103edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Intervals == | == Intervals == | ||
{{Main|Table of 103edo intervals}} | {{Main|Table of 103edo intervals}} | ||
== Approximation to JI == | |||
=== Interval mappings === | |||
{{Q-odd-limit intervals}} | |||
=== Zeta peak index === | |||
{{ZPI | |||
| zpi = 596 | |||
| steps = 102.936629522070 | |||
| step size = 11.6576577800491 | |||
| tempered height = 8.543510 | |||
| pure height = 5.620365 | |||
| integral = 1.340775 | |||
| gap = 18.270998 | |||
| octave = 1200.73875134506 | |||
| consistent = 15 | |||
| distinct = 15 | |||
}} | |||
== 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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| 5.10 | | 5.10 | ||
|} | |} | ||
* 103et (103h val) has lower absolute errors than any smaller equal temperaments in the [[13-limit|13-]], [[17-limit|17-]], and [[19-limit]]s, being beaten by [[111edo|111]] in all of them. | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| [[Neptune]] | | [[Neptune]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||