17L 12s: Difference between revisions

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Replaced content with "{{todo|cleanup|inline=1|text=populate with entries}} {{Infobox MOS | nLargeSteps=17 | nSmallSteps=12 | Equalized=17 | Collapsed=10 | Pattern=LLs Ls Ls LLs Ls Ls LLs Ls Ls..."
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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 ¢)

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