166edo: Difference between revisions

166edo is [[consistent]] through the [[13-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 to 13 all tuned flat. Its principal interest lies in the usefulness of its approximations. In addition to the 5-limit [[amity comma]], it [[tempering out|tempers out]] [[225/224]], [[325/324]], [[385/384]], [[540/539]], and [[729/728]], hence being an excellent tuning for the [[rank-3 temperament]] [[marvel]], in both the [[11-limit]] and in the 13-limit extension [[hecate]], the [[rank-2 temperament]] [[wizard]], which also tempers out [[4000/3993]], and [[houborizic]], which also tempers out [[2200/2197]], 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 {{nowrap|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]], of which it is only flat by 0.15121 cent.

 

166edo's approximated harmonics 3, 5, 7, 11, and 13 can all be improved by slightly [[stretched and compressed tuning|stretching the octave]], using tunings such as [[263edt]] or [[429ed6]].

 

Since 166 factors into primes as 2 × 83, 166edo contains [[2edo]] and [[83edo]] as subsets.

== Regular temperament properties ==

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

| {{mapping| 166 263 385 466 }}

| {{mapping| 166 263 385 466 574 614 }}

 

* [[Prisun]]

* [[Fifteentofourteen]]

[[Category:Wizard]]

[[Category:Houborizic]]