1L 10s: Difference between revisions

Latest revision as of 18:48, 3 March 2025

	↑ 1L 9s	2L 9s ↗
	1L 10s	2L 10s →
	↓ 1L 11s	2L 11s ↘

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│║│││││││││││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

Lssssssssss
ssssssssssL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

10\11 to 1\1 (1090.9 ¢ to 1200.0 ¢)

Dark

0\1 to 1\11 (0.0 ¢ to 109.1 ¢)

TAMNAMS information

Related to

1L 9s (antisinatonic)

With tunings

2:1 to 1:0 (hard-of-basic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

10\11 (1090.9 ¢)

Supersoft (L:s = 4:3)

31\34 (1094.1 ¢)

21\23 (1095.7 ¢)

32\35 (1097.1 ¢)

11\12 (1100.0 ¢)

23\25 (1104.0 ¢)

12\13 (1107.7 ¢)

Superhard (L:s = 4:1)

13\14 (1114.3 ¢)

Collapsed (L:s = 1:0)

1\1 (1200.0 ¢)

1L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 10 small steps, repeating every octave. 1L 10s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 1090.9 ¢ to 1200 ¢, or from 0 ¢ to 109.1 ¢.

This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).

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 1L 10s
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	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 109.1 ¢
1-mosstep	Augmented 1-mosstep	A1ms	L	109.1 ¢ to 1200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 218.2 ¢
2-mosstep	Major 2-mosstep	M2ms	L + s	218.2 ¢ to 1200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 327.3 ¢
3-mosstep	Major 3-mosstep	M3ms	L + 2s	327.3 ¢ to 1200.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 436.4 ¢
4-mosstep	Major 4-mosstep	M4ms	L + 3s	436.4 ¢ to 1200.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 545.5 ¢
5-mosstep	Major 5-mosstep	M5ms	L + 4s	545.5 ¢ to 1200.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 654.5 ¢
6-mosstep	Major 6-mosstep	M6ms	L + 5s	654.5 ¢ to 1200.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0 ¢ to 763.6 ¢
7-mosstep	Major 7-mosstep	M7ms	L + 6s	763.6 ¢ to 1200.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0 ¢ to 872.7 ¢
8-mosstep	Major 8-mosstep	M8ms	L + 7s	872.7 ¢ to 1200.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0 ¢ to 981.8 ¢
9-mosstep	Major 9-mosstep	M9ms	L + 8s	981.8 ¢ to 1200.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	10s	0.0 ¢ to 1090.9 ¢
10-mosstep	Perfect 10-mosstep	P10ms	L + 9s	1090.9 ¢ to 1200.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	L + 10s	1200.0 ¢

Generator chain

Generator chain of 1L 10s
Bright gens	Scale degree	Abbrev.
11	Augmented 0-mosdegree	A0md
10	Augmented 1-mosdegree	A1md
9	Major 2-mosdegree	M2md
8	Major 3-mosdegree	M3md
7	Major 4-mosdegree	M4md
6	Major 5-mosdegree	M5md
5	Major 6-mosdegree	M6md
4	Major 7-mosdegree	M7md
3	Major 8-mosdegree	M8md
2	Major 9-mosdegree	M9md
1	Perfect 10-mosdegree	P10md
0	Perfect 0-mosdegree Perfect 11-mosdegree	P0md P11md
−1	Perfect 1-mosdegree	P1md
−2	Minor 2-mosdegree	m2md
−3	Minor 3-mosdegree	m3md
−4	Minor 4-mosdegree	m4md
−5	Minor 5-mosdegree	m5md
−6	Minor 6-mosdegree	m6md
−7	Minor 7-mosdegree	m7md
−8	Minor 8-mosdegree	m8md
−9	Minor 9-mosdegree	m9md
−10	Diminished 10-mosdegree	d10md
−11	Diminished 11-mosdegree	d11md

Modes

Scale degrees of the modes of 1L 10s
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
10\|0	1	Lssssssssss	Perf.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
9\|1	11	sLsssssssss	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
8\|2	10	ssLssssssss	Perf.	Perf.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
7\|3	9	sssLsssssss	Perf.	Perf.	Min.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
6\|4	8	ssssLssssss	Perf.	Perf.	Min.	Min.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
5\|5	7	sssssLsssss	Perf.	Perf.	Min.	Min.	Min.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
4\|6	6	ssssssLssss	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Maj.	Maj.	Maj.	Perf.	Perf.
3\|7	5	sssssssLsss	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Maj.	Perf.	Perf.
2\|8	4	ssssssssLss	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Perf.	Perf.
1\|9	3	sssssssssLs	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0\|10	2	ssssssssssL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Perf.

Scale tree

Scale tree and tuning spectrum of 1L 10s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
10\11						1090.909	109.091	1:1	1.000	Equalized 1L 10s
					51\56	1092.857	107.143	6:5	1.200
				41\45		1093.333	106.667	5:4	1.250
					72\79	1093.671	106.329	9:7	1.286
			31\34			1094.118	105.882	4:3	1.333	Supersoft 1L 10s
					83\91	1094.505	105.495	11:8	1.375
				52\57		1094.737	105.263	7:5	1.400
					73\80	1095.000	105.000	10:7	1.429	Septendesemi
		21\23				1095.652	104.348	3:2	1.500	Soft 1L 10s
					74\81	1096.296	103.704	11:7	1.571
				53\58		1096.552	103.448	8:5	1.600
					85\93	1096.774	103.226	13:8	1.625	Golden ripple (103.288 ¢)
			32\35			1097.143	102.857	5:3	1.667	Semisoft 1L 10s
					75\82	1097.561	102.439	12:7	1.714
				43\47		1097.872	102.128	7:4	1.750
					54\59	1098.305	101.695	9:5	1.800
	11\12					1100.000	100.000	2:1	2.000	Basic 1L 10s Scales with tunings softer than this are proper
					45\49	1102.041	97.959	9:4	2.250	Passion
				34\37		1102.703	97.297	7:3	2.333
					57\62	1103.226	96.774	12:5	2.400
			23\25			1104.000	96.000	5:2	2.500	Semihard 1L 10s
					58\63	1104.762	95.238	13:5	2.600	Unnamed golden tuning
				35\38		1105.263	94.737	8:3	2.667
					47\51	1105.882	94.118	11:4	2.750
		12\13				1107.692	92.308	3:1	3.000	Hard 1L 10s
					37\40	1110.000	90.000	10:3	3.333
				25\27		1111.111	88.889	7:2	3.500
					38\41	1112.195	87.805	11:3	3.667	Octacot
			13\14			1114.286	85.714	4:1	4.000	Superhard 1L 10s Nuke
					27\29	1117.241	82.759	9:2	4.500	Nautilus
				14\15		1120.000	80.000	5:1	5.000	Valentine
					15\16	1125.000	75.000	6:1	6.000	↓ Slurpee
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 10s

@@ Line 4: / Line 4: @@
 This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).
-== Modes ==
+== Scale properties ==
-{{MOS modes}}
+{{TAMNAMS use}}
-== Intervals ==
+=== Intervals ===
 {{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
 == Scale tree ==
-{{Todo|review|inline=1|text=Review entries from past page revision and enter them into the scale tree.}}Generator ranges:
+{{MOS tuning spectrum
-* Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
+| 10/7 = [[Septendesemi]]
-* Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)
+| 13/8 = Golden [[ripple]] (103.288{{c}})
-{{Scale tree}}
+| 9/4 = [[Passion]]
+| 13/5 = Unnamed golden tuning
+| 11/3 = [[Octacot]]
+| 4/1 = [[Nuke]]
+| 9/2 = [[Nautilus]]
+| 5/1 = [[Valentine]]
+| 6/1 = ↓ [[Slurpee]]
+}}
 [[Category:11-tone scales]]

1L 10s: Difference between revisions

Latest revision as of 18:48, 3 March 2025

Contents

Scale properties

Intervals

Generator chain

Modes

Scale tree

Navigation menu

1L 10s: Difference between revisions

Latest revision as of 18:48, 3 March 2025

Scale properties

Intervals

Generator chain

Modes

Scale tree

Navigation menu

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