan mode | | Vivecan mode | ||
| <nowiki>5|1</nowiki> | |||
| LSLLSLS | | LSLLSLS | ||
|- | |- | ||
| Lorkhanic mode | | Lorkhanic mode | ||
| <nowiki>4|2</nowiki> | |||
| LSLSLLS | | LSLSLLS | ||
|- | |- | ||
| Sothic mode | | Sothic mode | ||
| <nowiki>3|3</nowiki> | |||
| LSLSLSL | | LSLSLSL | ||
|- | |- | ||
| Kagrenacan mode | | Kagrenacan mode | ||
| <nowiki>2|4</nowiki> | |||
| SLLSLSL | | SLLSLSL | ||
|- | |- | ||
| Almalexian mode | | Almalexian mode | ||
| <nowiki>1|5</nowiki> | |||
| SLSLLSL | | SLSLLSL | ||
|- | |- | ||
| Dagothic mode | | Dagothic mode | ||
| <nowiki>0|6</nowiki> | |||
| SLSLSLL | | SLSLSLL | ||
|} | |} | ||
| Line 89: | Line 40: | ||
* 3 and 6 (equally): .59 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. | 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: | |||
{| class="wikitable right-2 right-3 right-4 sortable " | {| class="wikitable right-2 right-3 right-4 sortable " | ||
|- | |- | ||
! class="unsortable"|Degree | ! class="unsortable"|Degree | ||
! [[ | ! [[11edo]] value | ||
! class="unsortable"| Note name on J | ! class="unsortable"| Note name on J | ||
! #Gens up | ! #Gens up | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| unison | |||
| 0\ | | 0\11, 0.0 | ||
| J | | J | ||
| 0 | | 0 | ||
|- | |- | ||
| minor mos2nd | | minor mos2nd | ||
| | | 1\11, 109.1 | ||
| | | [[/cdn-cgi/l/email-protection|[email protected]]] | ||
| | |||
| +4 | | +4 | ||
|- | |- | ||
| major mos2nd | | major mos2nd | ||
| | | 2\11, 218.2 | ||
| K | | K | ||
| -3 | | -3 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| perf. mos3rd | | perf. mos3rd | ||
| | | 3\11, 327.3 | ||
| L | | L | ||
| +1 | | +1 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| aug. mos3rd | | aug. mos3rd | ||
| | | 4\11, 436.4 | ||
| L& | | L& | ||
| -6 | | -6 | ||
|- | |- | ||
| minor mos4th | | minor mos4th | ||
| | | 4\11, 436.4 | ||
| [[/cdn-cgi/l/email-protection|[email protected]]] | |||
| | |||
| | |||
| +5 | | +5 | ||
|- | |- | ||
| major mos4th | | major mos4th | ||
| | | 5\11, 545.5 | ||
| M | |||
| M | |||
| -2 | | -2 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| minor mos5th | | minor mos5th | ||
| | | 6\11, 656.6 | ||
| N | | N | ||
| +2 | | +2 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| major mos5th | | major mos5th | ||
| 11 | | 7\11, 763.6 | ||
| N& | |||
| N& | |||
| -5 | | -5 | ||
|- | |- | ||
| dim. mos6th | | dim. mos6th | ||
| | | 7\11, 763.6 | ||
| | | [[/cdn-cgi/l/email-protection|[email protected]]] | ||
| | |||
| +6 | | +6 | ||
|- | |- | ||
| perf. mos6th | | perf. mos6th | ||
| | | 8\11, 872.7 | ||
| O | | O | ||
| -1 | | -1 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| minor mos7th | | minor mos7th | ||
| | | 9\11, 981.8 | ||
| P | | P | ||
| +3 | | +3 | ||
|-bgcolor="#eaeaff" | |-bgcolor="#eaeaff" | ||
| major mos7th | | major mos7th | ||
| | | 10\11, 1090.9 | ||
| P& | |||
| P& | |||
| -4 | | -4 | ||
|} | |} | ||
* consonances: major 2nd, minor 3rd, sharp fourth, the minor seventh | |||
* dissonances: minor 2nd, major 3nd, flat fifth, minor 6th, major seventh | |||
=== Modal harmony === | |||
My favorite 11edo smitonic modes are 6|0 (major analogue), 5|1 (minor analogue) and 0|6 (Freygish analogue). | |||
[[Category:Smitonic]] | |||
[[Category:Method]] | |||
[[Category:Approaches to tuning systems]] | |||
Latest revision as of 22:16, 31 January 2025
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 | [email protected] | +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 | [email protected] | +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 | [email protected] | +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
Modal harmony
My favorite 11edo smitonic modes are 6|0 (major analogue), 5|1 (minor analogue) and 0|6 (Freygish analogue).