4L 3s: Difference between revisions

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Line 60: Line 60:
| 2
| 2
| N
| N
| small smififth (aka minor fifth)
| minor smififth (aka minor fifth)
| -2
| -2
| M
| M
| large smifourth (aka major fourth)
| major smifourth (aka major fourth)
|-
|-
| 3
| 3
| P
| P
| small smiseventh
| minor smiseventh
| -3
| -3
| K
| K
| large smisecond
| major smisecond
|-
|-
| 4
| 4
| K@
| K@
| small smisecond
| minor smisecond
| -4
| -4
| Q&
| Q&
| large smiseventh
| major smiseventh
|-
|-
| 5
| 5
| M@
| M@
| small smifourth (aka minor fourth)
| minor smifourth (aka minor fourth)
| -5
| -5
| N&
| N&
| large smififth (aka major fifth)
| major smififth (aka major fifth)
|-
|-
| 6
| 6
Line 134: Line 134:


Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].
Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].
* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect smisixth) and falling fifths (666.7c, a large smififth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect smisixth) and falling fifths (666.7c, a major smififth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* [[25edo]] can be used to make the augmented smithird a good [[5/4]] (384¢).
* [[25edo]] can be used to make the augmented smithird a good [[5/4]] (384¢).


Line 201: Line 201:
| +11
| +11
|-
|-
| small smi2nd
| minor smi2nd
| 2\18, 133.3
| 2\18, 133.3
| 3\25, 144.0
| 3\25, 144.0
Line 209: Line 209:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 3\18, 200.0
| 3\18, 200.0
| 4\25, 192.0
| 4\25, 192.0
Line 265: Line 265:
| +12
| +12
|-
|-
| small smi4th
| minor smi4th
| 7\18, 466.7
| 7\18, 466.7
| 10\25, 480.0
| 10\25, 480.0
Line 273: Line 273:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 8\18, 533.3  
| 8\18, 533.3  
| 11\25, 528.0
| 11\25, 528.0
Line 297: Line 297:
| +9
| +9
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 10\18, 666.7
| 10\18, 666.7
| 14\25, 672.0
| 14\25, 672.0
Line 305: Line 305:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 11\18, 733.3
| 11\18, 733.3
| 15\25, 720.0
| 15\25, 720.0
Line 361: Line 361:
| +10
| +10
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 15\18, 1000.0
| 15\18, 1000.0
| 21\25, 1008.0
| 21\25, 1008.0
Line 369: Line 369:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 16\18, 1066.7
| 16\18, 1066.7
| 22\25, 1056.0
| 22\25, 1056.0
Line 437: Line 437:
| 0
| 0
|-
|-
| small smi2nd
| minor smi2nd
| 3\29, 124.1
| 3\29, 124.1
| K@
| K@
Line 443: Line 443:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 5\29, 206.9
| 5\29, 206.9
| K
| K
Line 461: Line 461:
| -6
| -6
|-
|-
| small smi4th
| minor smi4th
| 11\29, 455.2
| 11\29, 455.2
| M@
| M@
Line 467: Line 467:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 13\29, 537.9
| 13\29, 537.9
| M
| M
Line 473: Line 473:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 16\29, 662.1
| 16\29, 662.1
| N
| N
Line 479: Line 479:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 18\26, 744.8
| 18\26, 744.8
| N&
| N&
Line 497: Line 497:
| -1
| -1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 24\29, 993.1
| 24\29, 993.1
| P
| P
Line 503: Line 503:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 26\28, 1075.9
| 26\28, 1075.9
| P&
| P&
Line 511: Line 511:


=== Hypohard ===
=== Hypohard ===
[[Hypohard]] tunings have [[step ratio]]s between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate [[8/7]], and the large smifourth (2 large steps + 1 small step) tends to approximate [[11/8]]; [[26edo]] is stellar in both of these approximations. This set of JI approximations is called [[orgone]] temperament.
[[Hypohard]] tunings have [[step ratio]]s between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate [[8/7]], and the major smifourth (2 large steps + 1 small step) tends to approximate [[11/8]]; [[26edo]] is stellar in both of these approximations. This set of JI approximations is called [[orgone]] temperament.


Hypohard smitonic edos include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].
Hypohard smitonic edos include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].
Line 561: Line 561:
| 0
| 0
|-
|-
| small smi2nd
| minor smi2nd
| 1\11, 109.1
| 1\11, 109.1
| 1\15, 80.0
| 1\15, 80.0
Line 569: Line 569:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 2\11, 218.2
| 2\11, 218.2
| 3\15, 240.0
| 3\15, 240.0
Line 593: Line 593:
| -6
| -6
|-
|-
| small smi4th
| minor smi4th
| 4\11, 436.4
| 4\11, 436.4
| 5\15, 400.0
| 5\15, 400.0
Line 601: Line 601:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 5\11, 545.5
| 5\11, 545.5
| 7\15, 560.0
| 7\15, 560.0
Line 609: Line 609:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 6\11, 656.6
| 6\11, 656.6
| 8\15, 640.0
| 8\15, 640.0
Line 617: Line 617:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 7\11, 763.6
| 7\11, 763.6
| 10\15, 800.0
| 10\15, 800.0
Line 641: Line 641:
| -1
| -1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 9\11, 981.8
| 9\11, 981.8
| 12\15, 960.0
| 12\15, 960.0
Line 649: Line 649:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 10\11, 1090.9
| 10\11, 1090.9
| 14\15, 1120.0
| 14\15, 1120.0
Line 711: Line 711:
| 0
| 0
|-
|-
| small smi2nd
| minor smi2nd
| 1\19, 63.2
| 1\19, 63.2
| 2\34, 70.6
| 2\34, 70.6
Line 719: Line 719:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 4\19, 252.6
| 4\19, 252.6
| 7\34, 247.1
| 7\34, 247.1
Line 743: Line 743:
| -6
| -6
|-
|-
| small smi4th
| minor smi4th
| 6\19, 378.9
| 6\19, 378.9
| 11\34, 388.2
| 11\34, 388.2
Line 751: Line 751:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 9\19, 568.4
| 9\19, 568.4
| 16\34, 564.7
| 16\34, 564.7
Line 759: Line 759:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 10\19, 631.6
| 10\19, 631.6
| 18\34, 635.3
| 18\34, 635.3
Line 767: Line 767:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 16\19, 821.1
| 16\19, 821.1
| 23\34, 811.8
| 23\34, 811.8
Line 791: Line 791:
| -1
| -1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 15\19, 947.4
| 15\19, 947.4
| 27\34, 952.9
| 27\34, 952.9
Line 799: Line 799:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 18\19, 1136.8
| 18\19, 1136.8
| 32\34, 1129.4
| 32\34, 1129.4

Revision as of 19:51, 17 April 2021

↖ 3L 2s ↑ 4L 2s 5L 2s ↗
← 3L 3s 4L 3s 5L 3s →
↙ 3L 4s ↓ 4L 4s 5L 4s ↘
Scale structure
Step pattern LLsLsLs
sLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\7 to 3\4 (857.1 ¢ to 900.0 ¢)
Dark 1\4 to 2\7 (300.0 ¢ to 342.9 ¢)
TAMNAMS information
Name smitonic
Prefix smi-
Abbrev. smi
Related MOS scales
Parent 3L 1s
Sister 3L 4s
Daughters 7L 4s, 4L 7s
Neutralized 1L 6s
2-Flought 11L 3s, 4L 10s
Equal tunings
Equalized (L:s = 1:1) 5\7 (857.1 ¢)
Supersoft (L:s = 4:3) 18\25 (864.0 ¢)
Soft (L:s = 3:2) 13\18 (866.7 ¢)
Semisoft (L:s = 5:3) 21\29 (869.0 ¢)
Basic (L:s = 2:1) 8\11 (872.7 ¢)
Semihard (L:s = 5:2) 19\26 (876.9 ¢)
Hard (L:s = 3:1) 11\15 (880.0 ¢)
Superhard (L:s = 4:1) 14\19 (884.2 ¢)
Collapsed (L:s = 1:0) 3\4 (900.0 ¢)
View • Talk • Edit

4L 3s refers to an MOS scale with four large steps and three small steps, one mode of which is LLsLsLs. It is generated by any interval between 1\4edo (one degree of 4edo, or 300¢) and 2\7edo (two degrees of 7edo, or approx. 342.857¢).

4L 3s can be thought of as a warped diatonic scale, because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).

Names

The TAMNAMS MOS naming system (used in this article) uses the name smitonic smy-TON-ik /smaɪˈtɒnɪk/ for this pattern. The name is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.

Notation

The notation used in this article is LsLsLsL = JKLMNOPJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)

Thus the 11edo gamut is as follows:

J J&/K@ K L L&/M@ M N N&/O@ O P P&/J@ J

Intervals

Generators Notation (1/1 = J) Interval category name Generators Notation of 2/1 inverse Interval category name
The 7-note MOS has the following intervals (from some root):
0 J perfect unison 0 J octave
1 L perfect smithird -1 O perfect smisixth
2 N minor smififth (aka minor fifth) -2 M major smifourth (aka major fourth)
3 P minor smiseventh -3 K major smisecond
4 K@ minor smisecond -4 Q& major smiseventh
5 M@ minor smifourth (aka minor fourth) -5 N& major smififth (aka major fifth)
6 O@ diminished smisixth -6 L& augmented smithird
The chromatic 11-note MOS (either 7L 4s, 4L 7s, or 11edo) also has the following intervals (from some root):
7 J@ diminished smioctave -7 J& augmented smiunison; smichroma; smicomma (in parasoft smitonic contexts)
8 L@ diminished smithird -8 O& augmented smisixth
9 N@ diminished smififth -9 M& augmented smifourth
10 P@ diminished smiseventh -10 K& augmented smisecond

Tuning ranges

Parasoft

Parasoft smitonic tunings have step ratios between 4/3 and 3/2, which implies a generator sharper than 5\18 = 333.3¢ and flatter than 7\25 = 336.0¢.

Parasoft smitonic can be considered "meantone smitonic". This is because these tunings share the following features with meantone diatonic tunings:

  • The large step is a "meantone", somewhere between near-10/9 (as in 32edo) and near-9/8 (as in 18edo).
  • The augmented smithird (made of two large steps) is a roughly meantone-sized major third, thus is a stand-in for the classical diatonic major third.

Parasoft smitonic tunings have both minor fifths and major fifths about equally off a just fifth, and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like smichromas. For this reason, parasoft might be the most accessible smitonic tuning range.

Parasoft smitonic EDOs include 18edo, 25edo, and 43edo.

  • 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted 19edo diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect smisixth) and falling fifths (666.7c, a major smififth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
  • 25edo can be used to make the augmented smithird a good 5/4 (384¢).

The sizes of the generator, large step and small step of smitonic are as follows in various parasoft smitonic tunings.

18edo (soft) 25edo (supersoft) 43edo Optimized (2.9.5 POTE) tuning
generator (g) 5\18, 333.3 7\25, 336.0 12\43, 334.9 335.84
L (octave - 3g) 3\18, 200.0 4\25, 192.0 7\43, 195.3 193.16
s (4g - octave) 2\18, 133.3 3\25, 144.0 5\43, 139.5 143.36

Intervals

Sortable table of the extended generator chain (-13 to 13 generators) in parasoft smitonic tunings. The several different interval flavors separated by the smichroma shows that parasoft smitonic is a useful cluster MOS, though many of the intervals lack simple JI interpretations.

Degree 18edo (soft) 25edo (supersoft) 43edo Note name on J Approximate ratios #Gens up
unison 0\18, 0.0 0\25, 0.0 0\43, 0.0 J 1/1 0
smichroma 1\18, 66.7 1\25, 48.0 2\43, 55.8 J& -7
dim. smi2nd 1\18, 66.7 2\25, 96.0 3\43, 83.7 K@@ +11
minor smi2nd 2\18, 133.3 3\25, 144.0 5\43, 139.5 K@ 13/12 +4
major smi2nd 3\18, 200.0 4\25, 192.0 7\43, 195.3 K 9/8, 10/9 -3
aug. smi2nd 4\18, 266.7 5\25, 240.0 9\43, 251.2 K& -10
dim. smi3rd 4\18, 266.7 6\25, 288.0 10\43, 279.1 L@ +8
perf. smi3rd 5\18, 333.3 7\25, 336.0 12\43, 334.9 L 17/14, 40/33 +1
aug. smi3rd 6\18, 400.0 8\25, 384.4 14\43, 390.7 L& 5/4 -6
doubly aug. smi3rd 7\18, 466.7 9\25, 432.0 16\43, 446.5 L&& -13
dim. smi4th 6\18, 400.0 9\25, 432.0 15\43, 418.6 M@@ +12
minor smi4th 7\18, 466.7 10\25, 480.0 17\43, 474.4 M@ 21/16 +5
major smi4th 8\18, 533.3 11\25, 528.0 19\43, 530.2 M 19/14, 34/25 -2
aug. smi4th 9\18, 600.0 12\25, 576.0 21\43, 586.0 M& 7/5 -9
dim. smi5th 9\18, 600.0 13\25, 624.0 22\43, 614.0 N@ 10/7 +9
minor smi5th 10\18, 666.7 14\25, 672.0 24\43, 669.8 N 28/19, 25/17 +2
major smi5th 11\18, 733.3 15\25, 720.0 26\43, 725.6 N& 32/21 -5
aug. smi5th 12\18, 800.0 16\25, 768.0 28\43, 781.4 N&& -12
doubly dim. smi6th 11\18, 733.3 16\25, 768.0 27\43, 753.5 O@@ +13
dim. smi6th 12\18, 800.0 17\25, 816.0 29\43, 809.3 O@ 8/5 +6
perf. smi6th 13\18, 866.7 18\25, 864.0 31\43, 865.1 O 28/17, 33/20 -1
aug. smi6th 14\18, 933.3 19\25, 912.0 33\43, 920.9 O& -8
dim. smi7th 14\18, 933.3 20\25, 960.0 34\34, 948.8 P@ +10
minor smi7th 15\18, 1000.0 21\25, 1008.0 36\43, 1004.7 P 16/9, 9/5 +3
major smi7th 16\18, 1066.7 22\25, 1056.0 38\43, 1060.5 P& 24/13 -4
aug. smi7th 17\18, 1133.3 23\25, 1104.0 40\43, 1116.3 P& -11
dim. smioctave 17\18, 1133.3 24\25, 1152.0 41\43, 1144.2 J@ +7

Hyposoft

Hyposoft tunings of smitonic have step ratios between 3/2 and 2/1 which implies that the generator is a supraminor third sharper than 3\11 = 327.27¢ and flatter than 5\18 = 333.33¢.

The large step is a sharper major second in these tunings than in parasoft tunings. These tunings could be considered "neogothic smitonic" or "archy smitonic", in analogy to parasoft smitonic being meantone smitonic.

11edo (basic) 18edo (soft) 29edo (semisoft)
generator (g) 3\11, 327.27 5\18, 333.33 8\29, 331.03
L (octave - 3g) 2\11, 218.18 3\18, 200.00 5\29, 206.90
s (4g - octave) 1\11, 109.09 2\18, 133.33 3\29, 124.14

Intervals

Sortable table of major and minor intervals in hyposoft smitonic tunings (11edo and 18edo not shown):

Degree 29edo (semisoft) Note name on J Approximate ratios (for 29edo) #Gens up
unison 0\29, 0.0 J 1/1 0
minor smi2nd 3\29, 124.1 K@ 14/13 +4
major smi2nd 5\29, 206.9 K 9/8 -3
perf. smi3rd 8\29, 331.0 L 23/19, 40/33 +1
aug. smi3rd 10\29, 413.8 L& 14/11 -6
minor smi4th 11\29, 455.2 M@ 13/10 +5
major smi4th 13\29, 537.9 M 15/11 -2
minor smi5th 16\29, 662.1 N 19/13, 22/15 +2
major smi5th 18\26, 744.8 N& 20/13 -5
dim. smi6th 19\29, 786.2 O@ 11/7 +6
perf. smi6th 21\29, 869.0 O 33/20, 38/23 -1
minor smi7th 24\29, 993.1 P 16/9 +3
major smi7th 26\28, 1075.9 P& 13/7 -4

Hypohard

Hypohard tunings have step ratios between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate 8/7, and the major smifourth (2 large steps + 1 small step) tends to approximate 11/8; 26edo is stellar in both of these approximations. This set of JI approximations is called orgone temperament.

Hypohard smitonic edos include 11edo, 15edo, 26edo, and 37edo. The sizes of the generator, large step and small step of smitonic are as follows in various hypohard smitonic tunings.

11edo (basic) 15edo (hard) 26edo (semihard) Some JI approximations
generator (g) 3\11, 327.27 4\15, 320.00 7\26, 323.08 77/64, 6/5
L (octave - 3g) 2\11, 218.18 3\15, 240.00 5\26, 230.77 8/7
s (4g - octave) 1\11, 109.09 1\15, 80.00 2\26, 92.31 128/121, (16/15)

Intervals

Sortable table of major and minor intervals in hypohard smitonic tunings:

Degree 11edo (basic) 15edo (hard) 26edo (semihard) Note name on J Approximate ratios #Gens up
unison 0\11, 0.0 0\15, 0.0 0\26, 0.0 J 1/1 0
minor smi2nd 1\11, 109.1 1\15, 80.0 2\26, 92.3 K@ +4
major smi2nd 2\11, 218.2 3\15, 240.0 5\26, 230.8 K 8/7 -3
perf. smi3rd 3\11, 327.3 4\15, 320.0 7\26, 323.1 L 77/64, 6/5 +1
aug. smi3rd 4\11, 436.4 6\15, 480.0 10\26, 461.5 L& -6
minor smi4th 4\11, 436.4 5\15, 400.0 9\26, 415.4 M@ 14/11 +5
major smi4th 5\11, 545.5 7\15, 560.0 12\26, 553.9 M 11/8 -2
minor smi5th 6\11, 656.6 8\15, 640.0 14\26, 646.2 N 16/11 +2
major smi5th 7\11, 763.6 10\15, 800.0 17\26, 784.62 N& 11/7 -5
dim. smi6th 7\11, 763.6 9\15, 720.0 16\26, 738.5 O@ +6
perf. smi6th 8\11, 872.7 11\15, 880.0 19\26, 876.9 O 5/3 -1
minor smi7th 9\11, 981.8 12\15, 960.0 21\26, 969.2 P 7/4 +3
major smi7th 10\11, 1090.9 14\15, 1120.0 24\26, 1107.7 P& -4

Parahard

In parahard smitonic (step ratio between 3 and 4, thus with generator between 5\19, 315.79¢ and 4\15, 320¢), the generator is close to a pure 6/5 minor third, and 6 minor thirds are used to reach a perfect fifth. The parahard range contains very accurate edos such as 53edo and 72edo, and has very accurate approximations to many low-overtone JI intervals, namely basic 5-limit ratios and some ratios involving 13. However, the 7-note MOS only has one perfect fifth, so extending the chain to bigger MOSes, such as the 4L 7s 11-note MOS, is suggested for getting 5-limit harmony.

EDOs that have parahard smitonic include 15edo, 19edo, 34edo, and 53edo.

The sizes of the generator, large step and small step of smitonic are as follows in various parahard smitonic tunings (not including 15edo).

19edo (superhard) 34edo 53edo JI intervals represented
generator (g) 5\19, 315.79 9\34, 317.65 14\53, 316.98 6/5
L (octave - 3g) 4\19, 252.63 7\34, 247.06 11\53, 249.06 15/13
s (4g - octave) 1\19, 63.16 2\34, 70.59 3\53, 67.92 25/24, 26/25

Intervals

Sortable table of major and minor intervals in parahard smitonic tunings:

Degree 19edo (superhard) 34edo 53edo Note name on J Approximate ratios #Gens up
unison 0\19, 0.0 0\34, 0.0 0\53, 0.0 J 1/1 0
minor smi2nd 1\19, 63.2 2\34, 70.6 3\53, 67.9 K@ 25/24, 26/25 +4
major smi2nd 4\19, 252.6 7\34, 247.1 11\53, 249.1 K 15/13 -3
perf. smi3rd 5\19, 315.8 9\34, 317.6 14\53, 317.0 L 6/5 +1
aug. smi3rd 8\19, 505.3 14\34, 494.1 22\53, 498.1 L& 4/3 -6
minor smi4th 6\19, 378.9 11\34, 388.2 17\53, 384.9 M@ 5/4 +5
major smi4th 9\19, 568.4 16\34, 564.7 25\53, 566.0 M 18/13 -2
minor smi5th 10\19, 631.6 18\34, 635.3 28\53, 634.0 N 13/9 +2
major smi5th 16\19, 821.1 23\34, 811.8 39\53, 815.0 N& 8/5 -5
dim. smi6th 11\19, 694.7 20\34, 705.9 31\53, 701.9 O@ 3/2 +6
perf. smi6th 14\19, 884.2 25\34, 882.4 39\53, 883.0 O 5/3 -1
minor smi7th 15\19, 947.4 27\34, 952.9 42\53, 950.9 P 26/15 +3
major smi7th 18\19, 1136.8 32\34, 1129.4 50\53, 1132.1 P& 25/13 -4

Modes

A naming scheme proposed by Alexandru Ianu (User:Ayceman)[1], relating to the Almsivi in Morrowind (TES):

Mode UDP Name
LLsLsLs 6|0 Nerevarine
LsLLsLs 5|1 Vivecan
LsLsLLs 4|2 Lorkhanic
LsLsLsL 3|3 Sothic
sLLsLsL 2|4 Kagrenacan
sLsLLsL 1|5 Almalexian
sLsLsLL 0|6 Dagothic

Pseudo-diatonic theory

Hypohard

Parasoft

Primodal theory

Primodal chords

Nejis

Temperaments

Main article: 4L 3s/Temperaments

Scales

Music

Scale tree

The spectrum looks like this:

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
5\7 857.143 342.857 1 1 1.000
28\39 861.538 338.462 6 5 1.200 Amity/hitchcock↑
23\32 862.500 337.500 5 4 1.250 Sixix
41\57 863.158 336.842 9 7 1.286
18\25 864.000 336.000 4 3 1.333
49\68 864.706 335.294 11 8 1.375
31\43 865.116 334.884 7 5 1.400
17\58 865.574 334.426 10 7 1.428
13\18 866.667 333.333 3 2 1.500 L/s = 3/2
47\65 867.692 332.308 11 7 1.571
34\47 868.085 331.915 8 5 1.600
55\76 868.421 331.579 13 8 1.625 Golden smitonic (?)
21\29 868.966 331.034 5 3 1.667
50\69 869.565 330.435 12 7 1.714
29\40 870.000 330.000 7 4 1.750
37\51 870.588 329.422 9 5 1.800
8\11 872.727 327.273 2 1 2.000 Basic smitonic
(Generators smaller than this are proper)
35\48 875.000 325.000 9 4 2.250
27\37 875.676 324.324 7 3 2.333
46\63 876.190 323.810 12 5 2.400
19\26 876.923 323.077 5 2 2.500
49\67 877.612 322.388 13 5 2.600 Golden superkleismic
30\41 878.049 321.951 8 3 2.667 Superkleismic
41\56 878.571 321.429 11 4 2.750
11\15 880.000 320.000 3 1 3.000 L/s = 3/1
36\49 881.633 318.367 10 3 3.333
25\34 882.353 317.647 7 2 3.500
39\53 883.019 316.981 11 3 3.667 Hanson/keemun is in this region
14\19 884.211 315.789 4 1 4.000
31\42 885.714 314.286 9 2 4.500
17\23 886.957 313.043 5 1 5.000
20\27 888.889 311.111 6 1 6.000 Oolong, myna↓
3\4 900.000 300.000 1 0 → inf

References

  1. ↑ Description of Sylvian Moon Dance mentioning the naming proposal https://musescore.com/user/36772625/scores/6700443 – The theme relates to the mystical nature of the Tribunal and TES lore, which fits smitonic.
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