5L 2s (3/1-equivalent)

↖ 4L 1s⟨3/1⟩	↑ 5L 1s⟨3/1⟩	6L 1s⟨3/1⟩ ↗
← 4L 2s⟨3/1⟩	5L 2s (3/1-equivalent)	6L 2s⟨3/1⟩ →
↙ 4L 3s⟨3/1⟩	↓ 5L 3s⟨3/1⟩	6L 3s⟨3/1⟩ ↘

┌╥╥╥┬╥╥┬┐ │║║║│║║││ │││││││││ └┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLs sLLsLLL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
Generator size(edt)
Bright	4\7 to 3\5 (1086.8 ¢ to 1141.2 ¢)
Dark	2\5 to 3\7 (760.8 ¢ to 815.1 ¢)
Related MOS scales
Parent	2L 3s⟨3/1⟩
Sister	2L 5s⟨3/1⟩
Daughters	7L 5s⟨3/1⟩, 5L 7s⟨3/1⟩
Neutralized	3L 4s⟨3/1⟩
2-Flought	12L 2s⟨3/1⟩, 5L 9s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	4\7 (1086.8 ¢)
Supersoft (L:s = 4:3)	15\26 (1097.3 ¢)
Soft (L:s = 3:2)	11\19 (1101.1 ¢)
Semisoft (L:s = 5:3)	18\31 (1104.4 ¢)
Basic (L:s = 2:1)	7\12 (1109.5 ¢)
Semihard (L:s = 5:2)	17\29 (1114.9 ¢)
Hard (L:s = 3:1)	10\17 (1118.8 ¢)
Superhard (L:s = 4:1)	13\22 (1123.9 ¢)
Collapsed (L:s = 1:0)	3\5 (1141.2 ¢)

5L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1086.8 ¢ to 1141.2 ¢, or from 760.8 ¢ to 815.1 ¢.

Theory

As a macrodiatonic scale

It is the macrodiatonic scale with the period of a tritave. This means it is a diatonic scale, but has octaves stretched out to the size of a tritave. Other intervals are also stretched in a way that makes the unrecognizable–the diatonic fifth is now the size of a major seventh. Interestingly 19edt, an approximation of 12edo, has a tuning of this scale (being a stretched version of 19edo's diatonic scale), meaning it contains both the diatonic scale (identical to 12edo's) and the macrodiatonic scale.

Temperament interpretations

Although they have not been studied in detail, it is possible to construct no-twos rank-2 temperament interpretations of this scale, such as the as-of-yet unnamed b12 & b5 temperament in the 3.13.17 subgroup, in which the generator is ~17/9 and a stack of 4 generators tritave-reduced is ~13/9. See also the page for 12edt.

Modes

The modes have step patterns which are the same as the modes of the diatonic scale.

Modes of 5L 2s⟨3/1⟩

UDP	Cyclic order	Step pattern
6|0	1	LLLsLLs
5|1	5	LLsLLLs
4|2	2	LLsLLsL
3|3	6	LsLLLsL
2|4	3	LsLLsLL
1|5	7	sLLLsLL
0|6	4	sLLsLLL

Scale degrees

Scale degrees of the modes of 5L 2s⟨3/1⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7
6|0	1	LLLsLLs	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.
5|1	5	LLsLLLs	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
4|2	2	LLsLLsL	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.
3|3	6	LsLLLsL	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Perf.
2|4	3	LsLLsLL	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Min.	Perf.
1|5	7	sLLLsLL	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.
0|6	4	sLLsLLL	Perf.	Min.	Min.	Perf.	Dim.	Min.	Min.	Perf.

Notation

Being a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like diamond MOS notation.