If I counted correctly, a chromatic with standard Solo tuning has 4
notes that are only blows, 6 notes that are only draws, and 2 notes that
can be played either way. So if you pick two randomly sampled notes,
the probability that they can be played in the same breath direction in
Solo tuning is (4*5/11+6*7/11+2)/12 = 63.6%.
In a chromatic with with Legato tuning, 2 notes are only blows, 2 notes
are only draws, and 8 notes can be played either way. So if you pick
two randomly sampled notes, the probability that they can be played in
the same breath direction in Legato tuning is (2*9/11+2*9/11+8)/12 = 93.4%.
Of course you don't really want to talk about random pairs of notes.
Smooth transitions between notes that are close together may be
particularly important. Some calculations about those can be found at
http://www.slidemeister.com/forums/index.php?topic=3132.330
-Roger
/From/: David Fairweather, on 12 Aug 2014
--
Roger B. Myerson, Glen A. Lloyd Distinguished Service Professor
Department of Economics, University of Chicago
1126 East 59th Street, Chicago, IL 60637
Phone:
773-834-9071, Fax:
773-702-8490
http://home.uchicago.edu/~rmyerson/