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

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{{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===
MODMOSes and chroma modification become more important. Use MODMOSes with SS = diminished mos3rd = 266.67¢. For example, rotations of LLSSLLS, LLLSSLS, or LLLSLSS, or turning an SL to dA or an LS to an Ad (for example, dASLSLL from SLSLSLL)
=== Chords ===
The 533c 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
* 28:30:32:34:36:37:38:41:43:44:46:50:52:56 Septimal Smitonic Modal Union
* 38:43:46:52:56:63:70:76 Novemdecimal Lorkhanic
* 38:41:43:46:48:50:52:56:58:60:63:68:70:76 Novemdecimal Smitonic Modal Union
 
[[Category:Smitonic]]
[[Category:Smitonic]]
[[Category:Method]]
[[Category:Approaches to tuning systems]]

Latest revision as of 22:16, 31 January 2025

< 4L 3s

Modal harmony

Main article: Smitonic

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).

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