Septimal kleisma: Difference between revisions

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, . It is an interval of approximately 7.7 cents. 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 most 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, .

The septimal kleisma can also be viewed as the difference between the diatonic semitone (16:15) and the septimal diatonic semitone (15:14), .

See also

• Septimal meantone temperament
• Miracle temperament
• 72 equal temperament