89edo: Difference between revisions
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→Music: Add Bryan Deister's ''microtonal improvisation in 89edo'' (2025) |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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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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== Intervals == | == Intervals == | ||
{{Interval table}} | {{Interval table}} | ||
== Notation == | |||
=== Ups and downs notation === | |||
89edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals: | |||
{{Sharpness-sharp8}} | |||
== Approximation to JI == | |||
=== Zeta peak index === | |||
{{ZPI | |||
| zpi = 497 | |||
| steps = 89.0229355804124 | |||
| step size = 13.4796723133902 | |||
| tempered height = 7.567368 | |||
| pure height = 7.158697 | |||
| integral = 1.124501 | |||
| gap = 16.042570 | |||
| octave = 1199.69083589172 | |||
| consistent = 12 | |||
| distinct = 12 | |||
}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
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| [[Grackle]] | | [[Grackle]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
* [[Myna7]] | * [[Myna7]] | ||
* [[Myna11]] | * [[Myna11]] | ||
* [[Myna15]] | * [[Myna15]] | ||
== Instruments == | |||
; Lumatone | |||
''See [[Lumatone mapping for 89edo]].'' | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/watch?v=2JNIeqvXKlM ''microtonal improvisation in 89edo''] (2025) | |||
; [[Francium]] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=5Du9RfDUqCs ''Singing Golden Myna''] (2022) – myna[11] in 89edo | * [https://www.youtube.com/watch?v=5Du9RfDUqCs ''Singing Golden Myna''] (2022) – myna[11] in 89edo | ||