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From: Winslow Yerxa <76450.32~ompuServe.COM>
Date: 30 Aug 96 10:06:46 EDT
Subject: augmented triad tuned chromatic

TO: internet:harp~arply.com

Wim Dijkgraaf posits an augmented triad tuned chromatic:

DRAW+ Eb G B
DRAW D F# Bb
BLOW+ Db F A
BLOW C E G#

>So: the key of C=E=G#
> the key of D=F#=A#
> the key of Db=F=A
> the key of Eb=G=B

I built one of these out of a Koch 980 in 1971, thinking that to learn
this you only need to learn 4 key positions. Later, Richard Hunter
published a similar idea (where the harp is tuned to the complete
whole-tone scale, not just the augmented triad). He proposed it to
Toots Thielemans, and Toots said he didn't think it would necessarily be
any better than solo tuning - you'd gain some things, but you'd lose
things, too.

The present tuning system - Solo Tuning is the usual name for it -
does have one very strong advantage over symmetrical tuning systems like
the augmented-triad system or the whole tone system - it offers more
type of intervals, with more types of arpeggios and more types of
smooth-scale passages when the slide is used.

Why is this important? In jazz, smooth phrasing is highly desirable,
and the best way to produce this on the chromatic is to avoid hole-leaps
and changes of breath, playing as much as possible notes in adjacent
holes, on the same breath (all blow or all draw) and using the slide.
Measuring by this criterion, which has more to offer in variety of
intervals, the traditional tuning or the augmented-triad tuning?

By using the slide on a series of all-draw or all-blow notes in adjacent
holes on a solo-tuned chromatic, I can get -

semitones A#-B (1)
whole tones F-G A-B Bb-C C-D Eb-F (5)
minor thirds B-D C-Eb C#-E D-F Eb-Gb E-G F-Ab F#-A A-C (9)
major thirds C-E Db-F D-F# E-G# F-A F#-A# Ab-C B-D# (8)
perfect fourths C-F F-Bb (2)
tritones G-C# (1)

So solo tuning will give us 26 different intervals, of six different
kinds.

On the augmented-triad chromatic tuning, I can get

semitones - none
major seconds - none
minor thirds - C#-E F-Ab Eb-Gb G-Bb A-C B-D (6)
major thirds - C-E C#-E# D-F# Eb-G E-G# F-A F#-A# G-B Ab-C A-C# Bb-D B-D# (12)
perfect fourths - C-F D-G E-A F#-B G#-C# Bb-Eb (6)
tritones - none

I count only 24 intervals, limited to only three kinds, and awfully
heavy on the major thirds. Not so good.

Of course, we haven't even begun to get into the possibilities using
double embouchure (blocking out middle notes and corner switching) for
even larger smooth intervals, or the possibilities for stringing
together complete arpeggios, substitutions, or even same-breath scales.
But my bet is that the standard tuning offers far more possiblities
here, too.

I'd rather have an instrument that has more to offer, even if it is
harder to master. The twentieth century is about expanding
possibilities, not about reducing choices to symmetrical uniformity
(unless you like the hammer and sickle, symbol of a 19th-century idea
that is finally getting the heave-ho in most parts of the world).

Winslow Yerxa
Harmonica Information Press
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