- For the tritave-equivalent 4L 5s pattern, see 4L 5s (3/1-equivalent).
4L 5s, also called gramitonic, is a moment of symmetry scale consisting of 4 large steps and 5 small steps, repeating every octave. This scale is made using a generator ranging from 266.667¢ to 300¢, or from 900¢ to 933.333¢.
The TAMNAMS name for this pattern is gramitonic (from grave minor third).
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
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.
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.
- 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.
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'.
|UDP||Step pattern||Mode names|
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:
|19\84||271.429||11||8||1.375||Orwell is in this region|
|5\22||272.727||3||2||1.500||L/s = 3/2|
|21\92||273.913||13||8||1.625||Unnamed golden tuning|
(Generators smaller than this are proper)
|17\73||279.452||12||5||2.400||Lovecraft is around here|
|4\17||282.353||3||1||3.000||L/s = 3/1|
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.