[Harp-L] Interesting new tuning

[Roger Myerson <rmyerson@xxxxxxxxxxxx>]

I have recently tried an interesting new diatonic tuning and I wonder if 
anyone has seen it before.  The 12-hole version that Seydel made for me 
has the following note arrangement (in the key of C but with D as its 
low note):
BLOW  D  F  G  A  C  D  F  G  A  C  D  F
DRAW  E  G  A  B  D  E  G  A  B  D  E  G

What is so special about this?  It is the only tuning that has the 
following three properties:
(1) Regularity: Each octave should regularly repeat the same pattern, 
with draw higher than blow in each hole, and with notes going in the 
same direction (lower to higher) as you move from left to right.
(2) Cover a major scale without bends: The blow and draw notes should 
include all the notes of a major scale but no other notes, so that you 
don't have to worry about accidentally playing something out of the key.
(3) Cover the chromatic scale with bends: With draw bends (but no 
overblowing), you should be able to get all twelve notes of the 
chromatic scale in each octave.

These desirable properties can be achieved only by having five holes per 
octave.  Here, in a C harp, each hole contains two notes separated by a 
whole-tone interval with one of the five black notes of the piano 
available as a draw bend in between them.

Since the black notes form a pentatonic scale, the blow notes and the 
draw notes each also form a pentatonic scale.  Here the blow notes form 
an F-major (or D-minor) pentatonic scale, and the draw notes form a 
G-major (or E-minor) pentatonic scale.  Essentially we have decomposed 
the seven-note major scale into two overlapping pentatonic scales, whose 
paired notes enclose the other five chromatic notes   I believe that 
these are the pentatonic pairs that Willie Thomas talks about in 
jazzeveryone.com.

Gary Lehman suggested that this could be called "pentabender" tuning.  I 
have been playing my new pentabender harp for couple of days, and I find 
it very natural and intuitive.

In Pat Missin's catalog of tunings, the closest cousins to this 
pentabender seem to be 11.18 "chromatic pentatonic" tuning and 11.24 
"fourkey" tuning.  Both also have five-hole octaves, but 11.18 contains 
only the notes of one pentatonic scale, and fourkey tuning includes the 
notes of four different major scales.  Each octave in pentabender tuning 
contains three notes that repeat enharmonically in blow and draw, and if 
you flatten the draw enharmonic notes by a semitone then you get fourkey 
tuning.

If this natural tuning has been overlooked, it may be interesting to ask 
why.  I think that there are two main reasons.  First, it needs five 
holes per octave, which means that you can only get two octaves in a 
10-hole harp.  But I have enjoyed playing fourkey harmonicas with such a 
range for several years.  Second, most people who think about altered 
tunings tend to look for ways to get nice chords in three-hole triads of 
contiguous blow or draw notes.  However, this tuning (like fourkey 
tuning) was motivated by melodic properties, and so instead of nice 
triad chords we get pentatonic scales, which are basic melodic structure 
in many musical traditions.

This has also been discussed at Slidemeister.com at 
http://www.slidemeister.com/forums/index.php?topic=1205.390


--
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/