Xenharmonic Wiki

9L 1s

Revision as of 02:22, 16 December 2024 by BudjarnLambeth (talk | contribs) (Many small)

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.

← 8L 1s 9L 1s 10L 1s →
↙ 8L 2s ↓ 9L 2s 10L 2s ↘
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 ¢)
View • Talk • Edit

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.

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 ¢

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

  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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

Populate scale tree

Retrieved from "https://en.xen.wiki/index.php?title=9L_1s&oldid=170996"