3L 6s: Difference between revisions

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m == Intervals == {{MOS intervals}}
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{{MOS intro}}
{{MOS intro}}
== Name ==
== 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).
[[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).
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== Modes ==
== Modes ==
{{MOS mode degrees}}
{{MOS mode degrees}}
== Intervals ==
{{MOS intervals}}


== Scale tree ==
== Scale tree ==
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[[Category:9-tone scales]]
[[Category:9-tone scales]]
  <!--main article-->
  <!--main article-->
== External links ==
== External links ==
* Piano Encyclopedia, on Tcherepnin's 9-note scale: https://pianoencyclopedia.com/scales/tcherepnin-nine-note-mode-i/
* Piano Encyclopedia, on Tcherepnin's 9-note scale: https://pianoencyclopedia.com/scales/tcherepnin-nine-note-mode-i/

Revision as of 23:59, 15 December 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 ¢)
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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

Scale degrees of the modes of 3L 6s
UDP Cyclic
order 		Step
pattern 		Scale degree (cherdegree)
0 1 2 3 4 5 6 7 8 9
6|0(3) 1 LssLssLss Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf.
3|3(3) 3 sLssLssLs Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|6(3) 2 ssLssLssL Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf.

Intervals

Intervals of 3L 6s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-cherstep Perfect 0-cherstep P0chs 0 0.0 ¢
1-cherstep Perfect 1-cherstep P1chs s 0.0 ¢ to 133.3 ¢
Augmented 1-cherstep A1chs L 133.3 ¢ to 400.0 ¢
2-cherstep Diminished 2-cherstep d2chs 2s 0.0 ¢ to 266.7 ¢
Perfect 2-cherstep P2chs L + s 266.7 ¢ to 400.0 ¢
3-cherstep Perfect 3-cherstep P3chs L + 2s 400.0 ¢
4-cherstep Perfect 4-cherstep P4chs L + 3s 400.0 ¢ to 533.3 ¢
Augmented 4-cherstep A4chs 2L + 2s 533.3 ¢ to 800.0 ¢
5-cherstep Diminished 5-cherstep d5chs L + 4s 400.0 ¢ to 666.7 ¢
Perfect 5-cherstep P5chs 2L + 3s 666.7 ¢ to 800.0 ¢
6-cherstep Perfect 6-cherstep P6chs 2L + 4s 800.0 ¢
7-cherstep Perfect 7-cherstep P7chs 2L + 5s 800.0 ¢ to 933.3 ¢
Augmented 7-cherstep A7chs 3L + 4s 933.3 ¢ to 1200.0 ¢
8-cherstep Diminished 8-cherstep d8chs 2L + 6s 800.0 ¢ to 1066.7 ¢
Perfect 8-cherstep P8chs 3L + 5s 1066.7 ¢ to 1200.0 ¢
9-cherstep Perfect 9-cherstep P9chs 3L + 6s 1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 3L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\9 266.667 133.333 1:1 1.000 Equalized 3L 6s
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 Supersoft 3L 6s
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 1.429
5\21 285.714 114.286 3:2 1.500 Soft 3L 6s
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
8\33 290.909 109.091 5:3 1.667 Semisoft 3L 6s
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
3\12 300.000 100.000 2:1 2.000 Basic 3L 6s
Scales with tunings softer 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
7\27 311.111 88.889 5:2 2.500 Semihard 3L 6s
18\69 313.043 86.957 13:5 2.600
11\42 314.286 85.714 8:3 2.667
15\57 315.789 84.211 11:4 2.750
4\15 320.000 80.000 3:1 3.000 Hard 3L 6s
13\48 325.000 75.000 10:3 3.333
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 Superhard 3L 6s
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
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 6s

External links

Retrieved from "https://en.xen.wiki/index.php?title=3L_6s&oldid=170774"