User:MisterShafXen/2L 14s

2L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 14 small steps, with a period of 1 large step and 7 small steps that repeats every 600.0 ¢, or twice every octave. 2L 14s is a great-grandchild scale of 2L 8s, expanding it by 6 tones. Generators that produce this scale range from 525 ¢ to 600 ¢, or from 0 ¢ to 75 ¢.

↖ 1L 13s	↑ 2L 13s	3L 13s ↗
← 1L 14s	2L 14s	3L 14s →
↙ 1L 15s	↓ 2L 15s	3L 15s ↘

Scale structure
Step pattern	LsssssssLsssssss sssssssLsssssssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	7\16 to 1\2 (525.0 ¢ to 600.0 ¢)
Dark	0\2 to 1\16 (0.0 ¢ to 75.0 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	2L 12s
Sister	14L 2s
Daughters	16L 2s, 2L 16s
Neutralized	4L 12s
2-Flought	18L 14s, 2L 30s
Equal tunings
Equalized (L:s = 1:1)	7\16 (525.0 ¢)
Supersoft (L:s = 4:3)	22\50 (528.0 ¢)
Soft (L:s = 3:2)	15\34 (529.4 ¢)
Semisoft (L:s = 5:3)	23\52 (530.8 ¢)
Basic (L:s = 2:1)	8\18 (533.3 ¢)
Semihard (L:s = 5:2)	17\38 (536.8 ¢)
Hard (L:s = 3:1)	9\20 (540.0 ¢)
Superhard (L:s = 4:1)	10\22 (545.5 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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Scale properties

Intervals of 2L 14s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 75.0 ¢
	Augmented 1-mosstep	A1ms	L	75.0 ¢ to 600.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	L + s	150.0 ¢ to 600.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 225.0 ¢
	Major 3-mosstep	M3ms	L + 2s	225.0 ¢ to 600.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 300.0 ¢
	Major 4-mosstep	M4ms	L + 3s	300.0 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 375.0 ¢
	Major 5-mosstep	M5ms	L + 4s	375.0 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	L + 5s	450.0 ¢ to 600.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	7s	0.0 ¢ to 525.0 ¢
	Perfect 7-mosstep	P7ms	L + 6s	525.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	L + 7s	600.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	L + 8s	600.0 ¢ to 675.0 ¢
	Augmented 9-mosstep	A9ms	2L + 7s	675.0 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	600.0 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	2L + 8s	750.0 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	600.0 ¢ to 825.0 ¢
	Major 11-mosstep	M11ms	2L + 9s	825.0 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	600.0 ¢ to 900.0 ¢
	Major 12-mosstep	M12ms	2L + 10s	900.0 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	600.0 ¢ to 975.0 ¢
	Major 13-mosstep	M13ms	2L + 11s	975.0 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	600.0 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	2L + 12s	1050.0 ¢ to 1200.0 ¢
15-mosstep	Diminished 15-mosstep	d15ms	L + 14s	600.0 ¢ to 1125.0 ¢
	Perfect 15-mosstep	P15ms	2L + 13s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	2L + 14s	1200.0 ¢

Harmonic entropy info for 2L 14s

Interval	Range in cents	Average of HE (from HE Calc)	Min of HE
Perfect 0-mosstep	0.0 ¢	~2.4654 nats	~2.4654 nats
Perfect 1-mosstep	0.0 ¢ to 75.0 ¢	~4.7697 nats	~4.7464 nats
Augmented 1-mosstep	75.0 ¢ to 600.0 ¢	~4.6347 nats	~4.5842 nats
Minor 2-mosstep	0.0 ¢ to 150.0 ¢	~4.6417 nats	~4.6286 nats
Major 2-mosstep	150.0 ¢ to 600.0 ¢	~4.5888 nats	~4.5651 nats
Minor 3-mosstep	0.0 ¢ to 225.0 ¢	~4.5909 nats	~4.5843 nats
Major 3-mosstep	225.0 ¢ to 600.0 ¢	~4.5741 nats	~4.5616 nats
Minor 4-mosstep	0.0 ¢ to 300.0 ¢	~4.5773 nats	~4.5636 nats
Major 4-mosstep	300.0 ¢ to 600.0 ¢	~4.5613 nats	~4.4947 nats
Minor 5-mosstep	0.0 ¢ to 375.0 ¢	~4.5848 nats	~4.5379 nats
Major 5-mosstep	375.0 ¢ to 600.0 ¢	~4.5396 nats	~4.4847 nats
Minor 6-mosstep	0.0 ¢ to 450.0 ¢	~4.5720 nats	~4.5066 nats
Major 6-mosstep	450.0 ¢ to 600.0 ¢	~4.5638 nats	~4.4011 nats
Diminished 7-mosstep	0.0 ¢ to 525.0 ¢	~4.5045 nats	~4.3792 nats
Perfect 7-mosstep	525.0 ¢ to 600.0 ¢	~4.6198 nats	~4.6019 nats
Perfect 8-mosstep	600.0 ¢	~4.5799 nats	~4.5799 nats
Perfect 9-mosstep	600.0 ¢ to 675.0 ¢	~4.6343 nats	~4.6044 nats
Augmented 9-mosstep	675.0 ¢ to 1200.0 ¢	~4.4265 nats	~4.1313 nats
Minor 10-mosstep	600.0 ¢ to 750.0 ¢	~4.5075 nats	~4.1623 nats
Major 10-mosstep	750.0 ¢ to 1200.0 ¢	~4.5832 nats	~4.4823 nats
Minor 11-mosstep	600.0 ¢ to 825.0 ¢	~4.5903 nats	~4.5712 nats
Major 11-mosstep	825.0 ¢ to 1200.0 ¢	~4.5572 nats	~4.4208 nats
Minor 12-mosstep	600.0 ¢ to 900.0 ¢	~4.5175 nats	~4.4231 nats
Major 12-mosstep	900.0 ¢ to 1200.0 ¢	~4.5880 nats	~4.5498 nats
Minor 13-mosstep	600.0 ¢ to 975.0 ¢	~4.5596 nats	~4.4823 nats
Major 13-mosstep	975.0 ¢ to 1200.0 ¢	~4.5787 nats	~4.5569 nats
Minor 14-mosstep	600.0 ¢ to 1050.0 ¢	~4.5784 nats	~4.5421 nats
Major 14-mosstep	1050.0 ¢ to 1200.0 ¢	~4.6087 nats	~4.6077 nats
Diminished 15-mosstep	600.0 ¢ to 1125.0 ¢	~4.5980 nats	~4.5502 nats
Perfect 15-mosstep	1125.0 ¢ to 1200.0 ¢	~4.6821 nats	~4.6620 nats
Perfect 16-mosstep	1200.0 ¢	~3.3273 nats	~3.3273 nats

Simple Tunings of 2L 14s

Scale degree	Abbrev.	Basic (2:1) 18edo		Hard (3:1) 20edo		Soft (3:2) 34edo
		Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\18	0.0	0\20	0.0	0\34	0.0
Perfect 1-mosdegree	P1md	1\18	66.7	1\20	60.0	2\34	70.6
Augmented 1-mosdegree	A1md	2\18	133.3	3\20	180.0	3\34	105.9
Minor 2-mosdegree	m2md	2\18	133.3	2\20	120.0	4\34	141.2
Major 2-mosdegree	M2md	3\18	200.0	4\20	240.0	5\34	176.5
Minor 3-mosdegree	m3md	3\18	200.0	3\20	180.0	6\34	211.8
Major 3-mosdegree	M3md	4\18	266.7	5\20	300.0	7\34	247.1
Minor 4-mosdegree	m4md	4\18	266.7	4\20	240.0	8\34	282.4
Major 4-mosdegree	M4md	5\18	333.3	6\20	360.0	9\34	317.6
Minor 5-mosdegree	m5md	5\18	333.3	5\20	300.0	10\34	352.9
Major 5-mosdegree	M5md	6\18	400.0	7\20	420.0	11\34	388.2
Minor 6-mosdegree	m6md	6\18	400.0	6\20	360.0	12\34	423.5
Major 6-mosdegree	M6md	7\18	466.7	8\20	480.0	13\34	458.8
Diminished 7-mosdegree	d7md	7\18	466.7	7\20	420.0	14\34	494.1
Perfect 7-mosdegree	P7md	8\18	533.3	9\20	540.0	15\34	529.4
Perfect 8-mosdegree	P8md	9\18	600.0	10\20	600.0	17\34	600.0
Perfect 9-mosdegree	P9md	10\18	666.7	11\20	660.0	19\34	670.6
Augmented 9-mosdegree	A9md	11\18	733.3	13\20	780.0	20\34	705.9
Minor 10-mosdegree	m10md	11\18	733.3	12\20	720.0	21\34	741.2
Major 10-mosdegree	M10md	12\18	800.0	14\20	840.0	22\34	776.5
Minor 11-mosdegree	m11md	12\18	800.0	13\20	780.0	23\34	811.8
Major 11-mosdegree	M11md	13\18	866.7	15\20	900.0	24\34	847.1
Minor 12-mosdegree	m12md	13\18	866.7	14\20	840.0	25\34	882.4
Major 12-mosdegree	M12md	14\18	933.3	16\20	960.0	26\34	917.6
Minor 13-mosdegree	m13md	14\18	933.3	15\20	900.0	27\34	952.9
Major 13-mosdegree	M13md	15\18	1000.0	17\20	1020.0	28\34	988.2
Minor 14-mosdegree	m14md	15\18	1000.0	16\20	960.0	29\34	1023.5
Major 14-mosdegree	M14md	16\18	1066.7	18\20	1080.0	30\34	1058.8
Diminished 15-mosdegree	d15md	16\18	1066.7	17\20	1020.0	31\34	1094.1
Perfect 15-mosdegree	P15md	17\18	1133.3	19\20	1140.0	32\34	1129.4
Perfect 16-mosdegree	P16md	18\18	1200.0	20\20	1200.0	34\34	1200.0

Generator chain of 2L 14s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.
8	Augmented 0-mosdegree	A0md	Augmented 8-mosdegree	A8md
7	Augmented 1-mosdegree	A1md	Augmented 9-mosdegree	A9md
6	Major 2-mosdegree	M2md	Major 10-mosdegree	M10md
5	Major 3-mosdegree	M3md	Major 11-mosdegree	M11md
4	Major 4-mosdegree	M4md	Major 12-mosdegree	M12md
3	Major 5-mosdegree	M5md	Major 13-mosdegree	M13md
2	Major 6-mosdegree	M6md	Major 14-mosdegree	M14md
1	Perfect 7-mosdegree	P7md	Perfect 15-mosdegree	P15md
0	Perfect 0-mosdegree Perfect 8-mosdegree	P0md P8md	Perfect 8-mosdegree Perfect 16-mosdegree	P8md P16md
−1	Perfect 1-mosdegree	P1md	Perfect 9-mosdegree	P9md
−2	Minor 2-mosdegree	m2md	Minor 10-mosdegree	m10md
−3	Minor 3-mosdegree	m3md	Minor 11-mosdegree	m11md
−4	Minor 4-mosdegree	m4md	Minor 12-mosdegree	m12md
−5	Minor 5-mosdegree	m5md	Minor 13-mosdegree	m13md
−6	Minor 6-mosdegree	m6md	Minor 14-mosdegree	m14md
−7	Diminished 7-mosdegree	d7md	Diminished 15-mosdegree	d15md
−8	Diminished 8-mosdegree	d8md	Diminished 16-mosdegree	d16md

Modes of 2L 14s

UDP	Cyclic order	Step pattern
14|0(2)	1	LsssssssLsssssss
12|2(2)	8	sLsssssssLssssss
10|4(2)	7	ssLsssssssLsssss
8|6(2)	6	sssLsssssssLssss
6|8(2)	5	ssssLsssssssLsss
4|10(2)	4	sssssLsssssssLss
2|12(2)	3	ssssssLsssssssLs
0|14(2)	2	sssssssLsssssssL

Scale tree

Scale tree and tuning spectrum of 2L 14s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\16						525.000	75.000	1:1	1.000	Equalized 2L 14s
					36\82	526.829	73.171	6:5	1.200
				29\66		527.273	72.727	5:4	1.250
					51\116	527.586	72.414	9:7	1.286
			22\50			528.000	72.000	4:3	1.333	Supersoft 2L 14s
					59\134	528.358	71.642	11:8	1.375
				37\84		528.571	71.429	7:5	1.400
					52\118	528.814	71.186	10:7	1.429
		15\34				529.412	70.588	3:2	1.500	Soft 2L 14s
					53\120	530.000	70.000	11:7	1.571
				38\86		530.233	69.767	8:5	1.600
					61\138	530.435	69.565	13:8	1.625
			23\52			530.769	69.231	5:3	1.667	Semisoft 2L 14s
					54\122	531.148	68.852	12:7	1.714
				31\70		531.429	68.571	7:4	1.750
					39\88	531.818	68.182	9:5	1.800
	8\18					533.333	66.667	2:1	2.000	Basic 2L 14s Scales with tunings softer than this are proper
					33\74	535.135	64.865	9:4	2.250
				25\56		535.714	64.286	7:3	2.333
					42\94	536.170	63.830	12:5	2.400
			17\38			536.842	63.158	5:2	2.500	Semihard 2L 14s
					43\96	537.500	62.500	13:5	2.600
				26\58		537.931	62.069	8:3	2.667
					35\78	538.462	61.538	11:4	2.750
		9\20				540.000	60.000	3:1	3.000	Hard 2L 14s
					28\62	541.935	58.065	10:3	3.333
				19\42		542.857	57.143	7:2	3.500
					29\64	543.750	56.250	11:3	3.667
			10\22			545.455	54.545	4:1	4.000	Superhard 2L 14s
					21\46	547.826	52.174	9:2	4.500
				11\24		550.000	50.000	5:1	5.000
					12\26	553.846	46.154	6:1	6.000
1\2						600.000	0.000	1:0	→ ∞	Collapsed 2L 14s