82edo: Difference between revisions

{{EDO intro|82}}

82edo's [[patent val]] is [[contorted]] in the [[11-limit]], from 82 = 2 × 41. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] & [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead.  

|+

! #

! Cents

! Approximate Ratios*

! Additional Ratios<br>with 11's (82e Val)

! Additional Ratios<br>with 11's (Patent Val)

<nowiki>*</nowiki> as a no-11 19-limit temperament

==Zeta properties==

===Zeta peak index===

{| class="wikitable"

! colspan="3" |Tuning

! colspan="3" |Strength

! colspan="2" |Closest EDO

! colspan="2" |Integer limit

!ZPI

|-

|81.9541455954050

|14.6423343356444

|6.653983

|0.941321

|14.718732

|82edo

|1200.67141552284

|8

|8

|}