User:MisterShafXen/8L 11s

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Scale structure
Step pattern	LsLsLssLsLsLssLsLss ssLsLssLsLsLssLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\19 to 3\8 (442.1 ¢ to 450.0 ¢)
Dark	5\8 to 12\19 (750.0 ¢ to 757.9 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	8L 3s
Sister	11L 8s
Daughters	19L 8s, 8L 19s
Neutralized	16L 3s
2-Flought	27L 11s, 8L 30s
Equal tunings
Equalized (L:s = 1:1)	7\19 (442.1 ¢)
Supersoft (L:s = 4:3)	24\65 (443.1 ¢)
Soft (L:s = 3:2)	17\46 (443.5 ¢)
Semisoft (L:s = 5:3)	27\73 (443.8 ¢)
Basic (L:s = 2:1)	10\27 (444.4 ¢)
Semihard (L:s = 5:2)	23\62 (445.2 ¢)
Hard (L:s = 3:1)	13\35 (445.7 ¢)
Superhard (L:s = 4:1)	16\43 (446.5 ¢)
Collapsed (L:s = 1:0)	3\8 (450.0 ¢)
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8L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 11 small steps, repeating every octave. 8L 11s is a grandchild scale of 3L 5s, expanding it by 11 tones. Generators that produce this scale range from 442.1 ¢ to 450 ¢, or from 750 ¢ to 757.9 ¢.

Scale properties

Intervals of 8L 11s

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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 150.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	L + s	126.3 ¢ to 150.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	150.0 ¢ to 189.5 ¢
	Major 3-mosstep	M3ms	2L + s	189.5 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	150.0 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	2L + 2s	252.6 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	300.0 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	3L + 2s	315.8 ¢ to 450.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	300.0 ¢ to 378.9 ¢
	Major 6-mosstep	M6ms	3L + 3s	378.9 ¢ to 450.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	2L + 5s	300.0 ¢ to 442.1 ¢
	Perfect 7-mosstep	P7ms	3L + 4s	442.1 ¢ to 450.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	450.0 ¢ to 505.3 ¢
	Major 8-mosstep	M8ms	4L + 4s	505.3 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	450.0 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	4L + 5s	568.4 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	600.0 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	5L + 5s	631.6 ¢ to 750.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	600.0 ¢ to 694.7 ¢
	Major 11-mosstep	M11ms	5L + 6s	694.7 ¢ to 750.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	5L + 7s	750.0 ¢ to 757.9 ¢
	Augmented 12-mosstep	A12ms	6L + 6s	757.9 ¢ to 900.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	5L + 8s	750.0 ¢ to 821.1 ¢
	Major 13-mosstep	M13ms	6L + 7s	821.1 ¢ to 900.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	750.0 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	6L + 8s	884.2 ¢ to 900.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	6L + 9s	900.0 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	7L + 8s	947.4 ¢ to 1050.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	6L + 10s	900.0 ¢ to 1010.5 ¢
	Major 16-mosstep	M16ms	7L + 9s	1010.5 ¢ to 1050.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	7L + 10s	1050.0 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	8L + 9s	1073.7 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	7L + 11s	1050.0 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	8L + 10s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	8L + 11s	1200.0 ¢

Generator chain of 8L 11s

Bright gens	Scale degree	Abbrev.
26	Augmented 11-mosdegree	A11md
25	Augmented 4-mosdegree	A4md
24	Augmented 16-mosdegree	A16md
23	Augmented 9-mosdegree	A9md
22	Augmented 2-mosdegree	A2md
21	Augmented 14-mosdegree	A14md
20	Augmented 7-mosdegree	A7md
19	Augmented 0-mosdegree	A0md
18	Augmented 12-mosdegree	A12md
17	Major 5-mosdegree	M5md
16	Major 17-mosdegree	M17md
15	Major 10-mosdegree	M10md
14	Major 3-mosdegree	M3md
13	Major 15-mosdegree	M15md
12	Major 8-mosdegree	M8md
11	Major 1-mosdegree	M1md
10	Major 13-mosdegree	M13md
9	Major 6-mosdegree	M6md
8	Major 18-mosdegree	M18md
7	Major 11-mosdegree	M11md
6	Major 4-mosdegree	M4md
5	Major 16-mosdegree	M16md
4	Major 9-mosdegree	M9md
3	Major 2-mosdegree	M2md
2	Major 14-mosdegree	M14md
1	Perfect 7-mosdegree	P7md
0	Perfect 0-mosdegree Perfect 19-mosdegree	P0md P19md
−1	Perfect 12-mosdegree	P12md
−2	Minor 5-mosdegree	m5md
−3	Minor 17-mosdegree	m17md
−4	Minor 10-mosdegree	m10md
−5	Minor 3-mosdegree	m3md
−6	Minor 15-mosdegree	m15md
−7	Minor 8-mosdegree	m8md
−8	Minor 1-mosdegree	m1md
−9	Minor 13-mosdegree	m13md
−10	Minor 6-mosdegree	m6md
−11	Minor 18-mosdegree	m18md
−12	Minor 11-mosdegree	m11md
−13	Minor 4-mosdegree	m4md
−14	Minor 16-mosdegree	m16md
−15	Minor 9-mosdegree	m9md
−16	Minor 2-mosdegree	m2md
−17	Minor 14-mosdegree	m14md
−18	Diminished 7-mosdegree	d7md
−19	Diminished 19-mosdegree	d19md
−20	Diminished 12-mosdegree	d12md
−21	Diminished 5-mosdegree	d5md
−22	Diminished 17-mosdegree	d17md
−23	Diminished 10-mosdegree	d10md
−24	Diminished 3-mosdegree	d3md
−25	Diminished 15-mosdegree	d15md
−26	Diminished 8-mosdegree	d8md

Modes of 8L 11s

UDP	Cyclic order	Step pattern	Mode names
18|0	1	LsLsLssLsLsLssLsLss	Tonic
17|1	8	LsLsLssLsLssLsLsLss	Secondary leading tone
16|2	15	LsLssLsLsLssLsLsLss	Submediant
15|3	3	LsLssLsLsLssLsLssLs	Upper leading tone
14|4	10	LsLssLsLssLsLsLssLs	Lesser antitonic
13|5	17	LssLsLsLssLsLsLssLs	Subtonic
12|6	5	LssLsLsLssLsLssLsLs	Ultratonic
11|7	12	LssLsLssLsLsLssLsLs	Dominant
10|8	19	sLsLsLssLsLsLssLsLs	Ultradominant
9|9	7	sLsLsLssLsLssLsLsLs	Mediant
8|10	14	sLsLssLsLsLssLsLsLs	Minor submediant
7|11	2	sLsLssLsLsLssLsLssL	Upper ultradominant
6|12	9	sLsLssLsLssLsLsLssL	Subdominant
5|13	16	sLssLsLsLssLsLsLssL	Infratonic
4|14	4	sLssLsLsLssLsLssLsL	Supertonic
3|15	11	sLssLsLssLsLsLssLsL	Greater antitonic
2|16	18	ssLsLsLssLsLsLssLsL	Leading tone
1|17	6	ssLsLsLssLsLssLsLsL	Minor mediant
0|18	13	ssLsLssLsLsLssLsLsL	Inframediant

Simple Tunings of 8L 11s

Scale degree	Abbrev.	Basic (2:1) 27edo		Hard (3:1) 35edo		Soft (3:2) 46edo
		Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\27	0.0	0\35	0.0	0\46	0.0
Minor 1-mosdegree	m1md	1\27	44.4	1\35	34.3	2\46	52.2
Major 1-mosdegree	M1md	2\27	88.9	3\35	102.9	3\46	78.3
Minor 2-mosdegree	m2md	2\27	88.9	2\35	68.6	4\46	104.3
Major 2-mosdegree	M2md	3\27	133.3	4\35	137.1	5\46	130.4
Minor 3-mosdegree	m3md	4\27	177.8	5\35	171.4	7\46	182.6
Major 3-mosdegree	M3md	5\27	222.2	7\35	240.0	8\46	208.7
Minor 4-mosdegree	m4md	5\27	222.2	6\35	205.7	9\46	234.8
Major 4-mosdegree	M4md	6\27	266.7	8\35	274.3	10\46	260.9
Minor 5-mosdegree	m5md	7\27	311.1	9\35	308.6	12\46	313.0
Major 5-mosdegree	M5md	8\27	355.6	11\35	377.1	13\46	339.1
Minor 6-mosdegree	m6md	8\27	355.6	10\35	342.9	14\46	365.2
Major 6-mosdegree	M6md	9\27	400.0	12\35	411.4	15\46	391.3
Diminished 7-mosdegree	d7md	9\27	400.0	11\35	377.1	16\46	417.4
Perfect 7-mosdegree	P7md	10\27	444.4	13\35	445.7	17\46	443.5
Minor 8-mosdegree	m8md	11\27	488.9	14\35	480.0	19\46	495.7
Major 8-mosdegree	M8md	12\27	533.3	16\35	548.6	20\46	521.7
Minor 9-mosdegree	m9md	12\27	533.3	15\35	514.3	21\46	547.8
Major 9-mosdegree	M9md	13\27	577.8	17\35	582.9	22\46	573.9
Minor 10-mosdegree	m10md	14\27	622.2	18\35	617.1	24\46	626.1
Major 10-mosdegree	M10md	15\27	666.7	20\35	685.7	25\46	652.2
Minor 11-mosdegree	m11md	15\27	666.7	19\35	651.4	26\46	678.3
Major 11-mosdegree	M11md	16\27	711.1	21\35	720.0	27\46	704.3
Perfect 12-mosdegree	P12md	17\27	755.6	22\35	754.3	29\46	756.5
Augmented 12-mosdegree	A12md	18\27	800.0	24\35	822.9	30\46	782.6
Minor 13-mosdegree	m13md	18\27	800.0	23\35	788.6	31\46	808.7
Major 13-mosdegree	M13md	19\27	844.4	25\35	857.1	32\46	834.8
Minor 14-mosdegree	m14md	19\27	844.4	24\35	822.9	33\46	860.9
Major 14-mosdegree	M14md	20\27	888.9	26\35	891.4	34\46	887.0
Minor 15-mosdegree	m15md	21\27	933.3	27\35	925.7	36\46	939.1
Major 15-mosdegree	M15md	22\27	977.8	29\35	994.3	37\46	965.2
Minor 16-mosdegree	m16md	22\27	977.8	28\35	960.0	38\46	991.3
Major 16-mosdegree	M16md	23\27	1022.2	30\35	1028.6	39\46	1017.4
Minor 17-mosdegree	m17md	24\27	1066.7	31\35	1062.9	41\46	1069.6
Major 17-mosdegree	M17md	25\27	1111.1	33\35	1131.4	42\46	1095.7
Minor 18-mosdegree	m18md	25\27	1111.1	32\35	1097.1	43\46	1121.7
Major 18-mosdegree	M18md	26\27	1155.6	34\35	1165.7	44\46	1147.8
Perfect 19-mosdegree	P19md	27\27	1200.0	35\35	1200.0	46\46	1200.0

Scale tree

Scale tree and tuning spectrum of 8L 11s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\19						442.105	757.895	1:1	1.000	Equalized 8L 11s
					38\103	442.718	757.282	6:5	1.200
				31\84		442.857	757.143	5:4	1.250
					55\149	442.953	757.047	9:7	1.286
			24\65			443.077	756.923	4:3	1.333	Supersoft 8L 11s
					65\176	443.182	756.818	11:8	1.375
				41\111		443.243	756.757	7:5	1.400
					58\157	443.312	756.688	10:7	1.429
		17\46				443.478	756.522	3:2	1.500	Soft 8L 11s
					61\165	443.636	756.364	11:7	1.571
				44\119		443.697	756.303	8:5	1.600
					71\192	443.750	756.250	13:8	1.625
			27\73			443.836	756.164	5:3	1.667	Semisoft 8L 11s
					64\173	443.931	756.069	12:7	1.714
				37\100		444.000	756.000	7:4	1.750
					47\127	444.094	755.906	9:5	1.800
	10\27					444.444	755.556	2:1	2.000	Basic 8L 11s Scales with tunings softer than this are proper
					43\116	444.828	755.172	9:4	2.250
				33\89		444.944	755.056	7:3	2.333
					56\151	445.033	754.967	12:5	2.400
			23\62			445.161	754.839	5:2	2.500	Semihard 8L 11s
					59\159	445.283	754.717	13:5	2.600
				36\97		445.361	754.639	8:3	2.667
					49\132	445.455	754.545	11:4	2.750
		13\35				445.714	754.286	3:1	3.000	Hard 8L 11s
					42\113	446.018	753.982	10:3	3.333
				29\78		446.154	753.846	7:2	3.500
					45\121	446.281	753.719	11:3	3.667
			16\43			446.512	753.488	4:1	4.000	Superhard 8L 11s
					35\94	446.809	753.191	9:2	4.500
				19\51		447.059	752.941	5:1	5.000
					22\59	447.458	752.542	6:1	6.000
3\8						450.000	750.000	1:0	→ ∞	Collapsed 8L 11s