My question is from my MUS 204 course, which is the following: How many cents comprise a quarter-tone in 15-EDO?
I believe I am missing one piece of knowledge to answering such a seemingly simple question. First, I understand a quarter-tone is 50 cents and second, I understand the frequency ratio in 15-EDO, correct me if I'm wrong, is 2^1/15 and a cent is 1/1200 of an octave.
I wanted to solve the problem similar to solving for the number of cents in just perfect fifth. (i.e., log of base 2 to the 3/2 = (number of cents)/1200, which is approx. 702 cents.) However, substituting 3/2 for 1/15 produces an incorrect number. (The correct number should be 80 cents.)
What correct steps must be taken to find the correct answer to the question above?