Like all v.commers, I knew that using pure intonation leads into trouble when the music changes key. I was unaware of how soon the trouble starts.
Last night, I was practicing the scale of B flat major, in thirds, and I just could not get the first three (B flat-D, C-E flat, D-F) consistently in tune. Especially the C-E flat was difficult to reconcile with the others.
And when you calculate the intervals, that fits! Set the B flat to 1; the C would be 9/8, and the E flat would be 4/3. The interval between those two becomes 4/3 : 9/8 = 4*8/(3*9) = 32/27, not the "pure" 6/5 third I was naively expecting. When I want it to sound "pure", I have to compromise elsewhere.
Imagine, it has taken me 48 years of violin playing to find that out!
(and it's a left hand workout, too)
More entries: April 2009