Xenharmonic Wiki

User:Inthar/4L 3s: Difference between revisions

← Older edit
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,636 edits
Lériendil (talk | contribs)
8,033 edits
m breadcrumb
 
(14 intermediate revisions by 5 users not shown)
Line 1: Line 1:
{{breadcrumb|4L 3s}}
==Modal harmony==
==Modal harmony==
{{main|Smitonic}}
{{main|Smitonic}}
Line 5: 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 49: Line 58:
| minor mos2nd
| minor mos2nd
| 1\11, 109.1
| 1\11, 109.1
| K@
| [[/cdn-cgi/l/email-protection|[email protected]]]
| +4
| +4
|-
|-
Line 69: Line 78:
| minor mos4th
| minor mos4th
| 4\11, 436.4
| 4\11, 436.4
| M@
| [[/cdn-cgi/l/email-protection|[email protected]]]
| +5
| +5
|-
|-
Line 89: Line 98:
| dim. mos6th
| dim. mos6th
| 7\11, 763.6
| 7\11, 763.6
| O@
| [[/cdn-cgi/l/email-protection|[email protected]]]
| +6
| +6
|-
|-
Line 110: Line 119:
* consonances: major 2nd, minor 3rd, sharp fourth, the minor seventh
* consonances: major 2nd, minor 3rd, sharp fourth, the minor seventh
* dissonances: minor 2nd, major 3nd, flat fifth, minor 6th, major seventh
* dissonances: minor 2nd, major 3nd, flat fifth, minor 6th, major seventh
 
=== Modal harmony ===
== 18edo smitonic ==
My favorite 11edo smitonic modes are 6|0 (major analogue), 5|1 (minor analogue) and 0|6 (Freygish analogue).
{| class="wikitable right-2 right-3 right-4 sortable "
|-
! class="unsortable"|Degree
! [[18edo]] value
! class="unsortable"| Note name on J
! #Gens up
|-bgcolor="#eaeaff"
| | unison
| 0\18, 0.0
| J
| 0
|-bgcolor="#eaeaff"
| 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
|-bgcolor="#eaeaff"
| dim. mos3rd
| 4\18, 266.7
| L@
| +8
|-bgcolor="#eaeaff"
| perf. mos3rd
| 5\18, 333.3
| L
| +1
|-bgcolor="#eaeaff"
| aug. mos3rd
| 6\18, 400.0
| L&
| -6
|-bgcolor="#eaeaff"
| 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
|-bgcolor="#eaeaff"
| dim. mos5th
| 9\18, 600.0
| N@
| +9
|-bgcolor="#eaeaff"
| minor mos5th
| 10\18, 666.7
| N
| +2
|-bgcolor="#eaeaff"
| major mos5th
| 11\18, 733.3
| N&
| -5
|-bgcolor="#eaeaff"
| 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
|-bgcolor="#eaeaff"
| dim. mos7th
| 14\18, 933.3
| P@
| +10
|-bgcolor="#eaeaff"
| minor mos7th
| 15\18, 1000.0
| P
| +3
|-bgcolor="#eaeaff"
| major mos7th
| 16\18, 1066.7
| P&
| -4
|-bgcolor="#eaeaff"
| aug. mos7th
| 17\18, 1133.3
| P&
| -11
|-
| dim. mosoctave
| 17\18, 1133.3
| J@
| +7
|}
===Modal harmony===
I find 7|0, 6|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: [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)].
 
=== 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
 
[[Category:Smitonic]]
[[Category:Smitonic]]
[[Category:Method]]
[[Category:Approaches to tuning systems]]
Retrieved from "https://en.xen.wiki/w/User:Inthar/4L_3s"