12L 5s

↖ 11L 4s	↑ 12L 4s	13L 4s ↗
← 11L 5s	12L 5s	13L 5s →
↙ 11L 6s	↓ 12L 6s	13L 6s ↘

┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║║│║║│║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLsLLLsLLsLLs sLLsLLsLLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\17 to 5\12 (494.1 ¢ to 500.0 ¢)
Dark	7\12 to 10\17 (700.0 ¢ to 705.9 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	5L 7s
Sister	5L 12s
Daughters	17L 12s, 12L 17s
Neutralized	7L 10s
2-Flought	29L 5s, 12L 22s
Equal tunings
Equalized (L:s = 1:1)	7\17 (494.1 ¢)
Supersoft (L:s = 4:3)	26\63 (495.2 ¢)
Soft (L:s = 3:2)	19\46 (495.7 ¢)
Semisoft (L:s = 5:3)	31\75 (496.0 ¢)
Basic (L:s = 2:1)	12\29 (496.6 ¢)
Semihard (L:s = 5:2)	29\70 (497.1 ¢)
Hard (L:s = 3:1)	17\41 (497.6 ¢)
Superhard (L:s = 4:1)	22\53 (498.1 ¢)
Collapsed (L:s = 1:0)	5\12 (500.0 ¢)

12L 5s, also called p-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 5 small steps, repeating every octave. 12L 5s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 494.1 ¢ to 500 ¢, or from 700 ¢ to 705.9 ¢. Temperaments supported by this scale include those under the Pythagorean and schismic families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the chroma.

The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).

Intervals

Intervals of 12L 5s

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 70.6 ¢
	Major 1-mosstep	M1ms	L	70.6 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 141.2 ¢
	Major 2-mosstep	M2ms	2L	141.2 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	200.0 ¢ to 211.8 ¢
	Major 3-mosstep	M3ms	3L	211.8 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	200.0 ¢ to 282.4 ¢
	Major 4-mosstep	M4ms	3L + s	282.4 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	300.0 ¢ to 352.9 ¢
	Major 5-mosstep	M5ms	4L + s	352.9 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	400.0 ¢ to 423.5 ¢
	Major 6-mosstep	M6ms	5L + s	423.5 ¢ to 500.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	4L + 3s	400.0 ¢ to 494.1 ¢
	Perfect 7-mosstep	P7ms	5L + 2s	494.1 ¢ to 500.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	500.0 ¢ to 564.7 ¢
	Major 8-mosstep	M8ms	6L + 2s	564.7 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	600.0 ¢ to 635.3 ¢
	Major 9-mosstep	M9ms	7L + 2s	635.3 ¢ to 700.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	7L + 3s	700.0 ¢ to 705.9 ¢
	Augmented 10-mosstep	A10ms	8L + 2s	705.9 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	700.0 ¢ to 776.5 ¢
	Major 11-mosstep	M11ms	8L + 3s	776.5 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	800.0 ¢ to 847.1 ¢
	Major 12-mosstep	M12ms	9L + 3s	847.1 ¢ to 900.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	900.0 ¢ to 917.6 ¢
	Major 13-mosstep	M13ms	10L + 3s	917.6 ¢ to 1000.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	900.0 ¢ to 988.2 ¢
	Major 14-mosstep	M14ms	10L + 4s	988.2 ¢ to 1000.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	1000.0 ¢ to 1058.8 ¢
	Major 15-mosstep	M15ms	11L + 4s	1058.8 ¢ to 1100.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	11L + 5s	1100.0 ¢ to 1129.4 ¢
	Major 16-mosstep	M16ms	12L + 4s	1129.4 ¢ to 1200.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	12L + 5s	1200.0 ¢

Modes

Scale degrees of the modes of 12L 5s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
16|0	1	LLLsLLsLLLsLLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
15|1	8	LLLsLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
14|2	15	LLsLLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
13|3	5	LLsLLLsLLsLLsLLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.
12|4	12	LLsLLsLLLsLLsLLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.
11|5	2	LLsLLsLLLsLLsLLsL	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
10|6	9	LLsLLsLLsLLLsLLsL	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
9|7	16	LsLLLsLLsLLLsLLsL	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
8|8	6	LsLLLsLLsLLsLLLsL	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.
7|9	13	LsLLsLLLsLLsLLLsL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.
6|10	3	LsLLsLLLsLLsLLsLL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
5|11	10	LsLLsLLsLLLsLLsLL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
4|12	17	sLLLsLLsLLLsLLsLL	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
3|13	7	sLLLsLLsLLsLLLsLL	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.
2|14	14	sLLsLLLsLLsLLLsLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.
1|15	4	sLLsLLLsLLsLLsLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
0|16	11	sLLsLLsLLLsLLsLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.

Proposed names

Declan Paul Boushy has proposed names for these modes corresponding to step ratios 3:1 and 4:1.

Scales

• Edson17 – 29edo tuning
• Subaru scale – 41edo tuning
• Cotoneum17 – 217edo tuning
• Garibaldi17 – 94edo tuning
• Pythagorean17 – Pythagorean tuning
• Tanegashima scale – 53edo tuning
• Nestoria17 – 171edo tuning