89edo: Difference between revisions
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The [[17/1|17]] and [[19/1|19]] are tuned fairly well, making it [[consistent]] to the no-13 [[21-odd-limit]]. The equal temperament tempers out [[256/255]] and [[561/560]] in the 17-limit; and [[171/170]], [[361/360]], [[513/512]], and [[1216/1215]] in the 19-limit. | The [[17/1|17]] and [[19/1|19]] are tuned fairly well, making it [[consistent]] to the no-13 [[21-odd-limit]]. The equal temperament tempers out [[256/255]] and [[561/560]] in the 17-limit; and [[171/170]], [[361/360]], [[513/512]], and [[1216/1215]] in the 19-limit. | ||
89edo is the 11th in the {{w|Fibonacci sequence}}, which means its 55th step approximates logarithmic φ (i.e. {{nowrap| | 89edo is the 11th in the {{w|Fibonacci sequence}}, which means its 55th step approximates logarithmic φ (i.e. 1200{{nowrap|(φ − 1)}}{{c}} within a fraction of a cent. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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== Zeta properties == | == Zeta properties == | ||
===Zeta peak index=== | === Zeta peak index === | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! colspan="3" | Tuning | ||
! | ! colspan="3" | Strength | ||
! colspan="2" | Closest EDO | |||
! colspan="2" | Integer limit | |||
!EDO | |||
! | |||
|- | |- | ||
|[[497zpi]] | ! ZPI | ||
|89.0229355804124 | ! Steps per octave | ||
|13.4796723133902 | ! Step size (cents) | ||
|7.567368 | ! Height | ||
|1.124501 | ! Integral | ||
|16.042570 | ! Gap | ||
|89edo | ! EDO | ||
|1199.69083589172 | ! Octave (cents) | ||
|12 | ! Consistent | ||
|12 | ! Distinct | ||
|- | |||
| [[497zpi]] | |||
| 89.0229355804124 | |||
| 13.4796723133902 | |||
| 7.567368 | |||
| 1.124501 | |||
| 16.042570 | |||
| 89edo | |||
| 1199.69083589172 | |||
| 12 | |||
| 12 | |||
|} | |} | ||
== Scales == | == Scales == | ||
* [[Myna7]] | * [[Myna7]] | ||