Amity: Difference between revisions

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* 27 gens = 14/9
* 27 gens = 14/9


== List of patent vals ==
The following are non-contorted 5-limit patent vals supporting Amity:
{| class="wikitable sortable"
|-
!Edo!!Generator!!Fifth
|-
|39||338.462||707.692
|-
|46||339.130||704.348
|-
|92||339.130||704.348
|-
|145||339.310||703.448
|-
|244||339.344||703.279
|-
|99||339.394||703.030
|-
|198||339.394||703.030
|-
|297||339.394||703.030
|-
|449||339.421||702.895
|-
|350||339.429||702.857
|-
|251||339.442||702.789
|-
|502||339.442||702.789
|-
|654||339.450||702.752
|-
|403||339.454||702.730
|-
|555||339.459||702.703
|-
|707||339.463||702.687
|-
|152||339.474||702.632
|-
|304||339.474||702.632
|-
|456||339.474||702.632
|-
|608||339.474||702.632
|-
|760||339.474||702.632
|-
|813||339.483||702.583
|-
|661||339.486||702.572
|-
|509||339.489||702.554
|-
|866||339.492||702.540
|-
|357||339.496||702.521
|-
|714||339.496||702.521
|-
|919||339.499||702.503
|-
|562||339.502||702.491
|-
|767||339.505||702.477
|-
|972||339.506||702.469
|-
|1177||339.507||702.464
|-
|205||339.512||702.439
|-
|410||339.512||702.439
|-
|615||339.512||702.439
|-
|820||339.512||702.439
|-
|1025||339.512||702.439
|-
|1230||339.512||702.439
|-
|1283||339.517||702.416
|-
|1078||339.518||702.412
|-
|873||339.519||702.405
|-
|668||339.521||702.395
|-
|1336||339.521||702.395
|-
|1131||339.523||702.387
|-
|463||339.525||702.376
|-
|926||339.525||702.376
|-
|1389||339.525||702.376
|-
|1184||339.527||702.365
|-
|721||339.528||702.358
|-
|1442||339.528||702.358
|-
|979||339.530||702.349
|-
|1237||339.531||702.344
|-
|1495||339.532||702.341
|-
|258||339.535||702.326
|-
|516||339.535||702.326
|-
|774||339.535||702.326
|-
|1032||339.535||702.326
|-
|1290||339.535||702.326
|-
|1548||339.535||702.326
|-
|1601||339.538||702.311
|-
|1343||339.538||702.308
|-
|1085||339.539||702.304
|-
|827||339.541||702.297
|-
|1654||339.541||702.297
|-
|1396||339.542||702.292
|-
|569||339.543||702.285
|-
|1138||339.543||702.285
|-
|1449||339.545||702.277
|-
|880||339.545||702.273
|-
|1191||339.547||702.267
|-
|311||339.550||702.251
|-
|622||339.550||702.251
|-
|933||339.550||702.251
|-
|1244||339.550||702.251
|-
|986||339.554||702.231
|-
|675||339.556||702.222
|-
|1039||339.557||702.214
|-
|364||339.560||702.198
|-
|728||339.560||702.198
|-
|781||339.565||702.177
|-
|417||339.568||702.158
|-
|834||339.568||702.158
|-
|470||339.574||702.128
|-
|523||339.579||702.103
|-
|576||339.583||702.083
|-
|629||339.587||702.067
|-
|53||339.623||701.887
|-
|106||339.623||701.887
|-
|159||339.623||701.887
|-
|212||339.623||701.887
|-
|265||339.623||701.887
|-
|318||339.623||701.887
|-
|371||339.623||701.887
|-
|424||339.623||701.887
|-
|166||339.759||701.205
|-
|113||339.823||700.885
|-
|60||340.000||700.000
|-
|7||342.857||685.714
|}
{{Navbox regtemp}}
{{Navbox regtemp}}
{{Cat|temperaments}}
{{Cat|temperaments}}

Revision as of 08:51, 28 March 2026

Amity (from "acute minor third"), 2.3.5.7[46 & 53], is a complex temperament splitting 8/3 into 5 supraminor thirds about 339c-340c in size. It has a tuning that is very accurate in the 7-limit (namely 99edo).

Amity is a 7-cluster temperament due to its generator being only slightly flatter than 2\7.

Interval chain

Notes:

  • 243/200 is 6/5 sharpened by 81/80.
  • The extension to 13 given is called Hitchcock, whose 13 mapping tend to be flat due to tempering out S13.


  • 1 gen = 128/105 ~ 243/200 ~ 39/32 (=> tempers out 5120/5103 = S8/S9 and 4096/4095 = S64)
  • 2 gens = 40/27
  • 3 gens = 9/5
  • 4 gens = 35/32
  • 5 gens = 4/3
  • 6 gens = 13/8 ~ 21/13 (=> S13 is tempered out)
  • 7 gens = 80/81 ~ 63/64 ~ 64/65
  • 8 gens = 6/5
  • 9 gens = 48/35
  • 10 gens = 16/9
  • 11 gens = 13/12 ~ 14/13
  • 12 gens = 21/16
  • 13 gens = 8/5
  • 14 gens = 35/36
  • 15 gens = 32/27
  • 16 gens = 36/25 ~ 13/9
  • 17 gens = 7/4
  • 18 gens = 16/15
  • 19 gens = 13/10
  • 20 gens = 128/81
  • 21 gens = 20/21 ~ 24/25
  • 22 gens = 7/6
  • 23 gens = 64/45
  • 24 gens = 26/15
  • 25 gens = 256/243
  • 26 gens = 32/25
  • 27 gens = 14/9

List of patent vals

The following are non-contorted 5-limit patent vals supporting Amity:

Edo Generator Fifth
39 338.462 707.692
46 339.130 704.348
92 339.130 704.348
145 339.310 703.448
244 339.344 703.279
99 339.394 703.030
198 339.394 703.030
297 339.394 703.030
449 339.421 702.895
350 339.429 702.857
251 339.442 702.789
502 339.442 702.789
654 339.450 702.752
403 339.454 702.730
555 339.459 702.703
707 339.463 702.687
152 339.474 702.632
304 339.474 702.632
456 339.474 702.632
608 339.474 702.632
760 339.474 702.632
813 339.483 702.583
661 339.486 702.572
509 339.489 702.554
866 339.492 702.540
357 339.496 702.521
714 339.496 702.521
919 339.499 702.503
562 339.502 702.491
767 339.505 702.477
972 339.506 702.469
1177 339.507 702.464
205 339.512 702.439
410 339.512 702.439
615 339.512 702.439
820 339.512 702.439
1025 339.512 702.439
1230 339.512 702.439
1283 339.517 702.416
1078 339.518 702.412
873 339.519 702.405
668 339.521 702.395
1336 339.521 702.395
1131 339.523 702.387
463 339.525 702.376
926 339.525 702.376
1389 339.525 702.376
1184 339.527 702.365
721 339.528 702.358
1442 339.528 702.358
979 339.530 702.349
1237 339.531 702.344
1495 339.532 702.341
258 339.535 702.326
516 339.535 702.326
774 339.535 702.326
1032 339.535 702.326
1290 339.535 702.326
1548 339.535 702.326
1601 339.538 702.311
1343 339.538 702.308
1085 339.539 702.304
827 339.541 702.297
1654 339.541 702.297
1396 339.542 702.292
569 339.543 702.285
1138 339.543 702.285
1449 339.545 702.277
880 339.545 702.273
1191 339.547 702.267
311 339.550 702.251
622 339.550 702.251
933 339.550 702.251
1244 339.550 702.251
986 339.554 702.231
675 339.556 702.222
1039 339.557 702.214
364 339.560 702.198
728 339.560 702.198
781 339.565 702.177
417 339.568 702.158
834 339.568 702.158
470 339.574 702.128
523 339.579 702.103
576 339.583 702.083
629 339.587 702.067
53 339.623 701.887
106 339.623 701.887
159 339.623 701.887
212 339.623 701.887
265 339.623 701.887
318 339.623 701.887
371 339.623 701.887
424 339.623 701.887
166 339.759 701.205
113 339.823 700.885
60 340.000 700.000
7 342.857 685.714


View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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