17L 12s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS
| nLargeSteps=17
| nLargeSteps=17
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}}
}}
{{MOS intro}}
{{MOS intro}}
This MOS, belonging to the Leapday and Grackle temperaments, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of [[17edo]] and [[29edo]] and divides at [[80edo]] into [[Margo Schulter]]'s [[gentle region]] extending down to 29edo and a yet-unnamed region extending up to 17edo. Only the latter region will be catalouged here, as cataloguing the former in a second place is inefficient.
This MOS, belonging to the Leapday and Grackle temperaments, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of [[17edo]] and [[29edo]] and divides at [[80edo]] into [[Margo Schulter]]'s [[gentle region]] extending down to 29edo and a yet-unnamed region extending up to 17edo.
 
== Scale tree ==
{| class="wikitable"
{{Scale tree}}
|-
| | 47/80
| |
| |
| |
| |
| |
| |
| | 705
| | <span style="background-color: #ffffff;">&lt; 80 127 225|</span>
|-
| |
| |
| |
| |
| |
| |
| | 292/497
| | 705.03
| | &lt; 497 789 1395|
|-
| |
| |
| |
| |
| |
| | 245/417
| |
| | 705.036
| | &lt; 417 662 1171|
|-
| |
| |
| |
| |
| |
| |
| | 443/754
| | 705.04
| | &lt; 754 1197 2117|
|-
| |
| |
| |
| |
| | 198/337
| |
| |
| | 705.0445
| | &lt; 337 535 946|
|-
| |
| |
| |
| |
| |
| |
| | 547/931
| | 705.048
| | &lt; 931 1478 2614|
|-
| |
| |
| |
| |
| |
| | 349/594
| |
| | 705 5/99
| | &lt; 594 943 1668|
|-
| |
| |
| |
| |
| |
| |
| | 500/851
| | 705.053
| | &lt; 851 1351 2389|
|-
| |
| |
| |
| | 151/257
| |
| |
| |
| | 705.058
| | &lt; 257 408 721|
|-
| |
| |
| |
| |
| |
| |
| | 557/948
| | 705.063
| | &lt; 948 1505 2661|
|-
| |
| |
| |
| |
| |
| | 406/691
| |
| | 705.065
| | &lt; 691 1095 1940|
|-
| |
| |
| |
| |
| |
| |
| | 661/1125
| | 705.067
| | &lt; 1125 1786 3158|
|-
| |
| |
| |
| |
| | 255/434
| |
| |
| | 705.069
| | &lt; 434 689 1218|
|-
| |
| |
| |
| |
| |
| |
| | 614/1045
| | 705.072
| | &lt; 1045 1659 2934|
|-
| |
| |
| |
| |
| |
| | 359/611
| |
| | 705.074
| | &lt; 611 970 1715|
|-
| |
| |
| |
| |
| |
| |
| | 463/788
| | 705.076
| | &lt; 788 1251 2212|
|-
| |
| |
| | 104/177
| |
| |
| |
| |
| | 705.085
| | &lt; 177 281 497|
|-
| |
| |
| |
| |
| |
| |
| | 473/805
| | 705.093
| | &lt; 805 1278 2260|
|-
| |
| |
| |
| |
| |
| | 369/628
| |
| | 705.0955
| | &lt; 628 997 1763|
|-
| |
| |
| |
| |
| |
| |
| | 634/1079
| | 705.097
| | &lt; 1079 1713 3029|
|-
| |
| |
| |
| |
| | 265/451
| |
| |
| | 705.1
| | &lt; 451 716 1266|
|-
| |
| |
| |
| |
| |
| |
| | 691/1176
| | 705.102
| | &lt; 1176 1867 3301|
|-
| |
| |
| |
| |
| |
| |
| |
| | 705.102
| | &lt; 17 27 48|+
 
<span style="background-color: #ffffff;">&lt; 80 127 225|*phi</span>
|-
| |
| |
| |
| |
| |
| | 426/725
| |
| | 705.103
| | &lt; 725 1151 2035|
|-
| |
| |
| |
| |
| |
| |
| | 587/999
| | 705.105
| | &lt; 999 1586 2805|
|-
| |
| |
| |
| | 161/274
| |
| |
| |
| | 705.1095
| | &lt; 274 435 769|
|-
| |
| |
| |
| |
| |
| |
| | 540/919
| | 705.114
| | &lt; 919 1459 2580|
|-
| |
| |
| |
| |
| |
| | 379/645
| |
| | 705.116
| | &lt; 645 1024 1811|
|-
| |
| |
| |
| |
| |
| |
| | 597/1016
| | 705.118
| | &lt; 1016 1613 2852|
|-
| |
| |
| |
| |
| | 218/371
| |
| |
| | 705.121
| | &lt; 371 589 1042|
|-
| |
| |
| |
| |
| |
| |
| | 493/839
| | 705.125
| | &lt; 839 1332 2355|
|-
| |
| |
| |
| |
| |
| | 275/468
| |
| | 705.128
| | &lt; 468 743 1314|
|-
| |
| |
| |
| |
| |
| |
| | 332/565
| | 705.133
| | &lt; 565 897 1586|
|-
| |
| | 57/97
| |
| |
| |
| |
| |
| | 705.155
| | &lt; 97 154 272|
|-
| |
| |
| |
| |
| |
| |
| | 295/502
| | 705.179
| | &lt; 502 797 1409|
|-
| |
| |
| |
| |
| |
| | 238/405
| |
| | 705.185
| | &lt; 405 643 1137|
|-
| |
| |
| |
| |
| |
| |
| | 419/713
| | 705.189
| | &lt; 713 1132 2002|
|-
| |
| |
| |
| |
| | 181/308
| |
| |
| | 705.195
| | &lt; 308 489 865|
|-
| |
| |
| |
| |
| |
| |
| | 486/827
| | 705.1995
| | &lt; 827 1313 2322|
|-
| |
| |
| |
| |
| |
| | 305/519
| |
| | 705.202
| | &lt; 519 824 1457|
|-
| |
| |
| |
| |
| |
| |
| | 429/730
| | 705.2055
| | &lt; 730 1159 2049|
|-
| |
| |
| |
| | 124/211
| |
| |
| |
| | 705.213
| | &lt; 211 335 592|
|-
| |
| |
| |
| |
| |
| |
| | 439/747
| | 705.221
| | &lt; 747 1186 2097|
|-
| |
| |
| |
| |
| |
| | 315/536
| |
| | 705.224
| | &lt; 536 851 1505|
|-
| |
| |
| |
| |
| |
| |
| | 506/861
| | 705.2265
| | &lt; 861 1367 2417|
|-
| |
| |
| |
| |
| | 191/325
| |
| |
| | 705.231
| | &lt; 325 516 912|
|-
| |
| |
| |
| |
| |
| |
| | 449/764
| | 705.236
| | &lt; 764 1213 2145|
|-
| |
| |
| |
| |
| |
| | 258/439
| |
| | 705.239
| | &lt; 439 697 1232|
|-
| |
| |
| |
| |
| |
| |
| | 325/553
| | 705.244
| | &lt; 553 878 1552|
|-
| |
| |
| | 67/114
| |
| |
| |
| |
| | 705.263
| | &lt; 114 181 320|
|-
| |
| |
| |
| |
| |
| |
| | 278/473
| | 705.285
| | &lt; 473 751 1328|
|-
| |
| |
| |
| |
| |
| | 211/359
| |
| | 705.2925
| | &lt; 359 570 1008|
|-
| |
| |
| |
| |
| |
| |
| | 355/604
| | 705.298
| | &lt; 604 959 1696|
|-
| |
| |
| |
| |
| | 144/245
| |
| |
| | 705.306
| | &lt; 245 389 688|
|-
| |
| |
| |
| |
| |
| |
| | 365/621
| | 705.314
| | &lt; 621 986 1743|
|-
| |
| |
| |
| |
| |
| | 221/376
| |
| | 705.319
| | &lt; 376 597 1056|
|-
| |
| |
| |
| |
| |
| |
| | 298/507
| | 705.325
| | &lt; 507 805 1423|
|-
| |
| |
| |
| | 77/131
| |
| |
| |
| | 705.3435
| | &lt; 131 208 368|
|-
| |
| |
| |
| |
| |
| |
| | 241/410
| | 705.366
| | &lt; 410 651 1151|
|-
| |
| |
| |
| |
| |
| | 164/279
| |
| | 705.376
| | &lt; 279 443 783|
|-
| |
| |
| |
| |
| |
| |
| | 251/427
| | 705.386
| | &lt; 427 678 1199|
|-
| |
| |
| |
| |
| | 87/148
| |
| |
| | 705.405
| | &lt; 148 235 415|
|-
| |
| |
| |
| |
| |
| |
| | 184/313
| | 705.431
| | &lt; 313 495 879|
|-
| |
| |
| |
| |
| |
| | 97/165
| |
| | 705.4545
| | &lt; 165 262 463|
|-
| |
| |
| |
| |
| |
| |
| | 107/182
| | 705.4945
| | &lt; 182 289 511|
|-
| | 10/17
| |
| |
| |
| |
| |
| |
| | 705.882
| | &lt; 17 27 48|
|}
 
[[Category:29-tone scales]]

Revision as of 07:50, 21 March 2024

Todo: cleanup

populate with entries

↖ 16L 11s ↑ 17L 11s 18L 11s ↗
← 16L 12s 17L 12s 18L 12s →
↙ 16L 13s ↓ 17L 13s 18L 13s ↘
Scale structure
Step pattern LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLsLLsLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\29 to 10\17 (703.4 ¢ to 705.9 ¢)
Dark 7\17 to 12\29 (494.1 ¢ to 496.6 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 5:2 to 3:1 (quasihard)
Related MOS scales
Parent 12L 5s
Sister 12L 17s
Daughters 29L 17s, 17L 29s
Neutralized 5L 24s
2-Flought 46L 12s, 17L 41s
Equal tunings
Equalized (L:s = 1:1) 17\29 (703.4 ¢)
Supersoft (L:s = 4:3) 61\104 (703.8 ¢)
Soft (L:s = 3:2) 44\75 (704.0 ¢)
Semisoft (L:s = 5:3) 71\121 (704.1 ¢)
Basic (L:s = 2:1) 27\46 (704.3 ¢)
Semihard (L:s = 5:2) 64\109 (704.6 ¢)
Hard (L:s = 3:1) 37\63 (704.8 ¢)
Superhard (L:s = 4:1) 47\80 (705.0 ¢)
Collapsed (L:s = 1:0) 10\17 (705.9 ¢)
ViewTalkEdit

17L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 12 small steps, repeating every octave. 17L 12s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 703.4 ¢ to 705.9 ¢, or from 494.1 ¢ to 496.6 ¢. This MOS, belonging to the Leapday and Grackle temperaments, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of 17edo and 29edo and divides at 80edo into Margo Schulter's gentle region extending down to 29edo and a yet-unnamed region extending up to 17edo.

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 17L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\29 703.448 496.552 1:1 1.000 Equalized 17L 12s
95\162 703.704 496.296 6:5 1.200
78\133 703.759 496.241 5:4 1.250
139\237 703.797 496.203 9:7 1.286
61\104 703.846 496.154 4:3 1.333 Supersoft 17L 12s
166\283 703.887 496.113 11:8 1.375
105\179 703.911 496.089 7:5 1.400
149\254 703.937 496.063 10:7 1.429
44\75 704.000 496.000 3:2 1.500 Soft 17L 12s
159\271 704.059 495.941 11:7 1.571
115\196 704.082 495.918 8:5 1.600
186\317 704.101 495.899 13:8 1.625
71\121 704.132 495.868 5:3 1.667 Semisoft 17L 12s
169\288 704.167 495.833 12:7 1.714
98\167 704.192 495.808 7:4 1.750
125\213 704.225 495.775 9:5 1.800
27\46 704.348 495.652 2:1 2.000 Basic 17L 12s
Scales with tunings softer than this are proper
118\201 704.478 495.522 9:4 2.250
91\155 704.516 495.484 7:3 2.333
155\264 704.545 495.455 12:5 2.400
64\109 704.587 495.413 5:2 2.500 Semihard 17L 12s
165\281 704.626 495.374 13:5 2.600
101\172 704.651 495.349 8:3 2.667
138\235 704.681 495.319 11:4 2.750
37\63 704.762 495.238 3:1 3.000 Hard 17L 12s
121\206 704.854 495.146 10:3 3.333
84\143 704.895 495.105 7:2 3.500
131\223 704.933 495.067 11:3 3.667
47\80 705.000 495.000 4:1 4.000 Superhard 17L 12s
104\177 705.085 494.915 9:2 4.500
57\97 705.155 494.845 5:1 5.000
67\114 705.263 494.737 6:1 6.000
10\17 705.882 494.118 1:0 → ∞ Collapsed 17L 12s