9L 1s

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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.

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 9L 1s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-sinastep Perfect 0-sinastep P0sis 0 0.0 ¢
1-sinastep Diminished 1-sinastep d1sis s 0.0 ¢ to 120.0 ¢
Perfect 1-sinastep P1sis L 120.0 ¢ to 133.3 ¢
2-sinastep Minor 2-sinastep m2sis L + s 133.3 ¢ to 240.0 ¢
Major 2-sinastep M2sis 2L 240.0 ¢ to 266.7 ¢
3-sinastep Minor 3-sinastep m3sis 2L + s 266.7 ¢ to 360.0 ¢
Major 3-sinastep M3sis 3L 360.0 ¢ to 400.0 ¢
4-sinastep Minor 4-sinastep m4sis 3L + s 400.0 ¢ to 480.0 ¢
Major 4-sinastep M4sis 4L 480.0 ¢ to 533.3 ¢
5-sinastep Minor 5-sinastep m5sis 4L + s 533.3 ¢ to 600.0 ¢
Major 5-sinastep M5sis 5L 600.0 ¢ to 666.7 ¢
6-sinastep Minor 6-sinastep m6sis 5L + s 666.7 ¢ to 720.0 ¢
Major 6-sinastep M6sis 6L 720.0 ¢ to 800.0 ¢
7-sinastep Minor 7-sinastep m7sis 6L + s 800.0 ¢ to 840.0 ¢
Major 7-sinastep M7sis 7L 840.0 ¢ to 933.3 ¢
8-sinastep Minor 8-sinastep m8sis 7L + s 933.3 ¢ to 960.0 ¢
Major 8-sinastep M8sis 8L 960.0 ¢ to 1066.7 ¢
9-sinastep Perfect 9-sinastep P9sis 8L + s 1066.7 ¢ to 1080.0 ¢
Augmented 9-sinastep A9sis 9L 1080.0 ¢ to 1200.0 ¢
10-sinastep Perfect 10-sinastep P10sis 9L + s 1200.0 ¢

Generator chain

Generator chain of 9L 1s
Bright gens Scale degree Abbrev.
18 Augmented 8-sinadegree A8sid
17 Augmented 7-sinadegree A7sid
16 Augmented 6-sinadegree A6sid
15 Augmented 5-sinadegree A5sid
14 Augmented 4-sinadegree A4sid
13 Augmented 3-sinadegree A3sid
12 Augmented 2-sinadegree A2sid
11 Augmented 1-sinadegree A1sid
10 Augmented 0-sinadegree A0sid
9 Augmented 9-sinadegree A9sid
8 Major 8-sinadegree M8sid
7 Major 7-sinadegree M7sid
6 Major 6-sinadegree M6sid
5 Major 5-sinadegree M5sid
4 Major 4-sinadegree M4sid
3 Major 3-sinadegree M3sid
2 Major 2-sinadegree M2sid
1 Perfect 1-sinadegree P1sid
0 Perfect 0-sinadegree
Perfect 10-sinadegree		 P0sid
P10sid
−1 Perfect 9-sinadegree P9sid
−2 Minor 8-sinadegree m8sid
−3 Minor 7-sinadegree m7sid
−4 Minor 6-sinadegree m6sid
−5 Minor 5-sinadegree m5sid
−6 Minor 4-sinadegree m4sid
−7 Minor 3-sinadegree m3sid
−8 Minor 2-sinadegree m2sid
−9 Diminished 1-sinadegree d1sid
−10 Diminished 10-sinadegree d10sid
−11 Diminished 9-sinadegree d9sid
−12 Diminished 8-sinadegree d8sid
−13 Diminished 7-sinadegree d7sid
−14 Diminished 6-sinadegree d6sid
−15 Diminished 5-sinadegree d5sid
−16 Diminished 4-sinadegree d4sid
−17 Diminished 3-sinadegree d3sid
−18 Diminished 2-sinadegree d2sid

Modes

Scale degrees of the modes of 9L 1s
UDP Cyclic
order 		Step
pattern 		Scale degree (sinadegree)
0 1 2 3 4 5 6 7 8 9 10
9|0 1 LLLLLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf.
8|1 2 LLLLLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|2 3 LLLLLLLsLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf.
6|3 4 LLLLLLsLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf.
5|4 5 LLLLLsLLLL Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf.
4|5 6 LLLLsLLLLL Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf.
3|6 7 LLLsLLLLLL Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf.
2|7 8 LLsLLLLLLL Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf.
1|8 9 LsLLLLLLLL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|9 10 sLLLLLLLLL Perf. Dim. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.

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
Todo: complete table , add examples, improve synopsis

Populate scale tree

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