Amity: Difference between revisions
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'''Amity''' (46 & 53 | '''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. | Amity is a 7-cluster temperament due to its generator being only slightly flatter than 2\7. | ||
== Interval chain == | == Interval chain == | ||
Notes: | |||
* 1 gen = 128/105 ~ 243/200 ~ 39/32 | * 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. | |||
<br/> | |||
* 1 gen = 128/105 ~ 243/200 ~ 39/32 (=> tempers out 5120/5103 = S8/S9 and 4096/4095 = S64) | |||
* 2 gens = 40/27 | * 2 gens = 40/27 | ||
* 3 gens = 9/5 | * 3 gens = 9/5 | ||
* 4 gens = 35/32 | * 4 gens = 35/32 | ||
* 5 gens = '''4/3''' | * 5 gens = '''4/3''' | ||
* 6 gens = '''13/8''' ~ 21/13 (=> S13 is tempered out) | * 6 gens = '''13/8''' ~ 21/13 (=> S13 is tempered out) | ||
* 7 gens = | * 7 gens = 80/81 ~ 63/64 ~ 64/65 | ||
* 8 gens = 6/5 | * 8 gens = 6/5 | ||
* 9 gens = | * 9 gens = 48/35 | ||
* 10 gens = '''16/9''' | * 10 gens = '''16/9''' | ||
* 11 gens = 13/12 ~ 14/13 | * 11 gens = 13/12 ~ 14/13 | ||
* 12 gens = 21/16 | * 12 gens = 21/16 | ||
* 13 gens = '''8/5''' | * 13 gens = '''8/5''' | ||
* 14 gens = | * 14 gens = 35/36 | ||
* 15 gens = 32/27 | * 15 gens = 32/27 | ||
* 16 gens = 36/25 ~ 13/9 | * 16 gens = 36/25 ~ 13/9 | ||
* 17 gens = '''7/4''' | * 17 gens = '''7/4''' | ||
| Line 24: | Line 27: | ||
* 19 gens = 13/10 | * 19 gens = 13/10 | ||
* 20 gens = 128/81 | * 20 gens = 128/81 | ||
* 21 gens = | * 21 gens = 20/21 ~ 24/25 | ||
* 22 gens = 7/6 | * 22 gens = 7/6 | ||
* 23 gens = 64/45 | * 23 gens = 64/45 | ||
* 24 gens = 26/15 | * 24 gens = 26/15 | ||
* 25 gens = 256/243 | * 25 gens = 256/243 | ||
* 26 gens = 32/25 | * 26 gens = 32/25 | ||
* 27 gens = 14/9 | * 27 gens = 14/9 | ||
== List of patent vals == | |||
:''Main article: [[Amity/Patent vals]]'' | |||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|temperaments}} | {{Cat|temperaments}} | ||
Latest revision as of 23:49, 3 April 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 tends 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
- 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 • Leapday • 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 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperament | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
