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Encyclopedia > Septimal kleisma

In music, the ratio 225/224 is called the septimal kleisma. Another name for it is the marvel comma, since the temperament tempering it out is sometimes called the marvel temperament. Factoring it into primes gives 2-5 32 52 7-1, which can be rewritten 2 -1 (5/4)2 (9/7). That tells us that it is the amount that two major thirds of 5/4 and a septimal major third, or supermajor third, of 9/7 exceeds the octave. If the septimal kleisma is tempered out, as it is for instance in miracle temperament, septimal meantone temperament and in a number of equal temperaments, for example 12, 19, 22, 31, 41, 53, 72 or 84 equal, then an augmented triad consisting of two major thirds and a supermajor third making up an octave becomes possible. The existence of such a chord, which might be termed the septimal kleisma augmented triad, is a significant feature of a tuning system. A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... 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. ... In music, septimal meantone temperament, also called standard septimal meantone or simply septimal meantone, refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the amount of fifths for 12 equal temperament to those as flat as 19 equal... In general, an augmented chord is any chord which contains an augmented interval. ...

Septimal meantone temperament Miracle temperament 72 equal temperament In music, septimal meantone temperament, also called standard septimal meantone or simply septimal meantone, refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the amount of fifths for 12 equal temperament to those as flat as 19 equal... 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. ... In music, 72 equal temperament, called 72-tet, 72-edo, or 72-et, is the scale derived by dividing the octave into twelfth-tones, or in other words 72 equally large steps. ...

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