3L 6s: Difference between revisions

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→Scale tree: Added scale tree template, transferred all entries (except for golden tunings)
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{{MOS modes}}
{{MOS modes}}
== Scale tree ==
== Scale tree ==
{| class="wikitable center-all"
{{Scale tree|Comments=9/5: August;
! colspan="6" rowspan="2" | Generator
12/5: Augene;
! colspan="2" | Cents
11/4: August;
! rowspan="2" | L
10/3: Inflated;
! rowspan="2" | s
6/1: Hemiug, hemiaug↓}}
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
! Chroma-positive
! Chroma-negative
|-
| 2\9 || || || || || || 266.667 || 133.333 || 1 || 1 || 1.000 ||
|-
| || || || || || 11\48 || 275.000 || 125.000 || 6 || 5 || 1.200 ||
|-
| || || || || 9\39 || || 276.923 || 123.077 || 5 || 4 || 1.250 ||
|-
| || || || || || 16\69 || 278.261 || 121.739 || 9 || 7 || 1.286 ||
|-
| || || || 7\30 || || || 280.000 || 120.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 19\81 || 281.481 || 118.519 || 11 || 8 || 1.375 ||
|-
| || || || || 12\51 || || 282.353 || 117.647 || 7 || 5 || 1.400 ||
|-
| || || || || || 17\72 || 283.333 || 116.667 || 10 || 7 || 1.428 ||
|-
| || || 5\21 || || || || 285.714 || 114.286 || 3 || 2 || 1.500 ||
|-
| || || || || || 18\75 || 288.000 || 112.000 || 11 || 7 || 1.571 ||
|-
| || || || || 13\54 || || 288.889 || 111.111 || 8 || 5 || 1.600 ||
|-
| || || || || || 21\87 || 289.655 || 110.345 || 13 || 8 || 1.625 || Unnamed golden tuning
|-
| || || || 8\33 || || || 290.909 || 109.091 || 5 || 3 || 1.667 ||
|-
| || || || || || 19\78 || 292.308 || 107.692 || 12 || 7 || 1.714 ||
|-
| || || || || 11\45 || || 293.333 || 106.667 || 7 || 4 || 1.750 ||
|-
| || || || || || 14\57 || 294.737 || 105.263 || 9 || 5 || 1.800 || August
|-
| || 3\12 || || || || || 300.000 || 100.000 || 2 || 1 || 2.000 || Basic tcherepnin<br>(Generators smaller than this are proper)
|-
| || || || || || 13\51 || 305.882 || 94.118 || 9 || 4 || 2.250 ||
|-
| || || || || 10\39 || || 307.692 || 92.308 || 7 || 3 || 2.333 ||
|-
| || || || || || 17\66 || 309.091 || 90.909 || 12 || 5 || 2.400 || Augene (optimal around here)
|-
| || || || 7\27 || || || 311.111 || 88.889 || 5 || 2 || 2.500 ||
|-
| || || || || || 18\69 || 313.043 || 86.957 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 11\42 || || 314.286 || 85.714 || 8 || 3 || 2.667 ||
|-
| || || || || || 15\57 || 315.789 || 84.211 || 11 || 4 || 2.750 || August
|-
| || || 4\15 || || || || 320.000 || 80.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 13\48 || 325.000 || 75.000 || 10 || 3 || 3.333 || Inflated
|-
| || || || || 9\33 || || 327.273 || 72.727 || 7 || 2 || 3.500 ||
|-
| || || || || || 14\51 || 329.412 || 70.588 || 11 || 3 || 3.667 ||
|-
| || || || 5\18 || || || 333.333 || 66.667 || 4 || 1 || 4.000 ||
|-
| || || || || || 11\39 || 338.462 || 61.538 || 9 || 2 || 4.500 ||
|-
| || || || || 6\21 || || 342.857 || 57.143 || 5 || 1 || 5.000 ||
|-
| || || || || || 7\24 || 350.000 || 50.000 || 6 || 1 || 6.000 || Hemiug, hemiaug↓
|-
| 1\3 || || || || || || 400.000 || 0.000 || 1 || 0 || → inf ||
|}
 
[[Category:Tcherepnin| ]]
[[Category:Tcherepnin| ]]
[[Category:9-tone scales]]
[[Category:9-tone scales]]

Revision as of 09:08, 24 April 2024

↖ 2L 5s ↑ 3L 5s 4L 5s ↗
← 2L 6s 3L 6s 4L 6s →
↙ 2L 7s ↓ 3L 7s 4L 7s ↘ 
┌╥┬┬╥┬┬╥┬┬┐
│║││║││║│││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLss
ssLssLssL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 2\9 to 1\3 (266.7 ¢ to 400.0 ¢)
Dark 0\3 to 1\9 (0.0 ¢ to 133.3 ¢)
TAMNAMS information
Name tcherepnin
Prefix cher-
Abbrev. ch
Related MOS scales
Parent 3L 3s
Sister 6L 3s
Daughters 9L 3s, 3L 9s
Neutralized 6L 3s
2-Flought 12L 6s, 3L 15s
Equal tunings
Equalized (L:s = 1:1) 2\9 (266.7 ¢)
Supersoft (L:s = 4:3) 7\30 (280.0 ¢)
Soft (L:s = 3:2) 5\21 (285.7 ¢)
Semisoft (L:s = 5:3) 8\33 (290.9 ¢)
Basic (L:s = 2:1) 3\12 (300.0 ¢)
Semihard (L:s = 5:2) 7\27 (311.1 ¢)
Hard (L:s = 3:1) 4\15 (320.0 ¢)
Superhard (L:s = 4:1) 5\18 (333.3 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 6s, named tcherepnin in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 6 small steps, with a period of 1 large step and 2 small steps that repeats every 400.0 ¢, or 3 times every octave. Generators that produce this scale range from 266.7 ¢ to 400 ¢, or from 0 ¢ to 133.3 ¢.

Name

TAMNAMS suggests the temperaement-agnostic name tcherepnin for this scale. This is named after Alexander Tcherepnin's 9-note scale which, in 12edo, is notated as C Db Eb E F G Ab A B C, forming the step pattern of HWHHWHHWH in standard notation (assuming a root of C).

Modes

Modes of 3L 6s
UDP Cyclic
order		 Step
pattern
6|0(3) 1 LssLssLss
3|3(3) 3 sLssLssLs
0|6(3) 2 ssLssLssL

Scale tree

Template:Scale tree

External links

Retrieved from "https://en.xen.wiki/index.php?title=3L_6s&oldid=141817"