 Miracle temperament

In music, miracle temperament is a regular temperament discovered by George Secor which has as a generator an interval, called the secor, that serves as both the 15:14 and 16:15 semitones. Because 15:14 and 16:15 are equated, their ratio 225:224 is tempered out, and two secors give an 8:7 interval, a septimal whole tone. Three of these 8:7 intervals, or six secors, make up a fifth, so that 1029:1024 is also tempered out. This gives the 7limit version of miracle.
A septimal whole tone of 8:7 as we have seen is approximated by two secors, and a neutral third of 11:9 by three secors. In miracle, a minor third plus a septimal whole tone is also equated with the 11th harmonic. This means that the gap between a minor third plus a septimal whole tone and the 11th harmonic (an 11:8 ratio), 385:384 ., 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 can be 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 twentyone notes derived from twenty successive secors, has been used by several composers, including New York composer Joseph Pehrson.
External links
Musical tunings Measurement Just intonation Euler–Fokker genus · Harmonic Scale · Harry Partch's 43tone scale · Hexany · Pythagorean tuning · Scale of harmonicsTemperaments IrregularTraditional nonWestern Chinese musicology · Dastgah · Maqam (Arabian maqam · Makam · Mugham · Muqam) · Octoechos · Pelog · Raga (Carnatic rāga) · Slendro · TetrachordNonoctave Categories: Linear temperaments
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