81/80: Difference between revisions

81/80 is the smallest [[superparticular]] interval which belongs to the [[5-limit]]. Like [[16/15]], [[625/624]], [[2401/2400]] and [[4096/4095]] it has a fourth power as a numerator. Fourth powers are squares, and any superparticular comma with a square numerator is the ratio between two wider successive superparticular intervals, because n²/(n²-1) = n/(n-1) ÷ (n+1)/n. 81/80 is in fact the difference between [[10/9]] and [[9/8]], the product of which is the just major third, [[5/4]]. That the numerator is a fourth power entails that the wider of these two intervals itself has a square numerator; 9/8 is the interval between the successive superparticulars 4/3 and 3/2. Tempering out a comma does not just depend on an edo's size; [[105edo]] tempers it out, while [[15edo|3edo]] does not.

According to [http://untwelve.org/interviews/golden.html this interview], Monroe Golden's ''Incongruity'' uses just-intonation chord progressions that exploit this comma.