9L 1s
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Scale structure
Step pattern
LLLLLLLLLs
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Step size ranges
Large
1\10 to 1\9 (120.0¢ to 133.3¢)
Small
0\9 to 1\10 (0.0¢ to 120.0¢)
Generator ranges
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 scales
Parent
1L 8s
Sister
1L 9s
Daughters
10L 9s
9L 10s
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¢)
Todo: expand
Populate scale tree
| ←8L 1s | 9L 1s | 10L 1s→ |
| ↙8L 2s | ↓9L 2s | 10L 2s↘ |
9L 10s
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
| 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
| Generator (in steps of edo) | Cents | Step ratio | Comments (Every tuning produces a proper scale) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 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 | |||||