7L 5s

↖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

Descends from

5L 2s (diatonic)

Required step ratio range

1:1 to 2:1 (soft-of-basic)

Related MOS scales

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¢)

7L 5s, also called m-chromatic, 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¢.

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.

Modes

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The latter scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, 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	Rotational order	Step pattern	Mode names
11\|0	1	LLsLsLLsLsLs	July
10\|1	6	LLsLsLsLLsLs	December
9\|2	11	LsLLsLsLLsLs	May
8\|3	4	LsLLsLsLsLLs	October
7\|4	9	LsLsLLsLsLLs	March
6\|5	2	LsLsLLsLsLsL	August
5\|6	7	LsLsLsLLsLsL	January
4\|7	12	sLLsLsLLsLsL	June
3\|8	5	sLLsLsLsLLsL	November
2\|9	10	sLsLLsLsLLsL	April
1\|10	3	sLsLLsLsLsLL	September
0\|11	8	sLsLsLLsLsLL	February

Modes of 7L 5s
UDP	Rotational order	Step pattern	Mode names
11\|0	1	LLsLsLLsLsLs	Martian
10\|1	6	LLsLsLsLLsLs	Aprilian
9\|2	11	LsLLsLsLLsLs	Maian
8\|3	4	LsLLsLsLsLLs	Junian
7\|4	9	LsLsLLsLsLLs	Quintillian or Julian
6\|5	2	LsLsLLsLsLsL	Sextilian or Augustan
5\|6	7	LsLsLsLLsLsL	Septembian
4\|7	12	sLLsLsLLsLsL	Octobian
3\|8	5	sLLsLsLsLLsL	Novembian
2\|9	10	sLsLLsLsLLsL	Decembian
1\|10	3	sLsLLsLsLsLL	Janian
0\|11	8	sLsLsLLsLsLL	Februan

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

Scale Tree and Tuning Spectrum of 7L 5s
Generator^(edo)						Cents		Step Ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
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 Meantone / meridetone
					49\117	502.564	697.436	11:8	1.375
				31\74		502.703	697.297	7:5	1.400	Meantone / huygens / grosstone
					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	Meantone
					55\131	503.817	696.183	13:8	1.625	Golden meantone (503.7855¢)
			21\50			504.000	696.000	5:3	1.667	Semisoft 7L 5s Meantone / meanpop
					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 ↕ Flattone
					49\116	506.897	693.103	13:5	2.600	Golden flattone (506.9365¢)
				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

7L 5s

Modes

Scales

Scale tree

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