152edo: Difference between revisions

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== 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 [[tempering out|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]].

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 [[tempering out|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]].

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 [[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]].

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]].

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

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* 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 ===

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* "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:~~Equal divisions of the octave|###~~]] ~~~~

[[Category:Amity]]

[[Category:Grendel]]

[[Category:Kwai]]

[[Category:Laka]]

[[Category:Listen]]

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 == Theory ==
-edo is a strong 11-limit system, with the [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] slightly sharp. It [[tempering out|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]].
+edo is a strong [[11-limit]] system, with the [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] slightly sharp. It [[tempering out|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]].
-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 [[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]].
+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]].
 [[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].
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+* 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 ===
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 * "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:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Amity]]
 [[Category:Grendel]]
 [[Category:Kwai]]
 [[Category:Laka]]
 [[Category:Listen]]