Miracle: Difference between revisions
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{{Wikipedia|Miracle temperament}} | {{Wikipedia|Miracle temperament}} | ||
'''Miracle | '''Miracle''' is a [[regular temperament]] discovered by [[George Secor]] in 1974 which has as a [[generator]] an interval, called a ''[[secor]]'' (after George), that serves as both [[15/14]] and [[16/15]] semitones. | ||
Miracle is an exceptionally efficient linear temperament which is a member of both the [[marvel temperaments]] and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/octave, meaning intervals of the [[11-odd-limit]] [[tonality diamond]] are represented with only one or two cents of error. Yet it is also very | Miracle is an exceptionally efficient linear temperament which is a member of both the [[marvel temperaments]] and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/[[octave]], meaning intervals of the [[11-odd-limit]] [[tonality diamond]] are represented with only one or two cents of error. Yet it is also very low-complexity (efficient), as evidenced by the high density of [[11-odd-limit]] ratios (in bold) in the [[#Interval chain]]. At least one inversion of every interval in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value. | ||
Some temperaments have [[11/9]] as a "neutral third", meaning it | Some temperaments have [[11/9]] as a "neutral third", meaning it is exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (→ [[Gamelismic clan]]) have [[8/7]] as exactly a third of [[3/2]]. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a ''secor'', and it represents both [[16/15]] and [[15/14]]. | ||
Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together. | Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together. | ||
In terms of [[13-limit]] extensions, it is discussed in [[Miracle extensions]]. See [[Gamelismic clan #Miracle]] for technical data. | |||
== Interval chain == | == Interval chain == | ||
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== Scales == | == Scales == | ||
; | {{See also| Miracle 10 MODMOS }} | ||
* [[Miracle 10]] | |||
* [[Blackjack]] | ; Mos scales | ||
* [[Miracle 10|Miracle{{lbrack}}10{{rbrack}}]] – 72edo tuning | |||
* [[Blackjack|Blackjack (miracle{{lbrack}}21{{rbrack}})]] – 72edo tuning | |||
* [[Blackwoo]] | * [[Blackwoo]] | ||
; Transversal scales | ; Transversal scales | ||
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* [[Miracle31trans511]] | * [[Miracle31trans511]] | ||
; Others | ; Others | ||
* [[Mir1]] | * [[Mir1]] – 6-tone scale, 72edo tuning | ||
* [[Mir2]] | * [[Mir2]] – 6-tone scale, 72edo tuning | ||
* [[Miracle 8]] | * [[Miracle 8]] – 8-tone scale, 72edo tuning | ||
* [[Miracle 12]] | * [[Miracle 12]] – 12-tone scale, 72edo tuning | ||
* [[Miracle 12a]] | * [[Miracle 12a]] – 12-tone scale, 72edo tuning | ||
* [[Miracle 24hi]] | * [[Miracle 24hi]] – 24-tone scale, 72edo tuning | ||
* [[Miracle 24lo]] | * [[Miracle 24lo]] – 24-tone scale, 72edo tuning | ||
== Tuning spectrum == | == Tuning spectrum == | ||
{| class="wikitable center-all" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! | ! Edo<br>Generator | ||
! [[ | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ||
! | ! Secor (¢) | ||
! | ! Comments | ||
|- | |- | ||
| | | | ||