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]]

Revision as of 06:50, 13 July 2021

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.

It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out 169/168, 325/324, 351/350, 364/363, 1001/1000, and 4096/4095. The 152f val tempers out 352/351, 625/624, 640/637, 729/728, 847/845, 1575/1573, 1716/1715 and 2080/2079.

It provides the optimal patent val for the 11-limit grendel and kwai linear temperaments, the 13-limit rank two temperament octopus, the 11-limit planar temperament laka, and the rank five temperament tempering out 169/168.

Paul Erlich has suggested that 152edo could be considered a sort of universal tuning.

152 = 8 × 19, with divisors 2, 4, 8, 19, 38, 76.

Prime harmonics

Script error: No such module "primes_in_edo".

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [241 -152⟩ [⟨152 241]] -0.213 0.213 2.70
2.3.5 1600000/1594323, [32 -7 -9⟩ [⟨152 241 353]] -0.218 0.174 2.21
2.3.5.7 4375/4374, 5120/5103, 16875/16807 [⟨152 241 353 427]] -0.362 0.291 3.69
2.3.5.7.11 540/539, 1375/1372, 4000/3993, 5120/5103 [⟨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 [⟨152 241 353 427 526 563]] (152f) -0.494 0.373 4.73

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
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
(33\152) 		339.47
(260.53) 		243/200
(64/55) 		Hemiamity
2 55\152
(21\152) 		434.21
(165.79) 		9/7
(11/10) 		Supers
4 63\152
(13\152) 		497.37
(102.63) 		4/3
(35/33) 		Undim
8 74\152
(2\152) 		584.21
(15.79) 		7/5
(126/125) 		Octoid (152f) / octopus (152)
19 63\152
(1\152) 		497.37
(7.89) 		4/3
(225/224) 		Enneadecal
38 63\152
(1\152) 		497.37
(7.89) 		4/3
(225/224) 		Hemienneadecal
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