3L 2s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:  
Generator ranges:  
* Chroma-positive generator: 720 cents (3\5) to 800 cents (2\3)
* Chroma-positive generator: 720{{c}} (3\5) to 800{{c}} (2\3)
* Chroma-negative generator: 400 cents (1\3) to 480 cents (2\5)
* Chroma-negative generator: 400{{c}} (1\3) to 480{{c}} (2\5)
 
{{Scale tree}}
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 3\5 || || || || || || 720.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 17\28 || 728.571 || 6 || 5 || 1.200 ||
|-
| || || || || 14\23 || || 730.435 || 5 || 4 || 1.250 ||
|-
| || || || || || 25\41 || 731.707 || 9 || 7 || 1.286 ||
|-
| || || || 11\18 || || || 733.333 || 4 || 3 || 1.333 ||
|-
| || || || || || 30\49 || 734.694 || 11 || 8 || 1.375 || [[Semisept]]
|-
| || || || || 19\31 || || 735.484 || 7 || 5 || 1.400 ||
|-
| || || || || || 27\44 || 736.364 || 10 || 7 || 1.429 ||
|-
| || || 8\13 || || || || 738.462 || 3 || 2 || 1.500 ||
|-
| || || || || || 29\47 || 740.426 || 11 || 7 || 1.571 ||
|-
| || || || || 21\34 || || 741.176 || 8 || 5 || 1.600 ||
|-
| || || || || || 34\55 || 741.818 || 13 || 8 || 1.625 || Golden [[father]]/[[petritri]]/[[aurora]] (741.6408¢)
|-
| || || || 13\21 || || || 742.857 || 5 || 3 || 1.667 ||
|-
| || || || || || 31\50 || 744.000 || 12 || 7 || 1.714 ||
|-
| || || || || 18\29 || || 744.828 || 7 || 4 || 1.750 ||
|-
| || || || || || 23\37 || 745.946 || 9 || 5 || 1.800 ||
|-
| || 5\8 || || || || || 750.000 || 2 || 1 || 2.000 || Basic antipentic <br>(Generators smaller than this are proper)
|-
| || || || || || 22\35 || 754.286 || 9 || 4 || 2.250 ||
|-
| || || || || 17\27 || || 755.556 || 7 || 3 || 2.333 ||
|-
| || || || || || 29\46 || 756.522 || 12 || 5 || 2.400 || [[Sensi]]
|-
| || || || 12\19 || || || 757.895 || 5 || 2 || 2.500 ||
|-
| || || || || || 31\49 || 759.184 || 13 || 5 || 2.600 || Golden [[sentry]] (759.4078¢)
|-
| || || || || 19\30 || || 760.000 || 8 || 3 || 2.667 ||
|-
| || || || || || 26\41 || 760.976 || 11 || 4 || 2.750 ||
|-
| || || 7\11 || || || || 763.636 || 3 || 1 || 3.000 ||
|-
| || || || || || 23\36 || 766.667 || 10 || 3 || 3.333 ||
|-
| || || || || 16\25 || || 768.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 25\39 || 769.231 || 11 || 3 || 3.667 ||
|-
| || || || 9\14 || || || 771.429 || 4 || 1 || 4.000 ||
|-
| || || || || || 20\31 || 774.194 || 9 || 2 || 4.500 || [[Squares]]/[[skwares]]
|-
| || || || || 11\17 || || 776.471 || 5 || 1 || 5.000 ||
|-
| || || || || || 13\20 || 780.000 || 6 || 1 || 6.000 ||
|-
| 2\3 || || || || || || 800.000 || 1 || 0 || → inf ||
|}


[[Category:Antipentic]]
[[Category:Antipentic]]
[[Category:5-tone scales]]
[[Category:5-tone scales]]

Revision as of 00:47, 28 February 2025

↖ 2L 1s ↑ 3L 1s 4L 1s ↗
← 2L 2s 3L 2s 4L 2s →
↙ 2L 3s ↓ 3L 3s 4L 3s ↘ 
┌╥╥┬╥┬┐
│║║│║││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern LLsLs
sLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\5 to 2\3 (720.0 ¢ to 800.0 ¢)
Dark 1\3 to 2\5 (400.0 ¢ to 480.0 ¢)
Related MOS scales
Parent 2L 1s
Sister 2L 3s
Daughters 5L 3s, 3L 5s
Neutralized 1L 4s
2-Flought 8L 2s, 3L 7s
Equal tunings
Equalized (L:s = 1:1) 3\5 (720.0 ¢)
Supersoft (L:s = 4:3) 11\18 (733.3 ¢)
Soft (L:s = 3:2) 8\13 (738.5 ¢)
Semisoft (L:s = 5:3) 13\21 (742.9 ¢)
Basic (L:s = 2:1) 5\8 (750.0 ¢)
Semihard (L:s = 5:2) 12\19 (757.9 ¢)
Hard (L:s = 3:1) 7\11 (763.6 ¢)
Superhard (L:s = 4:1) 9\14 (771.4 ¢)
Collapsed (L:s = 1:0) 2\3 (800.0 ¢)
For the 3/2-equivalent 3L 2s pattern, see 3L 2s (fifth-equivalent).

3L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 720 ¢ to 800 ¢, or from 400 ¢ to 480 ¢.

The only notable low-harmonic-entropy scale for this MOS pattern is sensi, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone[5]. It's also improper.

Name

The TAMNAMS system applies the name antipentic as the scale utilizes opposite step sizes to the “classic” pentatonic scale (2L 3s). The name antipentic can be used regardless of the equave.

Intervals

Intervals of 3L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 240.0 ¢
Major 1-mosstep M1ms L 240.0 ¢ to 400.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 400.0 ¢ to 480.0 ¢
Augmented 2-mosstep A2ms 2L 480.0 ¢ to 800.0 ¢
3-mosstep Diminished 3-mosstep d3ms L + 2s 400.0 ¢ to 720.0 ¢
Perfect 3-mosstep P3ms 2L + s 720.0 ¢ to 800.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 800.0 ¢ to 960.0 ¢
Major 4-mosstep M4ms 3L + s 960.0 ¢ to 1200.0 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 1200.0 ¢

Modes

Scale degrees of the modes of 3L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 LLsLs Perf. Maj. Aug. Perf. Maj. Perf.
3|1 4 LsLLs Perf. Maj. Perf. Perf. Maj. Perf.
2|2 2 LsLsL Perf. Maj. Perf. Perf. Min. Perf.
1|3 5 sLLsL Perf. Min. Perf. Perf. Min. Perf.
0|4 3 sLsLL Perf. Min. Perf. Dim. Min. Perf.

Scale tree

Generator ranges:

  • Chroma-positive generator: 720 ¢ (3\5) to 800 ¢ (2\3)
  • Chroma-negative generator: 400 ¢ (1\3) to 480 ¢ (2\5)

Template:Scale tree

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