89edo: Difference between revisions
→Theory: expand |
Rework and misc. cleanup |
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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. (φ - 1)×1200 cents) within a fraction of a cent. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
89edo is the 24th [[prime edo]], and | 89edo is the 24th [[prime edo]], following [[83edo]] and before [[97edo]]. | ||
== | == Intervals == | ||
{{Interval table}} | {{Interval table}} | ||
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| 175.28 | | 175.28 | ||
| 72/65 | | 72/65 | ||
| [[Sesquiquartififths]] / [[ | | [[Sesquiquartififths]] / [[sesquart]] | ||
|- | |- | ||
| 1 | | 1 | ||