4L 3s: Difference between revisions

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'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M/N@''' '''N/M&''' N&/O@ '''O/P@''' '''P/O@''' P&/J@ '''J'''
'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M/N@''' '''N/M&''' N&/O@ '''O/P@''' '''P/O@''' P&/J@ '''J'''
== Scale tree ==
== Scale tree ==
The spectrum looks like this:
The spectrum looks like this:
Line 84: Line 83:
| | 929.023
| | 929.023
| | 38.71
| | 38.71
| style="text-align:center;" | [[Myna]] is around here
| style="text-align:center;" |  
|-
|-
| |  
| |  
Line 129: Line 128:
| | 947.368
| | 947.368
| | 63.158
| | 63.158
| style="text-align:center;" | L/s = 4
| style="text-align:center;" |  
|-
|-
| |  
| |  
Line 144: Line 143:
| | 951.941
| | 951.941
| | 70.588
| | 70.588
| style="text-align:center;" | Kleismic is around here
| style="text-align:center;" |  
|-
|-
| |  
| |  
Line 159: Line 158:
| | 960
| | 960
| | 80
| | 80
| style="text-align:center;" | L/s = 3. Orgone starts here
| style="text-align:center;" | L/s = 3.
|-
|-
| |  
| |  
Line 249: Line 248:
| | 970.003
| | 970.003
| | 94.004
| | 94.004
| style="text-align:center;" | Orgone minmax tuning
| style="text-align:center;" |
|-
|-
| |  
| |  
Line 309: Line 308:
| | 981.818
| | 981.818
| | 109.091
| | 109.091
| style="text-align:center;" | Boundary of propriety (generators <br>larger than this are proper) Orgone ends here.
| style="text-align:center;" | Boundary of propriety (generators <br>larger than this are proper)
|-
|-
| |  
| |  
Line 384: Line 383:
| | 1000
| | 1000
| | 133.333
| | 133.333
| style="text-align:center;" | Optimum rank range (L/s=3/2)<br/> Sixix
| style="text-align:center;" | Optimum rank range (L/s=3/2)
|-
|-
| |  
| |  
Line 399: Line 398:
| | 1008
| | 1008
| | 144
| | 144
| style="text-align:center;" | Sixix
| style="text-align:center;" |  
|-
|-
| |  
| |  
Line 414: Line 413:
| | 1012.5
| | 1012.5
| | 150
| | 150
| style="text-align:center;" | Sixix
| style="text-align:center;" |  
|-
|-
| |  
| |  
Line 444: Line 443:
| | 1017.391
| | 1017.391
| | 156.522
| | 156.522
| style="text-align:center;" | (17/14)^3=9/5
| style="text-align:center;" |  
|-
|-
| |  
| |  
Line 459: Line 458:
| | 1018.868
| | 1018.868
| | 158.491
| | 158.491
| style="text-align:center;" | [[Amity]] is around here
| style="text-align:center;" |  
|-
|-
| | 2\7
| | 2\7
Line 476: Line 475:
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}
<!--
There are two notable harmonic entropy minima: [[Kleismic_family|kleismic]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling_temperaments|myna]], in which the generator is also 6/5 but now '''10''' of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).
There are two notable harmonic entropy minima: [[Kleismic_family|kleismic]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling_temperaments|myna]], in which the generator is also 6/5 but now '''10''' of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).
== Tuning ranges ==
== Tuning ranges ==
=== Sixix ===
=== Sixix ===
Line 724: Line 723:
* The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in [[porcupine]] harmony. Tempering out this comma leads to [[7edo]].
* The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in [[porcupine]] harmony. Tempering out this comma leads to [[7edo]].


-->
== Samples ==
== Samples ==
[[File:Sixix Fugue.mp3]] [[Sixix]] Fugue in [[18edo]] (WIP)
[[File:Sixix Fugue.mp3]] A fugue in [[18edo]] (WIP)
 
[[Category:Scales]]
[[Category:Scales]]
[[Category:MOS scales]]
[[Category:MOS scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 10:07, 27 March 2021

User:IlL/Template:RTT restriction

↖ 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 the structure of MOS scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 2\7edo (two degrees of 7edo, or approx. 342.857¢). The name smitonic smy-TON-ik /smaɪˈtɒnɪk/ has been proposed (derived from the obsolete temperament name smite for sixix, from 'sharp minor third', taking sharp to mean sharp of the 12edo minor third).

4L 3s is a distorted diatonic, because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).

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

Scale tree

The spectrum looks like this:

Generator Tetrachord g in cents 2g 3g 4g Comments
1\4 1 0 1 300 600 900 0
9\35 8 1 8 308.571 617.143 925.714 34.286
8\31 7 1 7 309.677 619.355 929.023 38.71
7\27 6 1 6 311.111 622.222 933.333 44.444
6\23 5 1 5 313.043 626.087 939.13 52.174
5\19 4 1 4 315.789 631.579 947.368 63.158
9\34 7 2 7 317.647 634.294 951.941 70.588
4\15 3 1 3 320 640 960 80 L/s = 3.
11\41 8 3 8 321.951 643.902 965.854 87.805
29\108 21 8 21 322.222 644.444 966.667 88.889
18\67 13 5 13 322.388 644.776 967.364 89.522
7\26 5 2 5 323.077 646.154 969.231 92.308
31/115 22 9 22 323.478 646.956 970.434 93.913
2.44 1 2.44 323.501 647.002 970.003 94.004
24/89 17 7 17 323.595 647.191 970.786 94.382
17/63 12 5 12 323.809 647.619 971.428 95.238
10/37 7 3 7 324.324 648.648 972.972 97.297
3\11 2 1 2 327.273 654.545 981.818 109.091 Boundary of propriety (generators
larger than this are proper)
8\29 5 3 5 331.034 662.069 993.013 124.138
21\76 13 8 13 331.579 663.158 994.739 126.316
34\123 21 13 21 331.707 663.415 995.122 126.829 Golden smitonic
13\47 8 5 8 331.915 663.83 995.745 127.66
5\18 3 2 3 333.333 666.667 1000 133.333 Optimum rank range (L/s=3/2)
7\25 4 3 4 336 672 1008 144
9\32 5 4 5 337.5 675 1012.5 150
11\39 6 5 6 338.462 676.923 1015.385 153.846
13\46 7 6 7 339.13 678.261 1017.391 156.522
15\53 8 7 8 339.623 679.245 1018.868 158.491
2\7 1 1 1 342.857 685.714 1028.571 171.429

Samples

A fugue in 18edo (WIP)

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