188edo: Difference between revisions

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'''188edo''' is the [[EDO|equal division of the octave]] into 188 parts of 6.3830 cents each. It is closely related to [[94edo]], but the patent vals differ on the mapping for 5. It tempers out 129140163/128000000 (graviton) and 268435456/263671875 (mabila comma) in the 5-limit; 2401/2400, 19683/19600, and 110592/109375 in the 7-limit. Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; 351/350, 352/351, 676/675, 1573/1568, and 16848/16807 in the 13-limit.

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

188edo is closely related to [[94edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]]. The equal temperament [[tempering out|tempers out]] 129140163/128000000 ([[graviton]]) and 268435456/263671875 ([[mabila comma]]) in the 5-limit; [[2401/2400]], [[19683/19600]], and 110592/109375 in the 7-limit. It [[support]]s [[harry]] and [[newt]], and provides the [[optimal patent val]] for [[tuskaloosa]], the 77 & 111 temperament.

Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; [[351/350]], [[352/351]], [[676/675]], [[1573/1568]], and 16848/16807 in the 13-limit; supporting 13-limit tuskaloosa. Using the alternative 188e val, [[243/242]], [[441/440]], [[540/539]], [[8019/8000]], and [[9801/9800]] in the 11-limit; 351/350, [[1716/1715]], and [[2080/2079]] in the 13-limit; supporting 13-limit harry.

The 188cef val is a tuning for the [[hemigari]] temperament in the 11- and 13-limit.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 188 factors into {{factorization|188}}, 188edo contains subset edos {{EDOs| 2, 4, 47, and 94 }}.

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 {{Infobox ET}}
-'''188edo''' is the [[EDO|equal division of the octave]] into 188 parts of 6.3830 cents each. It is closely related to [[94edo]], but the patent vals differ on the mapping for 5. It tempers out 129140163/128000000 (graviton) and 268435456/263671875 (mabila comma) in the 5-limit; 2401/2400, 19683/19600, and 110592/109375 in the 7-limit. Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; 351/350, 352/351, 676/675, 1573/1568, and 16848/16807 in the 13-limit.
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is closely related to [[94edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]]. The equal temperament [[tempering out|tempers out]] 129140163/128000000 ([[graviton]]) and 268435456/263671875 ([[mabila comma]]) in the 5-limit; [[2401/2400]], [[19683/19600]], and 110592/109375 in the 7-limit. It [[support]]s [[harry]] and [[newt]], and provides the [[optimal patent val]] for [[tuskaloosa]], the 77 & 111 temperament.
+Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; [[351/350]], [[352/351]], [[676/675]], [[1573/1568]], and 16848/16807 in the 13-limit; supporting 13-limit tuskaloosa. Using the alternative 188e val, [[243/242]], [[441/440]], [[540/539]], [[8019/8000]], and [[9801/9800]] in the 11-limit; 351/350, [[1716/1715]], and [[2080/2079]] in the 13-limit; supporting 13-limit harry.
+The 188cef val is a tuning for the [[hemigari]] temperament in the 11- and 13-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|188}}
+=== Subsets and supersets ===
+Since 188 factors into {{factorization|188}}, 188edo contains subset edos {{EDOs| 2, 4, 47, and 94 }}.