3L 2s: Difference between revisions

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: ''For the 3/2-equivalent 3L 2s pattern, see [[3L 2s (fifth-equivalent)]].''
{{Infobox MOS
{{Infobox MOS
| Name = antipentic
| Name = antipentic
Line 12: Line 9:
}}
}}


'''3L 2s''' or '''antipentic''' is a 5-tone scale. The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Sensipent_family|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. It's also improper.
: ''For the 3/2-equivalent 3L 2s pattern, see [[3L 2s (fifth-equivalent)]].''
 
{{MOS intro}}
 
The only notable low-[[harmonic entropy|harmonic-entropy]] scale for this [[MOSScales|MOS]] pattern is [[Sensipent_family|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 ==
== Name ==
The TAMNAMS system applies the name ''antipentic'' as the scale utilizes opposite step sizes to the “classic” pentatonic scale ([[2L 3s]]).
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 ==
{{MOS intervals}}


== Modes ==
== Modes ==
* 4|0 LLsLs
{{MOS mode degrees}}
* 3|1 LsLLs
* 2|2 LsLsL
* 1|3 sLLsL
* 0|4 sLsLL


== 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)
 
{{MOS tuning spectrum
{| class="wikitable center-all"
| 11/8 = [[Semisept]]
! colspan="6" | Generator
| 13/8 = Golden [[father]]/[[petritri]]/[[aurora]] (741.6408{{c}})
! Cents
| | 12/5 = [[Sensi]]
! L
13/5 = Golden [[sentry]] (759.4078{{c}})
! s
| 9/2 = [[Squares]]/[[skwares]]
! 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]]

Latest revision as of 06:51, 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)
Scale tree and tuning spectrum of 3L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\5 720.000 480.000 1:1 1.000 Equalized 3L 2s
17\28 728.571 471.429 6:5 1.200
14\23 730.435 469.565 5:4 1.250
25\41 731.707 468.293 9:7 1.286
11\18 733.333 466.667 4:3 1.333 Supersoft 3L 2s
30\49 734.694 465.306 11:8 1.375 Semisept
19\31 735.484 464.516 7:5 1.400
27\44 736.364 463.636 10:7 1.429
8\13 738.462 461.538 3:2 1.500 Soft 3L 2s
29\47 740.426 459.574 11:7 1.571
21\34 741.176 458.824 8:5 1.600
34\55 741.818 458.182 13:8 1.625 Golden father/petritri/aurora (741.6408 ¢)
13\21 742.857 457.143 5:3 1.667 Semisoft 3L 2s
31\50 744.000 456.000 12:7 1.714
18\29 744.828 455.172 7:4 1.750
23\37 745.946 454.054 9:5 1.800
5\8 750.000 450.000 2:1 2.000 Basic 3L 2s
Scales with tunings softer than this are proper
22\35 754.286 445.714 9:4 2.250
17\27 755.556 444.444 7:3 2.333
29\46 756.522 443.478 12:5 2.400 Sensi

13/5 = Golden sentry (759.4078 ¢)

12\19 757.895 442.105 5:2 2.500 Semihard 3L 2s
31\49 759.184 440.816 13:5 2.600
19\30 760.000 440.000 8:3 2.667
26\41 760.976 439.024 11:4 2.750
7\11 763.636 436.364 3:1 3.000 Hard 3L 2s
23\36 766.667 433.333 10:3 3.333
16\25 768.000 432.000 7:2 3.500
25\39 769.231 430.769 11:3 3.667
9\14 771.429 428.571 4:1 4.000 Superhard 3L 2s
20\31 774.194 425.806 9:2 4.500 Squares/skwares
11\17 776.471 423.529 5:1 5.000
13\20 780.000 420.000 6:1 6.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 2s
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