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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|152}}
{{ED intro}}


== Theory ==
== Theory ==
152edo is a strong [[11-limit]] system, with the [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] slightly sharp. It [[tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 32 -7 -9 }} ([[escapade comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the 7-limit; [[540/539]], [[1375/1372]], [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit. It provides the [[optimal patent val]] for the 11-limit linear temperaments [[amity]], [[grendel]], and [[kwai]], and the 11-limit planar temperament [[laka]].  
364edo is [[consistent]] through the [[21-odd-limit]] with good average accuracy.  


It has two reasonable mappings for 13, with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the 15-integer-limit. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the 13-limit rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].
As an equal temperament, it [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 ([[wizma]]) in the [[7-limit]] ([[support]]ing [[fifthplus]] and [[oquatonic]]); [[1375/1372]], [[6250/6237]], [[9801/9800]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]]; [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], [[10985/10976]], and 14641/14625 in the [[13-limit]]; [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], [[2431/2430]], [[4914/4913]], [[5832/5831]], and 8624/8619 in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], and [[1729/1728]] in the [[19-limit]].
 
[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|152}}
{{Harmonics in equal|364|columns=11}}
{{Harmonics in equal|364|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 364edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 152 factors into {{factorisation}}, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.  
Since 364 factors into primes as {{nowrap| 2<sup>2</sup> × 7 × 13 }}, 364edo has subset edos {{EDOs| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}.
 
=== Miscellany ===
364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after.


== Regular temperament properties ==
== Regular temperament properties ==
Line 21: Line 23:
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
Line 28: Line 30:
|-
|-
| 2.3
| 2.3
| {{monzo| 241 -152 }}
| {{Monzo| 577 -364 }}
| {{mapping| 152 241 }}
| {{Mapping| 364 577 }}
| −0.213
| −0.0766
| 0.213
| 0.0766
| 2.70
| 2.32
|-
|-
| 2.3.5
| 2.3.5
| 1600000/1594323, {{monzo| 32 -7 -9 }}
| 1600000/1594323, {{monzo| -65 0 28 }}
| {{mapping| 152 241 353 }}
| {{Mapping| 364 577 845 }}
| −0.218
| +0.0350
| 0.174
| 0.1698
| 2.21
| 5.15
|-
|-
| 2.3.5.7
| 2.3.5.7
| 4375/4374, 5120/5103, 16875/16807
| 65625/65536, 390625/388962, 420125/419904
| {{mapping| 152 241 353 427 }}
| {{Mapping| 364 577 845 1022 }}
| −0.362
| −0.0098
| 0.291
| 0.1662
| 3.69
| 5.04
|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 540/539, 1375/1372, 4000/3993, 5120/5103
| 1375/1372, 6250/6237, 19712/19683, 41503/41472
| {{mapping| 152 241 353 427 526 }}
| {{Mapping| 364 577 845 1022 1259 }}
| −0.365
| +0.0366
| 0.260
| 0.1753
| 3.30
| 5.32
|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 352/351, 540/539, 625/624, 729/728, 1575/1573
| 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625
| {{mapping| 152 241 353 427 526 563 }} (152f)
| {{Mapping| 364 577 845 1022 1259 1347 }}
| −0.494
| +0.0245
| 0.373
| 0.1622
| 4.73
| 4.92
|-
| 2.3.5.7.11.13.17
| 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197
| {{Mapping| 364 577 845 1022 1259 1347 1488 }}
| +0.0022
| 0.1599
| 4.85
|-
| 2.3.5.7.11.13.17.19
| 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728
| {{Mapping| 364 577 845 1022 1259 1347 1488 1546 }}
| +0.0257
| 0.1620
| 4.91
|}
|}
* 152et (152fg val) has lower absolute errors in the 11-, 19-, and 23-limit than any previous equal temperaments. In the 11-limit it is the first to beat [[130edo|130]] and is superseded by [[224edo|224]]. In the 19- and 23-limit it is the first to beat [[140edo|140]] and is superseded by [[159edo|159]].
* It is best at the no-17 19- and 23-limit, in which it has lower relative errors than any previous equal temperaments. Not until [[270edo|270]] do we find a better equal temperament that does better in either of those subgroups.


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
| 1
| 1
| 7\152
| 103\364
| 55.26
| 339.56
| 33/32
| 243/200
| [[Escapade]] / [[alphaquarter]]
| [[Paramity]]
|-
|-
| 1
| 1
| 31\152
| 125\364
| 244.74
| 412.09
| 15/13
| 80/63
| [[Subsemifourth]]
| [[Witcher]]
|-
|-
| 1
| 1
| 39\152
| 149\364
| 307.89
| 491.21
| 3200/2673
| 3645/2744
| [[Familia]]
| [[Fifthplus]]
|-
|-
| 1
| 1
| 43\152
| 151\364
| 339.47
| 497.80
| 243/200
| [[Amity]]
|-
| 1
| 49\152
| 386.84
| 5/4
| [[Grendel]]
|-
| 1
| 63\152
| 497.37
| 4/3
| 4/3
| [[Kwai]]
| [[Gary]]
|-
| 1
| 71\152
| 560.53
| 242/175
| [[Whoops]]
|-
| 2
| 7\152
| 55.26
| 33/32
| [[Septisuperfourth]]
|-
| 2
| 9\152
| 71.05
| 25/24
| [[Vishnu]] / [[acyuta]] (152f) / [[ananta]] (152)
|-
|-
| 2
| 2
| 43\152<br />(33\152)
| 125\364<br>(57\364)
| 339.47<br />(260.53)
| 412.09<br>(187.91)
| 243/200<br />(64/55)
| 80/63<br>(49/44)
| [[Hemiamity]]
| [[Semiwitcher]]
|-
|-
| 2
| 2
| 55\152<br />(21\152)
| 151\364<br>(31\364)
| 434.21<br />(165.79)
| 497.80<br>(102.20)
| 9/7<br />(11/10)
| 4/3<br>(35/33)
| [[Supers]]
| [[Gariwizmic]]
|-
|-
| 4
| 4
| 63\152<br />(13\152)
| 30\364
| 497.37<br />(102.63)
| 98.90
| 4/3<br />(35/33)
| 18/17
| [[Undim]] / [[unlit]]
| [[World calendar]]
|-
|-
| 8
| 13
| 63\152<br />(6\152)
| 151\364<br>(11\364)
| 497.37<br />(47.37)
| 497.80<br>(36.26)
| 4/3<br />(36/35)
| 4/3<br>(?)
| [[Twilight]]
| [[Aluminium]]
|-
|-
| 8
| 26
| 74\152<br />(2\152)
| 151\364<br>(11\364)
| 584.21<br />(15.79)
| 497.80<br>(36.26)
| 7/5<br />(126/125)
| 4/3<br>(?)
| [[Octoid]] (152f) / [[octopus]] (152)
| [[Iron]]
|-
|-
| 19
| 28
| 63\152<br />(1\152)
| 151\364<br>(5\364)
| 497.37<br />(7.89)
| 497.80<br>(16.48)
| 4/3<br />(225/224)
| 4/3<br>(105/104)
| [[Enneadecal]]
| [[Oquatonic]]
|-
|-
| 38
| 91
| 63\152<br />(1\152)
| 151\364<br>(3\364)
| 497.37<br />(7.89)
| 497.80<br>(3.30)
| 4/3<br />(225/224)
| 4/3<br>(176/175)
| [[Hemienneadecal]]
| [[Protactinium]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 
== Music ==
; [[birdshite stalactite]]
* "athlete's feet" from ''razorblade tiddlywinks'' (2023) – [https://open.spotify.com/track/32c34U3syZDMAJkBzgh2pd Spotify] | [https://birdshitestalactite.bandcamp.com/track/athletes-feet Bandcamp] | [https://www.youtube.com/watch?v=lXqVaVn3SrA YouTube]


[[Category:Amity]]
== Scales ==
[[Category:Grendel]]
* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30
[[Category:Kwai]]
[[Category:Laka]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/364edo"