182edo: Difference between revisions

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~~'''182edo''' is the [[~~EDO|~~equal division of the octave]] into~~ 182 ~~parts of 6.5934 [[cent]]s each. It~~ is inconsistent to the 5-limit and higher limit, with three mappings ~~possible~~ for the 11-limit: ~~<~~182 288 423 511 630| (patent val), ~~<~~182 289 423 511 630| (182b), and ~~<~~182 288 422 511 629| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |-4 -37 27~~&gt~~; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.

== Theory ==

182edo is inconsistent to the 5-limit and higher limit, with three mappings suitable for the 11-limit: {{val|182 288 423 511 630}} (patent val), {{val|182 289 423 511 630}} (182b), and {{val|182 288 422 511 629}} (182ce). It does have a potential as a 2.7.9.15.17.19 subgroup temperament.

182edo (182bef val) is a tuning for the [[shrutar]] temperament in the 19-limit and [[petrtri]] in the 2.11/5.13/5 subgroup.

=== Odd harmonics ===

== Regular temperament properties ==

=== Commas ===

Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit.

Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and {{monzo|-4 -37 27}}; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit.

Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit.

Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.

[[Category:Equal divisions of the octave|###]]

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 {{Infobox ET}}
-'''182edo''' is the [[EDO|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: &lt;182 288 423 511 630| (patent val), &lt;182 289 423 511 630| (182b), and &lt;182 288 422 511 629| (182ce). Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |-4 -37 27&gt; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.
+{{EDO intro|182}}
+== Theory ==
+edo is inconsistent to the 5-limit and higher limit, with three mappings suitable for the 11-limit: {{val|182 288 423 511 630}} (patent val), {{val|182 289 423 511 630}} (182b), and {{val|182 288 422 511 629}} (182ce). It does have a potential as a 2.7.9.15.17.19 subgroup temperament.
+edo (182bef val) is a tuning for the [[shrutar]] temperament in the 19-limit and [[petrtri]] in the 2.11/5.13/5 subgroup.
+=== Odd harmonics ===
+{{harmonics in equal|182}}
+== Regular temperament properties ==
+=== Commas ===
+Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit.
+Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and {{monzo|-4 -37 27}}; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit.
+Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit.
+Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->