196edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
The equal temperament [[tempering out|tempers out]] 9765625/9565938 (fifive comma) and {{monzo| 32 -7 -9 }} ([[escapade comma]]) in the 5-limit. Using the [[patent val]], it tempers out [[245/243]], [[65625/65536]], and 235298/234375 in the 7-limit; [[385/384]], [[896/891]], [[3388/3375]], and 117649/117128 in the 11-limit; [[352/351]], [[364/363]], [[625/624]], [[1001/1000]], and 9295/9261 in the 13-limit; [[289/288]], [[442/441]], [[715/714]], and [[1156/1155]] in the 17-limit. | |||
[[ | 196edo can also treated as a 2.9.5.7.11.13.17 [[subgroup]] temperament (with the patent 9), providing a distinct flat tendency for [[harmonic]]s [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], and [[17/1|17]]. With the patent 9, it tempers out 321489/320000, [[420175/419904]], and [[703125/702464]] in the 2.9.5.7 subgroup; [[441/440]], [[8019/8000]], [[41503/41472]], and 9453125/9437184 in the 2.9.5.7.11 subgroup; [[729/728]], [[1001/1000]], [[1575/1573]], [[6656/6655]], and [[10985/10976]] in the 2.9.5.7.11.13 subgroup; [[833/832]], [[936/935]], [[1089/1088]], [[1225/1224]], [[2025/2023]], and 14365/14336 in the 2.9.5.7.11.13.17 subgroup. | ||
Since it is part of the Fibonacci sequence beginning with 5 and 12, it closely approximates [[peppermint]] temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|196}} | |||
=== Subsets and supersets === | |||
Since 196 factors into {{factorization|196}}, 196edo has subset edos {{EDOs| 2, 4, 7, 14, 28, 49, and 98 }}. | |||
== Intervals == | |||
See: [[Table of 196edo intervals]] | |||