9L 5s

9L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 5 small steps, repeating every octave. 9L 5s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 257.1 ¢ to 266.7 ¢, or from 933.3 ¢ to 942.9 ¢.

↖ 8L 4s	↑ 9L 4s	10L 4s ↗
← 8L 5s	9L 5s	10L 5s →
↙ 8L 6s	↓ 9L 6s	10L 6s ↘

┌╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║║│║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLsLLsLLsLLsLs
sLsLLsLLsLLsLL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

3\14 to 2\9 (257.1 ¢ to 266.7 ¢)

Dark

7\9 to 11\14 (933.3 ¢ to 942.9 ¢)

TAMNAMS information

Related to

5L 4s (semiquartal)

With tunings

1:1 to 2:1 (soft-of-basic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

3\14 (257.1 ¢)

Supersoft (L:s = 4:3)

11\51 (258.8 ¢)

8\37 (259.5 ¢)

13\60 (260.0 ¢)

5\23 (260.9 ¢)

12\55 (261.8 ¢)

7\32 (262.5 ¢)

Superhard (L:s = 4:1)

9\41 (263.4 ¢)

Collapsed (L:s = 1:0)

2\9 (266.7 ¢)

The generator can be said to approximate 7/6, but just 7/6 is larger than 2\9edo, so it cannot be used as a generator. The simplest just interval that works as a generator is 36/31. Two generators are said to create a fourth like Godzilla, but in reality it is closer to 27/20, if that is considered a consonance. 9L5s is third smallest MOS of Semiphore.

Modes

Modes of 9L 5s
UDP	Cyclic order	Step pattern
13\|0	1	LLsLLsLLsLLsLs
12\|1	4	LLsLLsLLsLsLLs
11\|2	7	LLsLLsLsLLsLLs
10\|3	10	LLsLsLLsLLsLLs
9\|4	13	LsLLsLLsLLsLLs
8\|5	2	LsLLsLLsLLsLsL
7\|6	5	LsLLsLLsLsLLsL
6\|7	8	LsLLsLsLLsLLsL
5\|8	11	LsLsLLsLLsLLsL
4\|9	14	sLLsLLsLLsLLsL
3\|10	3	sLLsLLsLLsLsLL
2\|11	6	sLLsLLsLsLLsLL
1\|12	9	sLLsLsLLsLLsLL
0\|13	12	sLsLLsLLsLLsLL

Tuning spectrum

generator in degrees of an edo	generator in cents	L in cents	s in cents	notes
3\14	257¢	86¢	86¢	L=s
	258.87¢	94¢	70¢	Just interval 36/31
8\37	259¢	97¢	65¢
5\23	261¢	104¢	52¢	L≈2s
	~261.5¢	104¢	52¢	L=2s
7\32	262¢	113¢	38¢
2\9	266¢	266¢	0¢	s=0