Miracle temperament
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In music, miracle temperament is a regular temperament invented by George Secor which has as a generator an interval, called the secor, which serves as both the 15/14 and 16/15 semitones. Because 15/14 and 16/15 are equated, their ratio (15/14)/(16/15) = 225/224, sometimes called the septimal kleisma, is tempered out, and two secors give an 8/7 interval. Three of these 8/7 intervals, or six secors, make up a fifth, so that <math>(3/2)/(8/7)^3 = 1029/1024</math>, an interval sometimes called the gamelan residue, is also tempered out. This gives the 7-limit version of miracle.
In miracle, an 8/7 interval as we have seen is two secors, and a minor third of 6/5 is three secors. Their product, 48/35, is equated with 11/8, meaning that <math>(11/8)/(48/35) = 385/384</math>, an interval sometimes called the unidecimal kleisma, is also tempered out. Miracle, therefore, is the temperament tempering out 225/224, 1029/1024 and 385/384 at the same time. For tuning purposes, a secor of seven steps of 72 equal temperament is often used. While this also tempers out 4375/4374, the ragisma, doing this is not regarded as a part of the definition of miracle temperament.
Miracle temperament, particularly in the distributionally even scale known as Blackjack, a scale of twenty-one notes derived from twenty successive secors, has been used by several composers, including New York composer Joseph Pehrson.
[edit] External links
| Tunings | edit | ||||
| Pythagorean · Just intonation · Harry Partch's 43-tone scale | |||||
| Regular temperaments | |||||
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| Irregular temperaments | |||||
| Well temperament | |||||
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