7L 5s

7L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 5 small steps, repeating every octave. 7L 5s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 500 ¢ to 514.3 ¢, or from 685.7 ¢ to 700 ¢.

↖ 6L 4s	↑ 7L 4s	8L 4s ↗
← 6L 5s	7L 5s	8L 5s →
↙ 6L 6s	↓ 7L 6s	8L 6s ↘

Scale structure
Step pattern	LLsLsLLsLsLs sLsLsLLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\12 to 3\7 (500.0 ¢ to 514.3 ¢)
Dark	4\7 to 7\12 (685.7 ¢ to 700.0 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 2s
Sister	5L 7s
Daughters	12L 7s, 7L 12s
Neutralized	2L 10s
2-Flought	19L 5s, 7L 17s
Equal tunings
Equalized (L:s = 1:1)	5\12 (500.0 ¢)
Supersoft (L:s = 4:3)	18\43 (502.3 ¢)
Soft (L:s = 3:2)	13\31 (503.2 ¢)
Semisoft (L:s = 5:3)	21\50 (504.0 ¢)
Basic (L:s = 2:1)	8\19 (505.3 ¢)
Semihard (L:s = 5:2)	19\45 (506.7 ¢)
Hard (L:s = 3:1)	11\26 (507.7 ¢)
Superhard (L:s = 4:1)	14\33 (509.1 ¢)
Collapsed (L:s = 1:0)	3\7 (514.3 ¢)
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7L 5s represents the chromatic scale of meantone, or meantone chromatic scale. Such scales are characterized by having a small step (diatonic semitone) that is larger than the chroma (chromatic semitone), the reverse of 5L 7s.

Meantone is the only notable harmonic entropy minimum.

Intervals

Intervals of 7L 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 100.0 ¢
	Major 1-mosstep	M1ms	L	100.0 ¢ to 171.4 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	171.4 ¢ to 200.0 ¢
	Major 2-mosstep	M2ms	2L	200.0 ¢ to 342.9 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	171.4 ¢ to 300.0 ¢
	Major 3-mosstep	M3ms	2L + s	300.0 ¢ to 342.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	342.9 ¢ to 400.0 ¢
	Major 4-mosstep	M4ms	3L + s	400.0 ¢ to 514.3 ¢
5-mosstep	Diminished 5-mosstep	d5ms	2L + 3s	342.9 ¢ to 500.0 ¢
	Perfect 5-mosstep	P5ms	3L + 2s	500.0 ¢ to 514.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	514.3 ¢ to 600.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	600.0 ¢ to 685.7 ¢
7-mosstep	Perfect 7-mosstep	P7ms	4L + 3s	685.7 ¢ to 700.0 ¢
	Augmented 7-mosstep	A7ms	5L + 2s	700.0 ¢ to 857.1 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	685.7 ¢ to 800.0 ¢
	Major 8-mosstep	M8ms	5L + 3s	800.0 ¢ to 857.1 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	857.1 ¢ to 900.0 ¢
	Major 9-mosstep	M9ms	6L + 3s	900.0 ¢ to 1028.6 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	857.1 ¢ to 1000.0 ¢
	Major 10-mosstep	M10ms	6L + 4s	1000.0 ¢ to 1028.6 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	1028.6 ¢ to 1100.0 ¢
	Major 11-mosstep	M11ms	7L + 4s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	7L + 5s	1200.0 ¢

Modes

Scale degrees of the modes of 7L 5s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12
11|0	1	LLsLsLLsLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.
10|1	6	LLsLsLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
9|2	11	LsLLsLsLLsLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
8|3	4	LsLLsLsLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
7|4	9	LsLsLLsLsLLs	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
6|5	2	LsLsLLsLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
5|6	7	LsLsLsLLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
4|7	12	sLLsLsLLsLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
3|8	5	sLLsLsLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
2|9	10	sLsLLsLsLLsL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
1|10	3	sLsLLsLsLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
0|11	8	sLsLsLLsLsLL	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.

Proposed Names

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.

Modes of 7L 5s

UDP	Cyclic order	Step pattern
11|0	1	LLsLsLLsLsLs
10|1	6	LLsLsLsLLsLs
9|2	11	LsLLsLsLLsLs
8|3	4	LsLLsLsLsLLs
7|4	9	LsLsLLsLsLLs
6|5	2	LsLsLLsLsLsL
5|6	7	LsLsLsLLsLsL
4|7	12	sLLsLsLLsLsL
3|8	5	sLLsLsLsLLsL
2|9	10	sLsLLsLsLLsL
1|10	3	sLsLLsLsLsLL
0|11	8	sLsLsLLsLsLL

Scales

• Meaneb471a – an equal beating tuning of meantone
• Meantone12 – 31edo tuning
• Ratwolf – 20/13 wolf fifth tuning of meantone
• Meaneb471 – the other equal beating tuning of meantone
• Flattone12 – 13-limit POTE tuning of flattone

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 7L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\12						500.000	700.000	1:1	1.000	Equalized 7L 5s
					28\67	501.493	698.507	6:5	1.200
				23\55		501.818	698.182	5:4	1.250
					41\98	502.041	697.959	9:7	1.286
			18\43			502.326	697.674	4:3	1.333	Supersoft 7L 5s
					49\117	502.564	697.436	11:8	1.375
				31\74		502.703	697.297	7:5	1.400
					44\105	502.857	697.143	10:7	1.429
		13\31				503.226	696.774	3:2	1.500	Soft 7L 5s
					47\112	503.571	696.429	11:7	1.571
				34\81		503.704	696.296	8:5	1.600
					55\131	503.817	696.183	13:8	1.625
			21\50			504.000	696.000	5:3	1.667	Semisoft 7L 5s
					50\119	504.202	695.798	12:7	1.714
				29\69		504.348	695.652	7:4	1.750
					37\88	504.545	695.455	9:5	1.800
	8\19					505.263	694.737	2:1	2.000	Basic 7L 5s Scales with tunings softer than this are proper
					35\83	506.024	693.976	9:4	2.250
				27\64		506.250	693.750	7:3	2.333
					46\109	506.422	693.578	12:5	2.400
			19\45			506.667	693.333	5:2	2.500	Semihard 7L 5s
					49\116	506.897	693.103	13:5	2.600
				30\71		507.042	692.958	8:3	2.667
					41\97	507.216	692.784	11:4	2.750
		11\26				507.692	692.308	3:1	3.000	Hard 7L 5s
					36\85	508.235	691.765	10:3	3.333
				25\59		508.475	691.525	7:2	3.500
					39\92	508.696	691.304	11:3	3.667
			14\33			509.091	690.909	4:1	4.000	Superhard 7L 5s
					31\73	509.589	690.411	9:2	4.500
				17\40		510.000	690.000	5:1	5.000
					20\47	510.638	689.362	6:1	6.000
3\7						514.286	685.714	1:0	→ ∞	Collapsed 7L 5s