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152edo: Difference between revisions

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The '''152 equal division''' divides the octave into 152 equally sized parts of 7.895 cents each.  
The '''152 equal division''' divides the octave into 152 equally sized parts of 7.895 cents each.  


== Theory ==
152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323, the [[amity comma]], in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[4000/3993]], 5632/5625 and [[9801/9800]] in the 11-limit.  
152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323, the [[amity comma]], in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[4000/3993]], 5632/5625 and [[9801/9800]] in the 11-limit.  


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[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].
[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].


152 = 8 × 19, with divisors 2, 4, 8, 19, 38, 76.
152 = 8 × 19, with divisors 2, 4, 8, 19, 38, 76.  
 
=== Prime harmonics ===
{{Primes in edo|152}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 241 -152 }}
| [{{val| 152 241 }}]
| -0.213
| 0.213
| 2.70
|-
| 2.3.5
| 1600000/1594323, {{monzo| 32 -7 -9 }}
| [{{val| 152 241 353 }}]
| -0.218
| 0.174
| 2.21
|-
| 2.3.5.7
| 4375/4374, 5120/5103, 16875/16807
| [{{val| 152 241 353 427 }}]
| -0.362
| 0.291
| 3.69
|-
| 2.3.5.7.11
| 540/539, 1375/1372, 4000/3993, 5120/5103
| [{{val| 152 241 353 427 526 }}]
| -0.365
| 0.260
| 3.30
|-
| 2.3.5.7.11.13
| 352/351, 540/539, 625/624, 729/728, 1575/1573
| [{{val| 152 241 353 427 526 563 }}] (152f)
| -0.494
| 0.373
| 4.73
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 1
| 7\152
| 55.26
| 33/32
| [[Escapade]] / [[alphaquarter]]
|-
| 1
| 31\152
| 244.74
| 15/13
| [[Subsemifourth]]
|-
| 1
| 39\152
| 307.89
| 3200/2673
| [[Familia]]
|-
| 1
| 43\152
| 339.47
| 243/200
| [[Amity]]
|-
| 1
| 49\152
| 386.84
| 5/4
| [[Grendel]]
|-
| 1
| 63\152
| 497.37
| 4/3
| [[Kwai]]
|-
| 1
| 71\152
| 560.53
| 242/175
| [[Whoosh]] / [[whoops]]
|-
| 2
| 7\152
| 55.26
| 33/32
| [[Biscapade]]
|-
| 2
| 9\152
| 71.05
| 25/24
| [[Vishnuzmic]] / [[vishnu]] / [[acyuta]] (152f) / [[ananta]] (152)
|-
| 2
| 43\152<br>(33\152)
| 339.47<br>(260.53)
| 243/200<br>(64/55)
| [[Hemiamity]]
|-
| 2
| 55\152<br>(21\152)
| 434.21<br>(165.79)
| 9/7<br>(11/10)
| [[Supers]]
|-
| 4
| 63\152<br>(13\152)
| 497.37<br>(102.63)
| 4/3<br>(35/33)
| [[Undim]]
|-
| 8
| 74\152<br>(2\152)
| 584.21<br>(15.79)
| 7/5<br>(126/125)
| [[Octoid]] (152f) / [[octopus]] (152)
|-
| 19
| 63\152<br>(1\152)
| 497.37<br>(7.89)
| 4/3<br>(225/224)
| [[Enneadecal]]
|-
| 38
| 63\152<br>(1\152)
| 497.37<br>(7.89)
| 4/3<br>(225/224)
| [[Hemienneadecal]]
|}


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Grendel]]
[[Category:Grendel]]
[[Category:Kwai]]
[[Category:Kwai]]
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