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Bart Meijer

Intonation epiphany: in a pure major scale, the II-IV third is Pythagorean

February 20, 2010 at 7:51 AM


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)



From Jefferson Dixon
Posted on February 21, 2010 at 9:29 PM

Yes the Pythorean Interval is taught in music theory ;)


From Bart Meijer
Posted on February 22, 2010 at 9:02 AM


I was surprised at seeing a Pythagorean minor third show up in the pure, harmonic, scale. To many this discovery must have a "Duh. What else is new?" quality, I'm sure.


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