Amity: Difference between revisions

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'''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''' (from "acute minor third"), {{e|46}} & {{e|53}}, is a complex [[7-limit]] 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.
Amity is a 7-cluster temperament due to its generator being only slightly flatter than 2\7.
Line 5: Line 5:
Notes:
Notes:
* 243/200 is 6/5 sharpened by 81/80.
* 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.
* The extension to 13 given is called Hitchcock, whose 13 mapping tends to be flat due to tempering out S13.
<br/>
<br/>
* 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 ==
{| class="wikitable"
The following are non-contorted 5-limit patent vals supporting Amity:
!|# gens up !! 13-lim. interpretation !! Notes
{| 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
!|1
||128/105 ~ 243/200 ~ 39/32||tempers out 5120/5103 = S8/S9 and 4096/4095 = S64
|-
|-
|866||339.492||702.540
!|2
||40/27||
|-
|-
|357||339.496||702.521
!|3
||9/5||
|-
|-
|714||339.496||702.521
!|4
||35/32||
|-
|-
|919||339.499||702.503
!|5
||'''4/3'''||
|-
|-
|562||339.502||702.491
!|6
||'''13/8''' ~ 21/13||S13 is tempered out
|-
|-
|767||339.505||702.477
!|7
||80/81 ~ 63/64 ~ 64/65||
|-
|-
|972||339.506||702.469
!|8
||6/5||
|-
|-
|1177||339.507||702.464
!|9
||48/35||
|-
|-
|205||339.512||702.439
!|10
||'''16/9'''||
|-
|-
|410||339.512||702.439
!|11
||13/12 ~ 14/13||
|-
|-
|615||339.512||702.439
!|12
||21/16||
|-
|-
|820||339.512||702.439
!|13
||'''8/5'''||
|-
|-
|1025||339.512||702.439
!|14
||35/36||
|-
|-
|1230||339.512||702.439
!|15
||32/27||
|-
|-
|1283||339.517||702.416
!|16
||36/25 ~ 13/9||
|-
|-
|1078||339.518||702.412
!|17
||'''7/4'''||
|-
|-
|873||339.519||702.405
!|18
||'''16/15'''||
|-
|-
|668||339.521||702.395
!|19
||13/10||
|-
|-
|1336||339.521||702.395
!|20
||128/81||
|-
|-
|1131||339.523||702.387
!|21
||20/21 ~ 24/25||
|-
|-
|463||339.525||702.376
!|22
||7/6||
|-
|-
|926||339.525||702.376
!|23
||64/45||
|-
|-
|1389||339.525||702.376
!|24
||26/15||
|-
|-
|1184||339.527||702.365
!|25
||256/243||
|-
|-
|721||339.528||702.358
!|26
||32/25||
|-
|-
|1442||339.528||702.358
!|27
|-
||14/9||
|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
|}
|}
== List of patent vals ==
:''Main article: [[Amity/Patent vals]]''
{{Navbox regtemp}}
{{Navbox regtemp}}
{{Cat|temperaments}}
{{Cat|temperaments}}

Latest revision as of 23:21, 29 May 2026

Amity (from "acute minor third"), ​46 & ​53, is a complex 7-limit 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 tends to be flat due to tempering out S13.


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

List of patent vals

Main article: Amity/Patent vals


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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