Relative cent: Difference between revisions

In other words, only each 12th divisor of the next 28 after 100 has the same problem as 100 does for use as the base of a relative cent.

If you want to quantify the approximation of a given [[JI|JI]] interval in a given [[Equal|equal-stepped]] tonal system, you can consider the absolute distance of 50 r¢ as the worst possible and 0 r¢ as the best possible. For example, [[5edo|5edo]] has a relatively good approximated [[Natural_seventh|natural seventh]] with the ratio [[7/4|7/4]]: the absolute distance of 4\5 in 5edo is 8.826 ¢ or 3.677 r¢ flat of 7/4. But the approximations of its multiple edos [[10edo|10edo]] (7.355 r¢), [[15edo|15edo]] (11.032 r¢) ... become progressively worse (in a relative sense). So in [[65edo|65edo]], there is the 7/4 situated halfway between two adjacent pitches (off by at least 47.807 r¢), but its absolute distance from this interval in cents is still the same as for 5edo: 8.826 ¢ flat. See [[Pepper_ambiguity|Pepper ambiguity]] for a mathematical approach to quantify the approximations for sets of intervals.