9edt: Difference between revisions

The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]].

Following [[4edt|4edt]], this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to [[7edo|7edo]] in diatonic music.

This scale is also related to [[17edo|17edo]] by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1.

0: 1/1

 

 

 

 

 

 

 

 

9: 3/1

[[category:macrotonal]]