9L 1s

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← 8L 1s9L 1s 10L 1s →
↙ 8L 2s ↓9L 2s 10L 2s ↘
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│║║║║║║║║║││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLs
sLLLLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 1\10 to 1\9 (120.0¢ to 133.3¢)
Dark 8\9 to 9\10 (1066.7¢ to 1080.0¢)
TAMNAMS information
Name sinatonic
Prefix sina-
Abbrev. si
Related MOS scales
Parent 1L 8s
Sister 1L 9s
Daughters 10L 9s, 9L 10s
Neutralized 8L 2s
2-Flought 19L 1s, 9L 11s
Equal tunings
Equalized (L:s = 1:1) 1\10 (120.0¢)
Supersoft (L:s = 4:3) 4\39 (123.1¢)
Soft (L:s = 3:2) 3\29 (124.1¢)
Semisoft (L:s = 5:3) 5\48 (125.0¢)
Basic (L:s = 2:1) 2\19 (126.3¢)
Semihard (L:s = 5:2) 5\47 (127.7¢)
Hard (L:s = 3:1) 3\28 (128.6¢)
Superhard (L:s = 4:1) 4\37 (129.7¢)
Collapsed (L:s = 1:0) 1\9 (133.3¢)

9L 1s, named sinatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 120¢ to 133.3¢, or from 1066.7¢ to 1080¢. Scales of this form are always proper because there is only one small step. It appears as the albitonic scale in temperaments such as Negri and Twothirdtonic.

Names

The TAMNAMS system calls this scale pattern sinatonic after sinaic, a proposed interval category name for 14/13-like intervals that generate the scale. Graham Breed's MOS naming calls this the "Grumpy" decatonic scale.

Modes

Modes of 9L 1s
UDP Rotational order Step pattern
9 | 0 1 LLLLLLLLLs
8 | 1 2 LLLLLLLLsL
7 | 2 3 LLLLLLLsLL
6 | 3 4 LLLLLLsLLL
5 | 4 5 LLLLLsLLLL
4 | 5 6 LLLLsLLLLL
3 | 6 7 LLLsLLLLLL
2 | 7 8 LLsLLLLLLL
1 | 8 9 LsLLLLLLLL
0 | 9 10 sLLLLLLLLL

Scale tree

Scale Tree and Tuning Spectrum of 9L 1s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\10 120.000 1080.000 1:1 1.000 Equalized 9L 1s
6\59 122.034 1077.966 6:5 1.200
5\49 122.449 1077.551 5:4 1.250
9\88 122.727 1077.273 9:7 1.286
4\39 123.077 1076.923 4:3 1.333 Supersoft 9L 1s
11\107 123.364 1076.636 11:8 1.375
7\68 123.529 1076.471 7:5 1.400
10\97 123.711 1076.289 10:7 1.429
3\29 124.138 1075.862 3:2 1.500 Soft 9L 1s
11\106 124.528 1075.472 11:7 1.571
8\77 124.675 1075.325 8:5 1.600
13\125 124.800 1075.200 13:8 1.625
5\48 125.000 1075.000 5:3 1.667 Semisoft 9L 1s
12\115 125.217 1074.783 12:7 1.714
7\67 125.373 1074.627 7:4 1.750
9\86 125.581 1074.419 9:5 1.800
2\19 126.316 1073.684 2:1 2.000 Basic 9L 1s
9\85 127.059 1072.941 9:4 2.250
7\66 127.273 1072.727 7:3 2.333
12\113 127.434 1072.566 12:5 2.400
5\47 127.660 1072.340 5:2 2.500 Semihard 9L 1s
13\122 127.869 1072.131 13:5 2.600
8\75 128.000 1072.000 8:3 2.667
11\103 128.155 1071.845 11:4 2.750
3\28 128.571 1071.429 3:1 3.000 Hard 9L 1s
10\93 129.032 1070.968 10:3 3.333
7\65 129.231 1070.769 7:2 3.500
11\102 129.412 1070.588 11:3 3.667
4\37 129.730 1070.270 4:1 4.000 Superhard 9L 1s
9\83 130.120 1069.880 9:2 4.500
5\46 130.435 1069.565 5:1 5.000
6\55 130.909 1069.091 6:1 6.000
1\9 133.333 1066.667 1:0 → ∞ Collapsed 9L 1s