3L 10s: Difference between revisions
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{{Infobox MOS}} | {{Infobox MOS}} | ||
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Some notable temperaments that form a | Some notable temperaments that form a mos with this pattern are [[magic]] and [[würschmidt]]. Of course, Magic[13] is still slightly improper and Würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13-tone-per-octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13-tone circles favor multiple times over. | ||
== Scale properties == | == Scale properties == | ||
| Line 10: | Line 9: | ||
== Scale tree == | == Scale tree == | ||
{{MOS tuning spectrum}} | {{MOS tuning spectrum | ||
| 3/2 = [[Sephiroth]] | |||
| 13/8 = Golden sephiroth | |||
| 13/5 = Unnamed golden tuning | |||
| 8/3 = [[Muggles]] | |||
| 10/3 = [[Magic]] / witchcraft | |||
| 7/2 = Magic | |||
| 11/3 = Magic / necromancy | |||
| 9/2 = [[Marveltri]] | |||
| 6/1 = [[Würschmidt]] ↓ | |||
}} | |||
[[Category:Abstract MOS patterns]] | [[Category:Abstract MOS patterns]] | ||
Revision as of 08:00, 3 March 2025
| ↖ 2L 9s | ↑ 3L 9s | 4L 9s ↗ |
| ← 2L 10s | 3L 10s | 4L 10s → |
| ↙ 2L 11s | ↓ 3L 11s | 4L 11s ↘ |
Scale structure
ssssLsssLsssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
3L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 10 small steps, repeating every octave. 3L 10s is a child scale of 3L 7s, expanding it by 3 tones. Generators that produce this scale range from 369.2 ¢ to 400 ¢, or from 800 ¢ to 830.8 ¢.
Some notable temperaments that form a mos with this pattern are magic and würschmidt. Of course, Magic[13] is still slightly improper and Würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13-tone-per-octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13-tone circles favor multiple times over.
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.
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Template:MOS data is deprecated.
Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 4\13 | 369.231 | 830.769 | 1:1 | 1.000 | Equalized 3L 10s | |||||
| 21\68 | 370.588 | 829.412 | 6:5 | 1.200 | ||||||
| 17\55 | 370.909 | 829.091 | 5:4 | 1.250 | ||||||
| 30\97 | 371.134 | 828.866 | 9:7 | 1.286 | ||||||
| 13\42 | 371.429 | 828.571 | 4:3 | 1.333 | Supersoft 3L 10s | |||||
| 35\113 | 371.681 | 828.319 | 11:8 | 1.375 | ||||||
| 22\71 | 371.831 | 828.169 | 7:5 | 1.400 | ||||||
| 31\100 | 372.000 | 828.000 | 10:7 | 1.429 | ||||||
| 9\29 | 372.414 | 827.586 | 3:2 | 1.500 | Soft 3L 10s Sephiroth | |||||
| 32\103 | 372.816 | 827.184 | 11:7 | 1.571 | ||||||
| 23\74 | 372.973 | 827.027 | 8:5 | 1.600 | ||||||
| 37\119 | 373.109 | 826.891 | 13:8 | 1.625 | Golden sephiroth | |||||
| 14\45 | 373.333 | 826.667 | 5:3 | 1.667 | Semisoft 3L 10s | |||||
| 33\106 | 373.585 | 826.415 | 12:7 | 1.714 | ||||||
| 19\61 | 373.770 | 826.230 | 7:4 | 1.750 | ||||||
| 24\77 | 374.026 | 825.974 | 9:5 | 1.800 | ||||||
| 5\16 | 375.000 | 825.000 | 2:1 | 2.000 | Basic 3L 10s Scales with tunings softer than this are proper | |||||
| 21\67 | 376.119 | 823.881 | 9:4 | 2.250 | ||||||
| 16\51 | 376.471 | 823.529 | 7:3 | 2.333 | ||||||
| 27\86 | 376.744 | 823.256 | 12:5 | 2.400 | ||||||
| 11\35 | 377.143 | 822.857 | 5:2 | 2.500 | Semihard 3L 10s | |||||
| 28\89 | 377.528 | 822.472 | 13:5 | 2.600 | Unnamed golden tuning | |||||
| 17\54 | 377.778 | 822.222 | 8:3 | 2.667 | Muggles | |||||
| 23\73 | 378.082 | 821.918 | 11:4 | 2.750 | ||||||
| 6\19 | 378.947 | 821.053 | 3:1 | 3.000 | Hard 3L 10s | |||||
| 19\60 | 380.000 | 820.000 | 10:3 | 3.333 | Magic / witchcraft | |||||
| 13\41 | 380.488 | 819.512 | 7:2 | 3.500 | Magic | |||||
| 20\63 | 380.952 | 819.048 | 11:3 | 3.667 | Magic / necromancy | |||||
| 7\22 | 381.818 | 818.182 | 4:1 | 4.000 | Superhard 3L 10s | |||||
| 15\47 | 382.979 | 817.021 | 9:2 | 4.500 | Marveltri | |||||
| 8\25 | 384.000 | 816.000 | 5:1 | 5.000 | ||||||
| 9\28 | 385.714 | 814.286 | 6:1 | 6.000 | Würschmidt ↓ | |||||
| 1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 10s | |||||