Amity: Difference between revisions

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'''Amity''' (from "acute minor third"), 2.3.5.7[{{e|46}} & {{e|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 7: Line 7:
* The extension to 13 given is called Hitchcock, whose 13 mapping tends 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
{| class="wikitable"
* 3 gens = 9/5
!|# gens up !! 13-lim. interpretation !! Notes
* 4 gens = 35/32
|-
* 5 gens = '''4/3'''
!|1
* 6 gens = '''13/8''' ~ 21/13 (=> S13 is tempered out)
||128/105 ~ 243/200 ~ 39/32||tempers out 5120/5103 = S8/S9 and 4096/4095 = S64
* 7 gens = 80/81 ~ 63/64 ~ 64/65
|-
* 8 gens = 6/5
!|2
* 9 gens = 48/35
||40/27||
* 10 gens = '''16/9'''
|-
* 11 gens = 13/12 ~ 14/13
!|3
* 12 gens = 21/16
||9/5||
* 13 gens = '''8/5'''
|-
* 14 gens = 35/36
!|4
* 15 gens = 32/27
||35/32||
* 16 gens = 36/25 ~ 13/9
|-
* 17 gens = '''7/4'''
!|5
* 18 gens = '''16/15'''
||'''4/3'''||
* 19 gens = 13/10
|-
* 20 gens = 128/81
!|6
* 21 gens = 20/21 ~ 24/25
||'''13/8''' ~ 21/13||S13 is tempered out
* 22 gens = 7/6
|-
* 23 gens = 64/45
!|7
* 24 gens = 26/15
||80/81 ~ 63/64 ~ 64/65||
* 25 gens = 256/243
|-
* 26 gens = 32/25
!|8
* 27 gens = 14/9
||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 ==
== List of patent vals ==

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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