14L 13s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 13L 12s ↑ 14L 12s 15L 12s ↗
← 13L 13s 14L 13s 15L 13s →
↙ 13L 14s ↓ 14L 14s 15L 14s ↘ 
┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐
│║║│║│║│║│║│║│║│║│║│║│║│║│║││
│││││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsLsLsLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 25\27 to 13\14 (1111.1¢ to 1114.3¢)
Dark 1\14 to 2\27 (85.7¢ to 88.9¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 9:2 to 5:1
Related MOS scales
Parent 13L 1s
Sister 13L 14s
Daughters 27L 14s, 14L 27s
Neutralized 1L 26s
2-Flought 41L 13s, 14L 40s
Equal tunings
Equalized (L:s = 1:1) 25\27 (1111.1¢)
Supersoft (L:s = 4:3) 88\95 (1111.6¢)
Soft (L:s = 3:2) 63\68 (1111.8¢)
Semisoft (L:s = 5:3) 101\109 (1111.9¢)
Basic (L:s = 2:1) 38\41 (1112.2¢)
Semihard (L:s = 5:2) 89\96 (1112.5¢)
Hard (L:s = 3:1) 51\55 (1112.7¢)
Superhard (L:s = 4:1) 64\69 (1113.0¢)
Collapsed (L:s = 1:0) 13\14 (1114.3¢)

14L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 13 small steps, repeating every octave. 14L 13s is related to 1L 9s, expanding it by 17 tones. Generators that produce this scale range from 1111.1¢ to 1114.3¢, or from 85.7¢ to 88.9¢.

The harmonic entropy minimum for this scale has +8 dark generators equal 3/2, which is approximately 41edo.

Modes

Modes of 14L 13s
UDP Cyclic
order		 Step
pattern
26|0 1 LLsLsLsLsLsLsLsLsLsLsLsLsLs
25|1 26 LsLLsLsLsLsLsLsLsLsLsLsLsLs
24|2 24 LsLsLLsLsLsLsLsLsLsLsLsLsLs
23|3 22 LsLsLsLLsLsLsLsLsLsLsLsLsLs
22|4 20 LsLsLsLsLLsLsLsLsLsLsLsLsLs
21|5 18 LsLsLsLsLsLLsLsLsLsLsLsLsLs
20|6 16 LsLsLsLsLsLsLLsLsLsLsLsLsLs
19|7 14 LsLsLsLsLsLsLsLLsLsLsLsLsLs
18|8 12 LsLsLsLsLsLsLsLsLLsLsLsLsLs
17|9 10 LsLsLsLsLsLsLsLsLsLLsLsLsLs
16|10 8 LsLsLsLsLsLsLsLsLsLsLLsLsLs
15|11 6 LsLsLsLsLsLsLsLsLsLsLsLLsLs
14|12 4 LsLsLsLsLsLsLsLsLsLsLsLsLLs
13|13 2 LsLsLsLsLsLsLsLsLsLsLsLsLsL
12|14 27 sLLsLsLsLsLsLsLsLsLsLsLsLsL
11|15 25 sLsLLsLsLsLsLsLsLsLsLsLsLsL
10|16 23 sLsLsLLsLsLsLsLsLsLsLsLsLsL
9|17 21 sLsLsLsLLsLsLsLsLsLsLsLsLsL
8|18 19 sLsLsLsLsLLsLsLsLsLsLsLsLsL
7|19 17 sLsLsLsLsLsLLsLsLsLsLsLsLsL
6|20 15 sLsLsLsLsLsLsLLsLsLsLsLsLsL
5|21 13 sLsLsLsLsLsLsLsLLsLsLsLsLsL
4|22 11 sLsLsLsLsLsLsLsLsLLsLsLsLsL
3|23 9 sLsLsLsLsLsLsLsLsLsLLsLsLsL
2|24 7 sLsLsLsLsLsLsLsLsLsLsLLsLsL
1|25 5 sLsLsLsLsLsLsLsLsLsLsLsLLsL
0|26 3 sLsLsLsLsLsLsLsLsLsLsLsLsLL

Intervals

Intervals of 14L 13s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 44.4¢
Major 1-mosstep M1ms L 44.4¢ to 85.7¢
2-mosstep Perfect 2-mosstep P2ms L + s 85.7¢ to 88.9¢
Augmented 2-mosstep A2ms 2L 88.9¢ to 171.4¢
3-mosstep Minor 3-mosstep m3ms L + 2s 85.7¢ to 133.3¢
Major 3-mosstep M3ms 2L + s 133.3¢ to 171.4¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 171.4¢ to 177.8¢
Major 4-mosstep M4ms 3L + s 177.8¢ to 257.1¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 171.4¢ to 222.2¢
Major 5-mosstep M5ms 3L + 2s 222.2¢ to 257.1¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 257.1¢ to 266.7¢
Major 6-mosstep M6ms 4L + 2s 266.7¢ to 342.9¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 257.1¢ to 311.1¢
Major 7-mosstep M7ms 4L + 3s 311.1¢ to 342.9¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 342.9¢ to 355.6¢
Major 8-mosstep M8ms 5L + 3s 355.6¢ to 428.6¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 342.9¢ to 400.0¢
Major 9-mosstep M9ms 5L + 4s 400.0¢ to 428.6¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 428.6¢ to 444.4¢
Major 10-mosstep M10ms 6L + 4s 444.4¢ to 514.3¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 428.6¢ to 488.9¢
Major 11-mosstep M11ms 6L + 5s 488.9¢ to 514.3¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 514.3¢ to 533.3¢
Major 12-mosstep M12ms 7L + 5s 533.3¢ to 600.0¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 514.3¢ to 577.8¢
Major 13-mosstep M13ms 7L + 6s 577.8¢ to 600.0¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 600.0¢ to 622.2¢
Major 14-mosstep M14ms 8L + 6s 622.2¢ to 685.7¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 600.0¢ to 666.7¢
Major 15-mosstep M15ms 8L + 7s 666.7¢ to 685.7¢
16-mosstep Minor 16-mosstep m16ms 8L + 8s 685.7¢ to 711.1¢
Major 16-mosstep M16ms 9L + 7s 711.1¢ to 771.4¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 685.7¢ to 755.6¢
Major 17-mosstep M17ms 9L + 8s 755.6¢ to 771.4¢
18-mosstep Minor 18-mosstep m18ms 9L + 9s 771.4¢ to 800.0¢
Major 18-mosstep M18ms 10L + 8s 800.0¢ to 857.1¢
19-mosstep Minor 19-mosstep m19ms 9L + 10s 771.4¢ to 844.4¢
Major 19-mosstep M19ms 10L + 9s 844.4¢ to 857.1¢
20-mosstep Minor 20-mosstep m20ms 10L + 10s 857.1¢ to 888.9¢
Major 20-mosstep M20ms 11L + 9s 888.9¢ to 942.9¢
21-mosstep Minor 21-mosstep m21ms 10L + 11s 857.1¢ to 933.3¢
Major 21-mosstep M21ms 11L + 10s 933.3¢ to 942.9¢
22-mosstep Minor 22-mosstep m22ms 11L + 11s 942.9¢ to 977.8¢
Major 22-mosstep M22ms 12L + 10s 977.8¢ to 1028.6¢
23-mosstep Minor 23-mosstep m23ms 11L + 12s 942.9¢ to 1022.2¢
Major 23-mosstep M23ms 12L + 11s 1022.2¢ to 1028.6¢
24-mosstep Minor 24-mosstep m24ms 12L + 12s 1028.6¢ to 1066.7¢
Major 24-mosstep M24ms 13L + 11s 1066.7¢ to 1114.3¢
25-mosstep Diminished 25-mosstep d25ms 12L + 13s 1028.6¢ to 1111.1¢
Perfect 25-mosstep P25ms 13L + 12s 1111.1¢ to 1114.3¢
26-mosstep Minor 26-mosstep m26ms 13L + 13s 1114.3¢ to 1155.6¢
Major 26-mosstep M26ms 14L + 12s 1155.6¢ to 1200.0¢
27-mosstep Perfect 27-mosstep P27ms 14L + 13s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 14L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
25\27 1111.111 88.889 1:1 1.000 Equalized 14L 13s
138\149 1111.409 88.591 6:5 1.200
113\122 1111.475 88.525 5:4 1.250
201\217 1111.521 88.479 9:7 1.286
88\95 1111.579 88.421 4:3 1.333 Supersoft 14L 13s
239\258 1111.628 88.372 11:8 1.375
151\163 1111.656 88.344 7:5 1.400
214\231 1111.688 88.312 10:7 1.429
63\68 1111.765 88.235 3:2 1.500 Soft 14L 13s
227\245 1111.837 88.163 11:7 1.571
164\177 1111.864 88.136 8:5 1.600
265\286 1111.888 88.112 13:8 1.625
101\109 1111.927 88.073 5:3 1.667 Semisoft 14L 13s
240\259 1111.969 88.031 12:7 1.714
139\150 1112.000 88.000 7:4 1.750
177\191 1112.042 87.958 9:5 1.800
38\41 1112.195 87.805 2:1 2.000 Basic 14L 13s
Scales with tunings softer than this are proper
165\178 1112.360 87.640 9:4 2.250
127\137 1112.409 87.591 7:3 2.333
216\233 1112.446 87.554 12:5 2.400
89\96 1112.500 87.500 5:2 2.500 Semihard 14L 13s
229\247 1112.551 87.449 13:5 2.600
140\151 1112.583 87.417 8:3 2.667
191\206 1112.621 87.379 11:4 2.750
51\55 1112.727 87.273 3:1 3.000 Hard 14L 13s
166\179 1112.849 87.151 10:3 3.333
115\124 1112.903 87.097 7:2 3.500
179\193 1112.953 87.047 11:3 3.667
64\69 1113.043 86.957 4:1 4.000 Superhard 14L 13s
141\152 1113.158 86.842 9:2 4.500
77\83 1113.253 86.747 5:1 5.000
90\97 1113.402 86.598 6:1 6.000
13\14 1114.286 85.714 1:0 → ∞ Collapsed 14L 13s
Retrieved from "https://en.xen.wiki/index.php?title=14L_13s&oldid=170602"