Miracle: Difference between revisions

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'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. In terms of [[13-limit]] extensions, it is discussed in [[Miracle extensions|miraculous, benediction, and manna]].

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 ~~note~~ in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value.

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's 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]].

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 '''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. In terms of [[13-limit]] extensions, it is discussed in [[Miracle extensions|miraculous, benediction, and manna]].
-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 note in the 11-odd-limit tonality diamond is represented within 22 secors of the starting value.
+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's exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (&rarr; [[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]].