152edo: Difference between revisions
Note: 15-integer-limit consistency, 11-, 19- and 23-limit excellency. -redundant category; +category. |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 241 -152 }} | | {{monzo| 241 -152 }} | ||
| {{mapping| 152 241 }} | | {{mapping| 152 241 }} | ||
| | | −0.213 | ||
| 0.213 | | 0.213 | ||
| 2.70 | | 2.70 | ||
| Line 36: | Line 28: | ||
| 1600000/1594323, {{monzo| 32 -7 -9 }} | | 1600000/1594323, {{monzo| 32 -7 -9 }} | ||
| {{mapping| 152 241 353 }} | | {{mapping| 152 241 353 }} | ||
| | | −0.218 | ||
| 0.174 | | 0.174 | ||
| 2.21 | | 2.21 | ||
| Line 43: | Line 35: | ||
| 4375/4374, 5120/5103, 16875/16807 | | 4375/4374, 5120/5103, 16875/16807 | ||
| {{mapping| 152 241 353 427 }} | | {{mapping| 152 241 353 427 }} | ||
| | | −0.362 | ||
| 0.291 | | 0.291 | ||
| 3.69 | | 3.69 | ||
| Line 50: | Line 42: | ||
| 540/539, 1375/1372, 4000/3993, 5120/5103 | | 540/539, 1375/1372, 4000/3993, 5120/5103 | ||
| {{mapping| 152 241 353 427 526 }} | | {{mapping| 152 241 353 427 526 }} | ||
| | | −0.365 | ||
| 0.260 | | 0.260 | ||
| 3.30 | | 3.30 | ||
| Line 57: | Line 49: | ||
| 352/351, 540/539, 625/624, 729/728, 1575/1573 | | 352/351, 540/539, 625/624, 729/728, 1575/1573 | ||
| {{mapping| 152 241 353 427 526 563 }} (152f) | | {{mapping| 152 241 353 427 526 563 }} (152f) | ||
| | | −0.494 | ||
| 0.373 | | 0.373 | ||
| 4.73 | | 4.73 | ||
{{comma basis end}} | |||
* 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 In the 11-limit it is the first to beat [[130edo|130]] and is superseded by [[224edo|224]]. In the 19- and 23-limit it is the first to beat [[140edo|140]] and is superseded by [[159edo|159]]. | * 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 In the 11-limit it is the first to beat [[130edo|130]] and is superseded by [[224edo|224]]. In the 19- and 23-limit it is the first to beat [[140edo|140]] and is superseded by [[159edo|159]].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. | * 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 === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 128: | Line 114: | ||
|- | |- | ||
| 2 | | 2 | ||
| 43\152<br>(33\152) | | 43\152<br />(33\152) | ||
| 339.47<br>(260.53) | | 339.47<br />(260.53) | ||
| 243/200<br>(64/55) | | 243/200<br />(64/55) | ||
| [[Hemiamity]] | | [[Hemiamity]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 55\152<br>(21\152) | | 55\152<br />(21\152) | ||
| 434.21<br>(165.79) | | 434.21<br />(165.79) | ||
| 9/7<br>(11/10) | | 9/7<br />(11/10) | ||
| [[Supers]] | | [[Supers]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 63\152<br>(13\152) | | 63\152<br />(13\152) | ||
| 497.37<br>(102.63) | | 497.37<br />(102.63) | ||
| 4/3<br>(35/33) | | 4/3<br />(35/33) | ||
| [[Undim]] / [[unlit]] | | [[Undim]] / [[unlit]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 63\152<br>(6\152) | | 63\152<br />(6\152) | ||
| 497.37<br>(47.37) | | 497.37<br />(47.37) | ||
| 4/3<br>(36/35) | | 4/3<br />(36/35) | ||
| [[Twilight]] | | [[Twilight]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 74\152<br>(2\152) | | 74\152<br />(2\152) | ||
| 584.21<br>(15.79) | | 584.21<br />(15.79) | ||
| 7/5<br>(126/125) | | 7/5<br />(126/125) | ||
| [[Octoid]] (152f) / [[octopus]] (152) | | [[Octoid]] (152f) / [[octopus]] (152) | ||
|- | |- | ||
| 19 | | 19 | ||
| 63\152<br>(1\152) | | 63\152<br />(1\152) | ||
| 497.37<br>(7.89) | | 497.37<br />(7.89) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Enneadecal]] | | [[Enneadecal]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 63\152<br>(1\152) | | 63\152<br />(1\152) | ||
| 497.37<br>(7.89) | | 497.37<br />(7.89) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[birdshite stalactite]] | ; [[birdshite stalactite]] | ||
* "athlete's feet" from ''razorblade tiddlywinks'' (2023) | * "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]] | [[Category:Amity]] | ||
Revision as of 05:46, 16 November 2024
| ← 151edo | 152edo | 153edo → |
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 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.
Paul Erlich has suggested that 152edo could be considered a sort of universal tuning.
Prime harmonics
| 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
Template:Comma basis begin |- | 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 Template:Comma basis end
- 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 130 and is superseded by 224. In the 19- and 23-limit it is the first to beat 140 and is superseded by 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 270 do we find a better equal temperament that does better in either of those subgroups.
Rank-2 temperaments
Template:Rank-2 begin
|-
| 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
Template:Rank-2 end
Template:Orf