5L 3s (5/2-equivalent)

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

┌╥╥┬╥╥┬╥┬┐ │║║│║║│║││ ││││││││││ └┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLs sLsLLsLL
Equave	5/2 (1586.3 ¢)
Period	5/2 (1586.3 ¢)
Generator size(ed5/2)
Bright	3\8 to 2\5 (594.9 ¢ to 634.5 ¢)
Dark	3\5 to 5\8 (951.8 ¢ to 991.4 ¢)
Related MOS scales
Parent	3L 2s⟨5/2⟩
Sister	3L 5s⟨5/2⟩
Daughters	8L 5s⟨5/2⟩, 5L 8s⟨5/2⟩
Neutralized	2L 6s⟨5/2⟩
2-Flought	13L 3s⟨5/2⟩, 5L 11s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1)	3\8 (594.9 ¢)
Supersoft (L:s = 4:3)	11\29 (601.7 ¢)
Soft (L:s = 3:2)	8\21 (604.3 ¢)
Semisoft (L:s = 5:3)	13\34 (606.5 ¢)
Basic (L:s = 2:1)	5\13 (610.1 ¢)
Semihard (L:s = 5:2)	12\31 (614.1 ¢)
Hard (L:s = 3:1)	7\18 (616.9 ¢)
Superhard (L:s = 4:1)	9\23 (620.7 ¢)
Collapsed (L:s = 1:0)	2\5 (634.5 ¢)

5L 3s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 3 small steps, repeating every interval of 5/2 (1586.3 ¢). Generators that produce this scale range from 594.9 ¢ to 634.5 ¢, or from 951.8 ¢ to 991.4 ¢.

Theory

This scale can be thought of as a MOS generated by 5/2-equivalent jubilic temperament where 50/49 vanishes. This is one of the most simple no-threes temperaments, although in this case it is using the second-best period choice of 5/2 rather than 2/1, causing strict MOS to be generated rather than multi-MOS. The bright generator of the MOS represents 7/5~10/7 and the dark generator represents 7/4~25/14. This gives 5L 3s⟨5/2⟩ many approximations of 4:5:7 chords for no-threes harmony.

Modes

Modes of 5L 3s⟨5/2⟩

UDP	Cyclic order	Step pattern
7|0	1	LLsLLsLs
6|1	4	LLsLsLLs
5|2	7	LsLLsLLs
4|3	2	LsLLsLsL
3|4	5	LsLsLLsL
2|5	8	sLLsLLsL
1|6	3	sLLsLsLL
0|7	6	sLsLLsLL

Intervals

Intervals of 5L 3s⟨5/2⟩

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 198.3 ¢
	Major 1-mosstep	M1ms	L	198.3 ¢ to 317.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	317.3 ¢ to 396.6 ¢
	Major 2-mosstep	M2ms	2L	396.6 ¢ to 634.5 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	317.3 ¢ to 594.9 ¢
	Perfect 3-mosstep	P3ms	2L + s	594.9 ¢ to 634.5 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	634.5 ¢ to 793.2 ¢
	Major 4-mosstep	M4ms	3L + s	793.2 ¢ to 951.8 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	951.8 ¢ to 991.4 ¢
	Augmented 5-mosstep	A5ms	4L + s	991.4 ¢ to 1269.1 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	951.8 ¢ to 1189.7 ¢
	Major 6-mosstep	M6ms	4L + 2s	1189.7 ¢ to 1269.1 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	1269.1 ¢ to 1388.0 ¢
	Major 7-mosstep	M7ms	5L + 2s	1388.0 ¢ to 1586.3 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	1586.3 ¢

Modes

Modes of 5L 3s⟨5/2⟩

UDP	Cyclic order	Step pattern
7|0	1	LLsLLsLs
6|1	4	LLsLsLLs
5|2	7	LsLLsLLs
4|3	2	LsLLsLsL
3|4	5	LsLsLLsL
2|5	8	sLLsLLsL
1|6	3	sLLsLsLL
0|7	6	sLsLLsLL