Way off what? Complex ratios are likely to be heard as out-of-tune simple ratios, that's why they sound off. A concept sometimes called tolerance in music cognition. Note that by "complexity" and "simplicity" I'm referring to harmonic distance here.
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.
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.
IsTom|2 months ago
pierrec|2 months ago
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.