166edo: Difference between revisions

The 166 equal temperament (in short 166-[[EDO|EDO]]) divides the [[Octave|octave]] into 166 equal steps of size 7.229 [[cent|cent]]s each. Its principle interest lies in the usefulness of its approximations; it tempers out 1600000/1594323, 225/224, 385/384, 540/539, 4000/3993, 325/324 and 729/728. It is an excellent tuning for the rank three temperament [[Marvel|marvel]], in both the [[11-limit|11-limit]] and in the 13-limit extension [[Marvel_family#Hecate|hecate]], and the rank two temperament wizard, which also tempers out 4000/3993, giving the [[Optimal_patent_val|optimal patent val]] for all of these. In the [[13-limit|13-limit]] it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell, and  tempering out both gives [[Marvel_temperaments|gizzard]], the 72&94 temperament, for which 166 is an excellent tuning through the [[19-limit|19 limit]].

166edo (as 83edo) contains a very good approximation of the [[7/4|harmonic 7th]]. It's 0.15121 [[cent|cent]] flat of the just interval 7:4.

<ul><li>[[prisun|prisun]]</li></ul>      [[Category:166edo]]

[[Category:gizzard]]

[[Category:marvel]]

[[Category:theory]]

[[Category:wizard]]