[Harp-L] Re: legato

[Roger Myerson <rmyerson@xxxxxxxxxxxx>]

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
> Daniel asked:
>
> "Of all the transitions between two notes
> what fraction can be done without a breath change? What is that fraction
> for the solo pitch layout?"
>
> I'm not in the mood to do math right now.  Let's just say every note in the
> chromatic scale can be played  either as blow or draw except Bb, B, Eb & E. Bb
> & Eb are strictly blow.   B & E are strictly draw.
>
> All these features are well discussed on Slidemeister.   No need to repeat
> them here.   Just look up "Fourkey" or "LeGato" over there and you'll find
> all the information you need.

--
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/