Hacker News Reader

7/4 ratio should be simple, but it'll sound out of tune (over 30 cents) in a normal context. Many BP intervals are just as simple and they'll sound very out of tune to people unused to them.

View on HN

7/4 happens to be approximately 30 cents away from 16/9. It's hard to tell what's "simple" when looking at fractions, but 16/9 is indeed simple: divide by 3 twice and adjust the octave. If we assume octave equivalence, that means one step in the "7" direction is perceived as more complex than 2 steps in the "3" direction, so the second interpretation wins, but is perceived as out-of-tune.

That said, we're trying to isolate things that are typically not isolated. If you get to 7/4 by following the harmonic series, it will sound in-tune. If you get to 16/9 by playing and applying 4/3 twice, then that will sound in tune. Unsurprisingly the second option is more common in music.

Before 7th harmonic all you have is octaves, fifths and major thirds. If you want to stick to making other pitches out of stacked fifths and major thirds you'll end up with other compromises.

Reply on news.ycombinator.com