4L 5s
| ↖ 3L 4s | ↑ 4L 4s | 5L 4s ↗ |
| ← 3L 5s | 4L 5s | 5L 5s → |
| ↙ 3L 6s | ↓ 4L 6s | 5L 6s ↘ |
┌╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
ssLsLsLsL
4L 5s refers to the structure of MOS scales whose generator falls between 2\9 (two degrees of 9edo = approx. 266.667¢) and 1\4 (one degree of 4edo = 300¢).
Names
The TAMNAMS name for this pattern is orwelloid (named after the abstract temperament orwell).
Notation
The notation used in this article is LsLsLsLss = JKLMNOPQRJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)
Thus the 13edo gamut is as follows:
J/R& J&/K@ K/L@ L/K& L&/M@ M/N@ N/M& N&/O@ O/P@ P/O& P&/Q@ Q/R@ R/Q&/J@ J
Tuning ranges
Parasoft
Parasoft tunings of orwelloid have a step ratio between 4/3 and 3/2, implying a generator sharper than 7\31 = 270.97¢ and flatter than 5\22 = 272.73¢.
In parasoft orwelloid, the generator (major mosthird) is an approximate 7/6, the major mosfifth is an approximate but rather flat 11/8, the minor mosfourth is an approximate 5/4, and the major mossixth is an approximate 3/2.
Parasoft orwelloid EDOs include 22edo, 31edo, 53edo, and 84edo.
- 22edo can be used to make large and small steps more distinct (the step ratio is 3/2).
- 31edo can be used for its nearly pure 5/4.
- 53edo can be used for its nearly pure 3/2 and good 5/4.
The sizes of the generator, large step and small step of orwelloid are as follows in various parasoft orwelloid tunings.
| 22edo | 31edo | 53edo | 84edo | JI intervals represented | |
|---|---|---|---|---|---|
| generator (g) | 5\22, 272.73 | 7\31, 270.97 | 12\53, 271.70 | 19\84, 271.43 | 7/6 |
| L (5g - octave) | 3\22, 163.64 | 4\31, 154.84 | 7\53, 158.49 | 11\84, 157.14 | 12/11, 11/10 |
| s (octave - 4g) | 2\22, 109.09 | 3\31, 116.13 | 5\53, 113.21 | 8\84, 114.29 | 16/15, 15/14 |
This set of JI interpretations is called orwell temperament in regular temperament theory.
Scale tree
In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2\9 | 266.667 | 1 | 1 | 1.000 | ||||||
| 11\49 | 269.388 | 6 | 5 | 1.200 | ||||||
| 9\40 | 270.000 | 5 | 4 | 1.250 | ||||||
| 16\71 | 270.423 | 9 | 7 | 1.286 | ||||||
| 7\31 | 270.968 | 4 | 3 | 1.333 | ||||||
| 19\84 | 271.429 | 11 | 8 | 1.375 | Orwell is in this region | |||||
| 12\53 | 271.698 | 7 | 5 | 1.400 | ||||||
| 17\75 | 272.000 | 10 | 7 | 1.428 | ||||||
| 5\22 | 272.727 | 3 | 2 | 1.500 | L/s = 3/2 | |||||
| 18\79 | 273.418 | 11 | 7 | 1.571 | ||||||
| 13\57 | 273.684 | 8 | 5 | 1.600 | ||||||
| 21\92 | 273.913 | 13 | 8 | 1.625 | Unnamed golden tuning | |||||
| 8\35 | 274.286 | 5 | 3 | 1.667 | ||||||
| 19\83 | 274.699 | 12 | 7 | 1.714 | ||||||
| 11\48 | 275.000 | 7 | 4 | 1.750 | ||||||
| 14\61 | 275.410 | 9 | 5 | 1.800 | ||||||
| 3\13 | 276.923 | 2 | 1 | 2.000 | Basic orwelloid (Generators smaller than this are proper) | |||||
| 13\56 | 278.571 | 9 | 4 | 2.250 | ||||||
| 10\43 | 279.070 | 7 | 3 | 2.333 | ||||||
| 17\73 | 279.452 | 12 | 5 | 2.400 | ||||||
| 7\30 | 280.000 | 5 | 2 | 2.500 | ||||||
| 18\77 | 280.519 | 13 | 5 | 2.600 | Unnamed golden tuning | |||||
| 11\47 | 280.851 | 8 | 3 | 2.667 | ||||||
| 15\64 | 281.250 | 11 | 4 | 2.750 | ||||||
| 4\17 | 282.353 | 3 | 1 | 3.000 | L/s = 3/1 | |||||
| 13\55 | 283.636 | 10 | 3 | 3.333 | ||||||
| 9\38 | 284.211 | 7 | 2 | 3.500 | ||||||
| 14\59 | 284.746 | 11 | 3 | 3.667 | ||||||
| 5\21 | 285.714 | 4 | 1 | 4.000 | ||||||
| 11\46 | 286.957 | 9 | 2 | 4.500 | ||||||
| 6\25 | 288.000 | 5 | 1 | 5.000 | ||||||
| 7\29 | 289.655 | 6 | 1 | 6.000 | ||||||
| 1\4 | 300.000 | 1 | 0 | → inf | ||||||