2L 3s: Difference between revisions
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: ''For the 3/2-equivalent 2L 3s pattern, see [[2L 3s (3/2-equivalent)]].'' | : ''For the 3/2-equivalent 2L 3s pattern, see [[2L 3s (3/2-equivalent)]].'' | ||
{{MOS intro}} | {{MOS intro}} This scale is the "classic" pentatonic scale, which is perhaps the most common scale in the world. | ||
This scale is the " | |||
The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]]. | The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest [[harmonic entropy]] of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]]. | ||
== Names == | == Names == | ||
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* [[Archy5]] – 472edo tuning | * [[Archy5]] – 472edo tuning | ||
* [[Edson5]] – 29edo tuning | * [[Edson5]] – 29edo tuning | ||
* [[Pythagorean5]] – Pythagorean tuning | * [[Pythagorean5]] – Pythagorean tuning via 53edo | ||
* [[Meantone5]] – 31edo tuning | * [[Meantone5]] – 31edo tuning | ||
Revision as of 17:39, 15 July 2024
| ↖ 1L 2s | ↑ 2L 2s | 3L 2s ↗ |
| ← 1L 3s | 2L 3s | 3L 3s → |
| ↙ 1L 4s | ↓ 2L 4s | 3L 4s ↘ |
ssLsL
- For the 3/2-equivalent 2L 3s pattern, see 2L 3s (3/2-equivalent).
2L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 3 small steps, repeating every octave. Generators that produce this scale range from 480 ¢ to 600 ¢, or from 600 ¢ to 720 ¢. This scale is the "classic" pentatonic scale, which is perhaps the most common scale in the world.
The meantone pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly proper.
Names
The TAMNAMS system suggests the name pentic, derived from an informal clipping of "pentatonic" that is sometimes used to refer to this scale.
Modes
- 4|0 LsLss
- 3|1 LssLs
- 2|2 sLsLs
- 1|3 sLssL
- 0|4 ssLsL
Scales
- Archy5 – 472edo tuning
- Edson5 – 29edo tuning
- Pythagorean5 – Pythagorean tuning via 53edo
- Meantone5 – 31edo tuning
Scale tree
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Todo: expand
Add back entries from original scale tree. |
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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
}}
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| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 2\5 | 480.000 | 720.000 | 1:1 | 1.000 | Equalized 2L 3s | |||||
| 11\27 | 488.889 | 711.111 | 6:5 | 1.200 | ||||||
| 9\22 | 490.909 | 709.091 | 5:4 | 1.250 | ||||||
| 16\39 | 492.308 | 707.692 | 9:7 | 1.286 | ||||||
| 7\17 | 494.118 | 705.882 | 4:3 | 1.333 | Supersoft 2L 3s | |||||
| 19\46 | 495.652 | 704.348 | 11:8 | 1.375 | ||||||
| 12\29 | 496.552 | 703.448 | 7:5 | 1.400 | ||||||
| 17\41 | 497.561 | 702.439 | 10:7 | 1.429 | ||||||
| 5\12 | 500.000 | 700.000 | 3:2 | 1.500 | Soft 2L 3s | |||||
| 18\43 | 502.326 | 697.674 | 11:7 | 1.571 | ||||||
| 13\31 | 503.226 | 696.774 | 8:5 | 1.600 | ||||||
| 21\50 | 504.000 | 696.000 | 13:8 | 1.625 | ||||||
| 8\19 | 505.263 | 694.737 | 5:3 | 1.667 | Semisoft 2L 3s | |||||
| 19\45 | 506.667 | 693.333 | 12:7 | 1.714 | ||||||
| 11\26 | 507.692 | 692.308 | 7:4 | 1.750 | ||||||
| 14\33 | 509.091 | 690.909 | 9:5 | 1.800 | ||||||
| 3\7 | 514.286 | 685.714 | 2:1 | 2.000 | Basic 2L 3s Scales with tunings softer than this are proper | |||||
| 13\30 | 520.000 | 680.000 | 9:4 | 2.250 | ||||||
| 10\23 | 521.739 | 678.261 | 7:3 | 2.333 | ||||||
| 17\39 | 523.077 | 676.923 | 12:5 | 2.400 | ||||||
| 7\16 | 525.000 | 675.000 | 5:2 | 2.500 | Semihard 2L 3s | |||||
| 18\41 | 526.829 | 673.171 | 13:5 | 2.600 | ||||||
| 11\25 | 528.000 | 672.000 | 8:3 | 2.667 | ||||||
| 15\34 | 529.412 | 670.588 | 11:4 | 2.750 | ||||||
| 4\9 | 533.333 | 666.667 | 3:1 | 3.000 | Hard 2L 3s | |||||
| 13\29 | 537.931 | 662.069 | 10:3 | 3.333 | ||||||
| 9\20 | 540.000 | 660.000 | 7:2 | 3.500 | ||||||
| 14\31 | 541.935 | 658.065 | 11:3 | 3.667 | ||||||
| 5\11 | 545.455 | 654.545 | 4:1 | 4.000 | Superhard 2L 3s | |||||
| 11\24 | 550.000 | 650.000 | 9:2 | 4.500 | ||||||
| 6\13 | 553.846 | 646.154 | 5:1 | 5.000 | ||||||
| 7\15 | 560.000 | 640.000 | 6:1 | 6.000 | ||||||
| 1\2 | 600.000 | 600.000 | 1:0 | → ∞ | Collapsed 2L 3s | |||||
From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.
From a 5-limit perspective, the most interesting temperaments with this kind of pentatonic scale are meantone and mavila.
There is also the interesting 2.3.7 temperament that tempers out 64/63 (archy, "no-fives dominant").