166edo: Difference between revisions
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The '''166 equal | The '''166 equal divisions of the octave''' ('''166edo'''), or the '''166(-tone) equal temperament''' ('''166tet''', '''166et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 166 equal steps of size 7.229 [[cent]]s each. | ||
== Theory == | |||
The principle interest of 166edo 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-3 temperament]] [[marvel]], in both the [[11-limit]] and in the 13-limit extension [[hecate]], and the [[rank-2 temperament]] [[wizard]], which also tempers out 4000/3993, giving the [[optimal patent val]] for all of these. In the [[13-limit]] it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell, and tempering out both gives [[gizzard]], the 72&94 temperament, for which 166 is an excellent tuning through the [[19-limit]]. | |||
166edo (as 83edo) contains a very good approximation of the [[7/4|harmonic 7th]]. It | Its prime factorization is 166 = [[2edo|2]] × [[83edo|83]]. | ||
166edo (as 83edo) contains a very good approximation of the [[7/4|harmonic 7th]]. It is 0.15121 cent flat of the just interval 7:4. | |||
=== Prime harmonics === | |||
{{Primes in edo|166}} | |||
== Scales == | == Scales == | ||
* [[prisun]] | * [[prisun]] | ||
Revision as of 18:29, 14 July 2021
The 166 equal divisions of the octave (166edo), or the 166(-tone) equal temperament (166tet, 166et) when viewed from a regular temperament perspective, divides the octave into 166 equal steps of size 7.229 cents each.
Theory
The principle interest of 166edo 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-3 temperament marvel, in both the 11-limit and in the 13-limit extension hecate, and the rank-2 temperament wizard, which also tempers out 4000/3993, giving the optimal patent val for all of these. In the 13-limit it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell, and tempering out both gives gizzard, the 72&94 temperament, for which 166 is an excellent tuning through the 19-limit.
Its prime factorization is 166 = 2 × 83.
166edo (as 83edo) contains a very good approximation of the harmonic 7th. It is 0.15121 cent flat of the just interval 7:4.
Prime harmonics
Script error: No such module "primes_in_edo".