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| | {{breadcrumb|4L 3s}} |
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| ==Modal harmony== | | ==Modal harmony== |
| {{main|Smitonic}} | | {{main|Smitonic}} |
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| | minor mos2nd | | | minor mos2nd |
| | 1\11, 109.1 | | | 1\11, 109.1 |
| | K@ | | | [[/cdn-cgi/l/email-protection|[email protected]]] |
| | +4 | | | +4 |
| |- | | |- |
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| | minor mos4th | | | minor mos4th |
| | 4\11, 436.4 | | | 4\11, 436.4 |
| | M@ | | | [[/cdn-cgi/l/email-protection|[email protected]]] |
| | +5 | | | +5 |
| |- | | |- |
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| | dim. mos6th | | | dim. mos6th |
| | 7\11, 763.6 | | | 7\11, 763.6 |
| | O@ | | | [[/cdn-cgi/l/email-protection|[email protected]]] |
| | +6 | | | +6 |
| |- | | |- |
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| === Modal harmony === | | === Modal harmony === |
| My favorite 11edo smitonic modes are 6|0 (major analogue), 5|1 (minor analogue) and 0|6 (Freygish analogue). | | My favorite 11edo smitonic modes are 6|0 (major analogue), 5|1 (minor analogue) and 0|6 (Freygish analogue). |
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| == 18edo smitonic ==
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| {| class="wikitable right-2 right-3 right-4 sortable "
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| |-
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| ! class="unsortable"|Degree
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| ! [[18edo]] value
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| ! class="unsortable"| Note name on J
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| ! #Gens up
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| |-bgcolor="#eaeaff"
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| | | unison
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| | 0\18, 0.0
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| | J
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| | 0
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| |-bgcolor="#eaeaff"
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| | chroma
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| | 1\18, 66.7
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| | J&
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| | -7
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| |-
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| | dim. mos2nd
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| | 1\18, 66.7
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| | K@@
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| | +11
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| |-
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| | minor mos2nd
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| | 2\18, 133.3
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| | K@
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| | +4
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| |-
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| | major mos2nd
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| | 3\18, 200.0
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| | K
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| | -3
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| |-
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| | aug. mos2nd
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| | 4\18, 266.7
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| | K&
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| | -10
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| |-bgcolor="#eaeaff"
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| | dim. mos3rd
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| | 4\18, 266.7
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| | L@
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| | +8
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| |-bgcolor="#eaeaff"
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| | perf. mos3rd
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| | 5\18, 333.3
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| | L
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| | +1
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| |-bgcolor="#eaeaff"
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| | aug. mos3rd
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| | 6\18, 400.0
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| | L&
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| | -6
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| |-bgcolor="#eaeaff"
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| | doubly aug. mos3rd
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| | 7\18, 466.7
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| | L&&
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| | -13
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| |-
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| | dim. mos4th
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| | 6\18, 400.0
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| | M@@
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| | +12
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| |-
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| | minor mos4th
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| | 7\18, 466.7
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| | M@
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| | +5
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| |-
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| | major mos4th
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| | 8\18, 533.3
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| | M
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| | -2
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| |-
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| | aug. mos4th
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| | 9\18, 600.0
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| | M&
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| | -9
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| |-bgcolor="#eaeaff"
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| | dim. mos5th
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| | 9\18, 600.0
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| | N@
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| | +9
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| |-bgcolor="#eaeaff"
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| | minor mos5th
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| | 10\18, 666.7
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| | N
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| | +2
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| |-bgcolor="#eaeaff"
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| | major mos5th
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| | 11\18, 733.3
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| | N&
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| | -5
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| |-bgcolor="#eaeaff"
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| | aug. mos5th
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| | 12\18, 800.0
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| | N&&
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| | -12
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| |-
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| | doubly dim. mos6th
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| | 11\18, 733.3
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| | O@@
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| | +13
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| |-
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| | dim. mos6th
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| | 12\18, 800.0
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| | O@
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| | +6
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| |-
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| | perf. mos6th
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| | 13\18, 866.7
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| | O
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| | -1
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| |-
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| | aug. mos6th
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| | 14\18, 933.3
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| | O&
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| | -8
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| |-bgcolor="#eaeaff"
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| | dim. mos7th
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| | 14\18, 933.3
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| | P@
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| | +10
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| |-bgcolor="#eaeaff"
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| | minor mos7th
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| | 15\18, 1000.0
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| | P
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| | +3
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| |-bgcolor="#eaeaff"
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| | major mos7th
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| | 16\18, 1066.7
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| | P&
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| | -4
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| |-bgcolor="#eaeaff"
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| | aug. mos7th
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| | 17\18, 1133.3
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| | P&
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| | -11
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| |-
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| | dim. mosoctave
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| | 17\18, 1133.3
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| | J@
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| | +7
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| |}
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| ===Modal harmony===
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| I find 6|0 and 5|1 to be the most stable modes in 18edo. (However, the modmos 0|6 &3 &4 &5 is more desirable than the native 0|6 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.
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| See also: [https://xenpaper.com/#%7Br358hz%7D(osc%3Asawtooth2)%0A%7B18edo%7D%0A%5B%600_3_6_%608_%6011_13_%6016%5D-------...%0A%5B%600_3_%605_%608_%6011_13_%6016%5D-------...%0A%5B%600_3_%605_%608_10_%6013_%6016%5D-------...%0A%5B%600_3_%605_%608_10_%6013_%6015%5D-------...%0A%5B%600_2_%605_%608_10_%6013_%6015%5D-------...%0A%5B%600_2_5_%607_%6010_%6013_15%5D-------...%0A%5B%600_2_5_%607_%6010_%6012_15%5D-------...%0A%0A%0A Mother chords for smitonic modes (xenpaper link)].
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| === Chords ===
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| 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.
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| ==== no fifth ====
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| Given in 18edo steps
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| *0 5 8 13 16
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| *0 3 16
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| *0 3 8
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| *0 3 8 16
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| *0 3 8 13
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| *0 3 8 13 16
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| *0 5 8
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| *0 5 8 13
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| *0 5 8 16
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| *0 5 8 13 16
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| *0 5 8 13 16 21
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| *0 5 8 13 16 21 28
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| *0 5 13 16 26
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| *0 5 14 17 26
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|
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| ==== flat fifth ====
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| *0 10 26
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| *0 5 10 15
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| *0 5 10 15 26: stabilized 0 5 10 15
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|
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| ==== sharp fifth ====
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|
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| == Nejis ==
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| Inthar-approved smitonic nejis.
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| * 22:25:28:30:34:(73):41:44 Undecimal Nerevarine
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| * 28:32:34:38:41:46:52:56 Septimal Lorkhanic
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| * 28:32:34:38:41:46:50:56 Septimal Sothic
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| * 28:30:34:38:41:46:50:56 Septimal Kagrenacan
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| * 28:30:34:37:41:46:50:56 Septimal Almalexian
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| * 28:30:34:37:41:44:50:56 Septimal Dagothic
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| === Non-puristic smitonic nejis ===
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| * 14:16:18:19:21:23:26:28 Septimal Nerevarine with 3/2 Fifth
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| * 14:16:17:19:21:23:26:28 Septimal Lorkhanic with 3/2 Fifth
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| * 14:16:17:19:21:23:25:28 Septimal Sothic with 3/2 Fifth
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| * 14:15:17:19:21:23:25:28 Septimal Kagrenacan with 3/2 Fifth
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| * 14:15:17:19:21:22:25:28 Septimal Kagrenacan @6 with 3/2 Fifth
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| * 28:30:34:37:42:46:50:56 Septimal Almalexian with 3/2 Fifth
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| * 28:30:34:37:42:44:50:56 Septimal Dagothic with 3/2 Fifth
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| [[Category:Smitonic]] | | [[Category:Smitonic]] |
| | [[Category:Method]] |
| | [[Category:Approaches to tuning systems]] |