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 is the MOS pattern of the Pythagorean/schismic enharmonic or mega-chromatic scale. In contrast to the superpyth enharmonic scale, in which the enharmonic diesis (negative diminished second) is larger than the chromatic semitone, here the reverse is true: the enharmonic diesis is smaller than the chromatic semitone, so the diatonic scale subset is actually proper.

This MOS separates its small steps by intervals of 3L-2L-3L-2L-2L. Its major third of -4 generators approximates an interval between 24/19 and 32/25, thus its generator is a perfect fourth between 7\17 (494.118 cents) and 5\12 (500 cents).

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).

Modes

• 16|0 LLLsLLsLLLsLLsLLs
• 15|1 LLLsLLsLLsLLLsLLs
• 14|2 LLsLLLsLLsLLLsLLs
• 13|3 LLsLLLsLLsLLsLLLs
• 12|4 LLsLLsLLLsLLsLLLs
• 11|5 LLsLLsLLLsLLsLLsL
• 10|6 LLsLLsLLsLLLsLLsL
• 9|7 LsLLLsLLsLLLsLLsL
• 8|8 LsLLLsLLsLLsLLLsL
• 7|9 LsLLsLLLsLLsLLLsL
• 6|10 LsLLsLLLsLLsLLsLL
• 5|11 LsLLsLLsLLLsLLsLL
• 4|12 sLLLsLLsLLLsLLsLL
• 3|13 sLLLsLLsLLsLLLsLL
• 2|14 sLLsLLLsLLsLLLsLL
• 1|15 sLLsLLLsLLsLLsLLL
• 0|16 sLLsLLsLLLsLLsLLL

Scales

• Pythagorean17 – Pythagorean tuning
• Nestoria17 – 171edo tuning
• Cotoneum17 – 217edo tuning
• Garibaldi17 – 94edo tuning

Scale tree

Generator ranges:

• Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)
• Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)

Generator						Cents	L	s	L/s	Comments
7\17						494.118	1	1	1.000
					40\97	494.845	6	5	1.200
				33\80		495.000	5	4	1.250
					59\143	495.105	9	7	1.286
			26\63			495.238	4	3	1.333	Leapfrog
					71\172	495.349	11	8	1.375
				45\109		495.413	7	5	1.400	Leapweek
					64\155	495.484	10	7	1.428
		19\46				495.652	3	2	1.500
					69\167	495.808	11	7	1.571	Leapday / polypyth
				50\121		495.868	8	5	1.600
					81\196	495.918	13	8	1.625	Golden neogothic (495.9044¢)
			31\75			496.000	5	3	1.667
					74\179	496.089	12	7	1.714
				43\104		496.154	7	4	1.750
					55\133	496.241	9	5	1.800
	12\29					496.552	2	1	2.000	Basic 12L 5s (Generators smaller than this are proper)
					53\128	496.875	9	4	2.250
				41\99		496.970	7	3	2.333	Undecental
					70\169	497.041	12	5	2.400	Argent tuning (497.0563¢)
			29\70			497.143	5	2	2.500
					75\181	497.238	13	5	2.600	Unnamed golden tuning (497.2540¢)
				46\111		497.297	8	3	2.667
					63\152	497.368	11	4	2.750	Kwai
		17\41				497.561	3	1	3.000	Garibaldi / andromeda
					56\135	497.778	10	3	3.333
				39\94		497.872	7	2	3.500	Garibaldi / cassandra
					61\147	497.959	11	3	3.667
			22\53			498.113	4	1	4.000	Garibaldi / helenus, Pythagorean tuning (498.0450¢)
					49\118	498.305	9	2	4.500	Pontiac
				27\65		498.462	5	1	5.000	Photia
					32\77	498.701	6	1	6.000	Grackle↓
5\12						500.000	1	0	→ inf