4L 5s

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For the tritave-equivalent 4L 5s pattern, see 4L 5s (3/1-equivalent).
↖3L 4s↑4L 4s 5L 4s↗
←3L 5s4L 5s5L 5s→
↙3L 6s↓4L 6s 5L 6s↘
Brightest mode LsLsLsLss
Period 2/1
Range for bright generator 2\9 (266.7¢) to 1\4 (300¢)
Range for dark generator 3\4 (900¢) to 7\9 (933.3¢)
TAMNAMS name gramitonic
TAMNAMS prefix gram-
Parent MOS 4L 1s
Sister MOS 5L 4s
Daughter MOSes 9L 4s, 4L 9s
Equal tunings
Supersoft (L:s = 4:3) 7\31 (271¢)
Soft (L:s = 3:2) 5\22 (272.7¢)
Semisoft (L:s = 5:3) 8\35 (274.3¢)
Basic (L:s = 2:1) 3\13 (276.9¢)
Semihard (L:s = 5:2) 7\30 (280¢)
Hard (L:s = 3:1) 4\17 (282.4¢)
Superhard (L:s = 4:1) 5\21 (285.7¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

4L 5s, named gramitonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 5 small steps, repeating every octave. Generators that produce this scale range from 266.7¢ to 300¢, or from 900¢ to 933.3¢.

Names

The TAMNAMS name for this pattern is gramitonic (from grave minor third).

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

Intervals

Note: In TAMNAMS, a k-step interval class in 4L 5s may be called a "k-step", "k-mosstep", or "k-orstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.

Tuning ranges

Parasoft

Parasoft tunings of 4L 5s 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 4L 5s, 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 4L 5s 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 4L 5s are as follows in various parasoft 4L 5s 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 (g = 7/6, 2g = 11/8, 3g = 8/5, 7g = 3/2) is called 11-limit orwell temperament in regular temperament theory.

Modes

The names have been proposed for these Modes of 2/1 by Lilly Flores.

He told us that he assigned the Greek name relating to water because the word Orwell comes from 'a spring situated near a promontory'.

Modes of 4L 5s
UDP Rotational order Step pattern Mode names
8|0 1 LsLsLsLss Roi
7|1 3 LsLsLssLs Steno
6|2 5 LsLssLsLs Limni
5|3 7 LssLsLsLs Telma
4|4 9 sLsLsLsLs Krini
3|5 2 sLsLsLssL Elos
2|6 4 sLsLssLsL Mychos
1|7 6 sLssLsLsL Akti
0|8 8 ssLsLsLsL Dini

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 Lovecraft is around here
7\30 280.000 5 2 2.500
18\77 280.519 13 5 2.600 Golden Lovecraft
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 Gariberttet
1\4 300.000 1 0 → inf

Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.