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Stern-Brocot tree and music

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

6/19/2000 8:32:41 AM

Hi Pierre, I was looking at http://www.cut-the-knot.com/blue/Stern.html
(thanks to Graham Breed) and your name was mentioned:

"Pierre Lamothe <mailto:plamothe@aei.ca> from Canada informed me recently of
a property of the Stern-Brocot tree I was unaware of. Pierre discovered that
property in ~éhis research <http://www.aei.ca/plamothe/asymtrie.htm> on
music and harmony.
Let's associate with any irreducible fraction p/q the number W(p/q) = 1/pq -
its width. The property discovered by Pierre states that the sum of widths
of all fractions in any row of the Stern-Brocot tree equals 1! We can easily
see that this is true for a few first rows: . . ."
I have been conducting similar research on music and harmony, and "widths"
of ratios, but have focused more on Farey series and the like. Is there any
way I can find out more about how you've applied your concepts to music? I'm
very excited to learn more!
-Paul Erlich

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🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

6/20/2000 11:08:00 AM

Pierre wrote me back -- everyone, check out these amazing web pages
in French:

http://www.aei.ca/~plamothe/asymetrie.htm

http://www.aei.ca/~plamothe/gammes-gsp.htm

On the first page, Pierre shows the stern-brocot tree applied to
harmonic ratios and even points out the golden ratio in the tree. It
appears he uses Tenney' harmonic distance (though he doesn't call it
that) as a complexity function -- I'm very hopeful this will all be
of great interest to me (once I get throught the French) and many of
the others of you out there.