152edo: Difference between revisions

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| 2.3
| 2.3
| {{monzo| 241 -152 }}
| {{monzo| 241 -152 }}
| [{{val| 152 241 }}]
| {{mapping| 152 241 }}
| -0.213
| -0.213
| 0.213
| 0.213
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| 2.3.5
| 2.3.5
| 1600000/1594323, {{monzo| 32 -7 -9 }}
| 1600000/1594323, {{monzo| 32 -7 -9 }}
| [{{val| 152 241 353 }}]
| {{mapping| 152 241 353 }}
| -0.218
| -0.218
| 0.174
| 0.174
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| 2.3.5.7
| 2.3.5.7
| 4375/4374, 5120/5103, 16875/16807
| 4375/4374, 5120/5103, 16875/16807
| [{{val| 152 241 353 427 }}]
| {{mapping| 152 241 353 427 }}
| -0.362
| -0.362
| 0.291
| 0.291
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| 2.3.5.7.11
| 2.3.5.7.11
| 540/539, 1375/1372, 4000/3993, 5120/5103
| 540/539, 1375/1372, 4000/3993, 5120/5103
| [{{val| 152 241 353 427 526 }}]
| {{mapping| 152 241 353 427 526 }}
| -0.365
| -0.365
| 0.260
| 0.260
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 352/351, 540/539, 625/624, 729/728, 1575/1573
| 352/351, 540/539, 625/624, 729/728, 1575/1573
| [{{val| 152 241 353 427 526 563 }}] (152f)
| {{mapping| 152 241 353 427 526 563 }} (152f)
| -0.494
| -0.494
| 0.373
| 0.373
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|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(reduced)
! Generator*
! Cents<br>(reduced)
! Cents*
! Associated<br>ratio
! Associated<br>Ratio*
! Temperaments
! Temperaments
|-
|-
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| 560.53
| 560.53
| 242/175
| 242/175
| [[Whoosh]] / [[whoops]]
| [[Whoops]]
|-
|-
| 2
| 2
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| 55.26
| 55.26
| 33/32
| 33/32
| [[Biscapade]]
| [[Septisuperfourth]]
|-
|-
| 2
| 2
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| [[Hemienneadecal]]
| [[Hemienneadecal]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct


== Music ==
== Music ==

Revision as of 08:46, 14 May 2024

← 151edo 152edo 153edo →
Prime factorization 23 × 19
Step size 7.89474 ¢ 
Fifth 89\152 (702.632 ¢)
Semitones (A1:m2) 15:11 (118.4 ¢ : 86.84 ¢)
Consistency limit 11
Distinct consistency limit 11

Template:EDO intro

Theory

152edo is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323 (amity comma) and [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.

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, supporting and giving an excellent tuning for amity, kwai, and laka. 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.

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

Prime harmonics

Approximation of prime harmonics in 152edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.68 +0.53 +2.23 +1.31 -3.69 -2.32 +2.49 +3.30 -3.26 -0.30
Relative (%) +0.0 +8.6 +6.7 +28.2 +16.6 -46.7 -29.4 +31.5 +41.9 -41.3 -3.8
Steps
(reduced) 		152
(0) 		241
(89) 		353
(49) 		427
(123) 		526
(70) 		562
(106) 		621
(13) 		646
(38) 		688
(80) 		738
(130) 		753
(145)

Subsets and supersets

Since 152 factors into 23 × 19, 152edo has subset edos 2, 4, 8, 19, 38, 76.

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 8ve 		Generator* Cents* 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 Whoops
2 7\152 55.26 33/32 Septisuperfourth
2 9\152 71.05 25/24 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 / unlit
8 63\152
(6\152) 		497.37
(47.37) 		4/3
(36/35) 		Twilight
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

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

birdshite stalactite
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