title: Septimal kleisma
text: # Septimal kleisma
  
  In music, the ratio 225/224 is called the septimal kleisma (play (help·info)). It is a minute comma type interval of approximately 7.7 cents. Factoring it into primes gives $2^{−5}$ $3^2$ $5^2$ $7^{−1},$ which can be rewritten $2^{−1}$ $(5/4)^2$ (9/7). That says 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.
  
  The septimal kleisma can also be viewed as the difference between the diatonic semitone (16:15) and the septimal diatonic semitone (15:14).
  
  