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 ¢)
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12L 5s 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).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 12L 5s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 70.6 ¢
1-mosstep	Major 1-mosstep	M1ms	L	70.6 ¢ to 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 141.2 ¢
2-mosstep	Major 2-mosstep	M2ms	2L	141.2 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	200.0 ¢ to 211.8 ¢
3-mosstep	Major 3-mosstep	M3ms	3L	211.8 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	200.0 ¢ to 282.4 ¢
4-mosstep	Major 4-mosstep	M4ms	3L + s	282.4 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	300.0 ¢ to 352.9 ¢
5-mosstep	Major 5-mosstep	M5ms	4L + s	352.9 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	400.0 ¢ to 423.5 ¢
6-mosstep	Major 6-mosstep	M6ms	5L + s	423.5 ¢ to 500.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	4L + 3s	400.0 ¢ to 494.1 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	494.1 ¢ to 500.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	500.0 ¢ to 564.7 ¢
8-mosstep	Major 8-mosstep	M8ms	6L + 2s	564.7 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	600.0 ¢ to 635.3 ¢
9-mosstep	Major 9-mosstep	M9ms	7L + 2s	635.3 ¢ to 700.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	7L + 3s	700.0 ¢ to 705.9 ¢
10-mosstep	Augmented 10-mosstep	A10ms	8L + 2s	705.9 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	700.0 ¢ to 776.5 ¢
11-mosstep	Major 11-mosstep	M11ms	8L + 3s	776.5 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	800.0 ¢ to 847.1 ¢
12-mosstep	Major 12-mosstep	M12ms	9L + 3s	847.1 ¢ to 900.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	900.0 ¢ to 917.6 ¢
13-mosstep	Major 13-mosstep	M13ms	10L + 3s	917.6 ¢ to 1000.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	900.0 ¢ to 988.2 ¢
14-mosstep	Major 14-mosstep	M14ms	10L + 4s	988.2 ¢ to 1000.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	1000.0 ¢ to 1058.8 ¢
15-mosstep	Major 15-mosstep	M15ms	11L + 4s	1058.8 ¢ to 1100.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	11L + 5s	1100.0 ¢ to 1129.4 ¢
16-mosstep	Major 16-mosstep	M16ms	12L + 4s	1129.4 ¢ to 1200.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	12L + 5s	1200.0 ¢

Generator chain

Generator chain of 12L 5s
Bright gens	Scale degree	Abbrev.
28	Augmented 9-mosdegree	A9md
27	Augmented 2-mosdegree	A2md
26	Augmented 12-mosdegree	A12md
25	Augmented 5-mosdegree	A5md
24	Augmented 15-mosdegree	A15md
23	Augmented 8-mosdegree	A8md
22	Augmented 1-mosdegree	A1md
21	Augmented 11-mosdegree	A11md
20	Augmented 4-mosdegree	A4md
19	Augmented 14-mosdegree	A14md
18	Augmented 7-mosdegree	A7md
17	Augmented 0-mosdegree	A0md
16	Augmented 10-mosdegree	A10md
15	Major 3-mosdegree	M3md
14	Major 13-mosdegree	M13md
13	Major 6-mosdegree	M6md
12	Major 16-mosdegree	M16md
11	Major 9-mosdegree	M9md
10	Major 2-mosdegree	M2md
9	Major 12-mosdegree	M12md
8	Major 5-mosdegree	M5md
7	Major 15-mosdegree	M15md
6	Major 8-mosdegree	M8md
5	Major 1-mosdegree	M1md
4	Major 11-mosdegree	M11md
3	Major 4-mosdegree	M4md
2	Major 14-mosdegree	M14md
1	Perfect 7-mosdegree	P7md
0	Perfect 0-mosdegree Perfect 17-mosdegree	P0md P17md
−1	Perfect 10-mosdegree	P10md
−2	Minor 3-mosdegree	m3md
−3	Minor 13-mosdegree	m13md
−4	Minor 6-mosdegree	m6md
−5	Minor 16-mosdegree	m16md
−6	Minor 9-mosdegree	m9md
−7	Minor 2-mosdegree	m2md
−8	Minor 12-mosdegree	m12md
−9	Minor 5-mosdegree	m5md
−10	Minor 15-mosdegree	m15md
−11	Minor 8-mosdegree	m8md
−12	Minor 1-mosdegree	m1md
−13	Minor 11-mosdegree	m11md
−14	Minor 4-mosdegree	m4md
−15	Minor 14-mosdegree	m14md
−16	Diminished 7-mosdegree	d7md
−17	Diminished 17-mosdegree	d17md
−18	Diminished 10-mosdegree	d10md
−19	Diminished 3-mosdegree	d3md
−20	Diminished 13-mosdegree	d13md
−21	Diminished 6-mosdegree	d6md
−22	Diminished 16-mosdegree	d16md
−23	Diminished 9-mosdegree	d9md
−24	Diminished 2-mosdegree	d2md
−25	Diminished 12-mosdegree	d12md
−26	Diminished 5-mosdegree	d5md
−27	Diminished 15-mosdegree	d15md
−28	Diminished 8-mosdegree	d8md

Modes

Scale degrees of the modes of 12L 5s
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	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 tuning-specific names

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

Modes of 12L 5s
UDP	Cyclic order	Step pattern	Mode Names	Hiragana
16\|0	1	LLLsLLsLLLsLLsLLs	Harumi	はるみ
15\|1	8	LLLsLLsLLsLLLsLLs	Yuzuha	ゆずは
14\|2	15	LLsLLLsLLsLLLsLLs	Maho	まほ
13\|3	5	LLsLLLsLLsLLsLLLs	Sakura	さくら
12\|4	12	LLsLLsLLLsLLsLLLs	Hanako	はなこ
11\|5	2	LLsLLsLLLsLLsLLsL	Saori	さおり
10\|6	9	LLsLLsLLsLLLsLLsL	Machiko	まちこ
9\|7	16	LsLLLsLLsLLLsLLsL	Sae	さえ
8\|8	6	LsLLLsLLsLLsLLLsL	Kaguya	かぐや
7\|9	13	LsLLsLLLsLLsLLLsL	Nae	なえ
6\|10	3	LsLLsLLLsLLsLLsLL	Sachiko	さちこ
5\|11	10	LsLLsLLsLLLsLLsLL	Kaori	かおり
4\|12	17	sLLLsLLsLLLsLLsLL	Kanako	かなこ
3\|13	7	sLLLsLLsLLsLLLsLL	Sakurajima	さくらじま
2\|14	14	sLLsLLLsLLsLLLsLL	Kaho	かほ
1\|15	4	sLLsLLLsLLsLLsLLL	Suzuha	すずは
0\|16	11	sLLsLLsLLLsLLsLLL	Narumi	なるみ

Scales

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

Scale tree

Scale tree and tuning spectrum of 12L 5s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
7\17						494.118	705.882	1:1	1.000	Equalized 12L 5s
					40\97	494.845	705.155	6:5	1.200
				33\80		495.000	705.000	5:4	1.250
					59\143	495.105	704.895	9:7	1.286
			26\63			495.238	704.762	4:3	1.333	Supersoft 12L 5s Leapfrog
					71\172	495.349	704.651	11:8	1.375
				45\109		495.413	704.587	7:5	1.400	Leapweek
					64\155	495.484	704.516	10:7	1.429
		19\46				495.652	704.348	3:2	1.500	Soft 12L 5s Leapday
					69\167	495.808	704.192	11:7	1.571	Polypyth
				50\121		495.868	704.132	8:5	1.600
					81\196	495.918	704.082	13:8	1.625	Golden neogothic (495.904 ¢)
			31\75			496.000	704.000	5:3	1.667	Semisoft 12L 5s
					74\179	496.089	703.911	12:7	1.714
				43\104		496.154	703.846	7:4	1.750
					55\133	496.241	703.759	9:5	1.800
	12\29					496.552	703.448	2:1	2.000	Basic 12L 5s Scales with tunings softer than this are proper
					53\128	496.875	703.125	9:4	2.250
				41\99		496.970	703.030	7:3	2.333	Undecental
					70\169	497.041	702.959	12:5	2.400	Argent tuning (497.056 ¢)
			29\70			497.143	702.857	5:2	2.500	Semihard 12L 5s
					75\181	497.238	702.762	13:5	2.600	Unnamed golden tuning (497.254 ¢)
				46\111		497.297	702.703	8:3	2.667
					63\152	497.368	702.632	11:4	2.750	Kwai
		17\41				497.561	702.439	3:1	3.000	Hard 12L 5s Garibaldi / andromeda
					56\135	497.778	702.222	10:3	3.333
				39\94		497.872	702.128	7:2	3.500	Garibaldi / cassandra
					61\147	497.959	702.041	11:3	3.667
			22\53			498.113	701.887	4:1	4.000	Superhard 12L 5s Garibaldi / helenus, Pythagorean tuning (498.045 ¢)
					49\118	498.305	701.695	9:2	4.500	Pontiac
				27\65		498.462	701.538	5:1	5.000	Photia
					32\77	498.701	701.299	6:1	6.000	↓ Grackle, ↓↓ gracecordial
5\12						500.000	700.000	1:0	→ ∞	Collapsed 12L 5s

12L 5s

Contents

Scale properties

Intervals

Generator chain

Modes

Proposed tuning-specific names

Scales

Scale tree

Navigation menu

12L 5s

Scale properties

Intervals

Generator chain

Modes

Proposed tuning-specific names

Scales

Scale tree

Navigation menu

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