Re: [Harp-L] Just Intonation and Difference Tones

[G <gigs@xxxxxxxxxxxxxxx>]

Date: Tue, 15 Mar 2005 20:39:05 -0000
From: "Tim Moyer" <wmharps@xxxxxxxxxxxxxxxxxxxx>
Subject: Re:  [Harp-L] Just Intonation and Difference Tones 
To: harp-l@xxxxxxxxxx

>>tuning [19-limit just]
>
>blow: +00 -14 +04 +00 -14 +04 +00 -14 +04 +00
>hole: 001 002 003 004 005 006 007 008 009 010
>draw: +02 +04 -10 +02 +03 +06 -10 +02 +03 +06
>Sorry for all the zeros, but it keeps the letters aligned better.  8<
>-tim

Hi Tim,
I think using the zeros in your table is a good idea.
However your table is out in a couple of places.  

Blow hole 3, 6 & 9 are a perfect fifth above the tonic, blow holes 1, 4, 7.
As draw hole 4 is a perfect fifth above draw hole 2,  and draw holes 1 & 8
are an octave above and below.
A perfect fifth is around 702cents above the tonic, so if the tonic is
tuned to 0cents on your tuner, then perfect fifths are tuned to +2cents on
your tuner: 702cents - 700 cents [12tET fifth]).  If you tune the tonic to
something else adjust the fifth accordingly.  For instance with draw hole
2, you've shown it as +4cents sharp, so draw holes 1, 4 & 8 would be tuned
to +6 on the tuner, 706cents -700 cents.

Draw hole 2 can be tuned to whatever works for the intended player.   For
heavy breathers +4cents for draw 2 is a good idea, since they'd tend to
bring the pitch down considerably.   If you do this, its important to tune
the other reeds relative to this... actually not quite, but more on that
later.
But it's worth noting its the same note as blow hole 3.   I'm a fairly
moderate player, so for myself I generally tune it to the same pitch as
blow 3 with the usual range of keys.  For low keys I may tune the bottom
octave draw notes a bit higher than the rest of the harmonica.

As you've indicated blow holes 2, 5, 8 are a pure major third above the
tonic by about 386 cents.  If the tonic is 0 cents on the tuner, they would
be tuned to -14cents.  As is draw hole 3 is a perfect major third above
draw hole 2 (draw hole 7 is an octave above that).

Draw holes 6 & 10  are a perfect fifth above draw holes 4 & 8 respectively,
again +702cents.

And as discussed Draw holes 5 & 9 are tuned a harmonic 19th (m3rd) above
draw holes 4 & 8 respectively, +297.51cents.

I describe this arrangement in relative terms because the absolute values
are changed by any adjustments you want to incorporate - your table is
evidence of the pitfalls of simply thinking in absolute terms of variations
from 12tET in cents.  Be it octave stretching, raising the bottom octave of
Low key harps to accomadate their tendancy to flatten more dramatically, or
raising the draw notes to accomadate heavy breathers, these will affect the
values of such a table.

This is what the layout could look like:
blow: +00 -14 +02 +00 -14 +02 +00 -14 +02 +00
hole: 001 002 003 004 005 006 007 008 009 010
draw: +04 +02 -12 +04 +1.5 +06 -12 +04 +1.5 +06

Or if you wanted to tune the draw holes a bit sharper for a heavy blower,
simply draw harder while tuning which will ensure the intervals are tuned
properly for that style.  But in theory the numbers would be :
draw: +06 +04 -10 +06 +3.5 +08 -10 +06 +3.5 +08

These tuning tables MUST be accompanied with informed advice on how to
approach tuning, and a huge caveat that the table in itself offers very
little insight.   I think its important to make people aware that these
tables aren't the secret to good tuning - they are merely the results of a
series of arbitary calculations, if you really desire to know the maths, a
table such as the one above is not going to tell you much at all, and
certainly very little about the Just Intonation system.  

The practical aspect of tuning requires a different approach to working out
the maths.  If you simply tune each note in isolation against a tuner,
there are too many variables which makes this inaccurate.  The reason for
tuning with the above approach is draw hole 4 is pulled out of tune by a
smaller degree by your embouchure and breath pressure than say draw hole 2.

As Pat advises in Altered states, tune holes blow holes 1, 4, 7 & 10 to a
tuner.   And again tune draw holes 1, 4 & 8 to a tuner.  Check and adjust
the octaves by ear.  Then tune the rest of reeds in relation to those.
Because of the nature of harmonicas and their sensitivity to one's
embouchure, you'll get far better results comparing and tuning intervals by
ear. A tuner can't read intervals.   That said, it takes a lot of practice
to learn how to tune by ear and recogonise intervals, it took me a couple
of years to get to a place where I can hear whats going - so I understand
everyone has to start somewhere. 

NCHtone and SCALA are two superb software tools which combined with
learning basic tuning theory will  aid you in training your ear.  I've
found the SawTooth tone in NCHtone is the closest to the harmonica's voice.

The big secret is in your approach to tuning - actually its no secret at
all, as has been stated a number of times, Pat Missin has made this
information publicly available http://www.patmissin.com

If you want to learn just enough about Just Intonation theory to apply it
to harmonicas, you don't need any mathmatical knowledge beyond what you
were taught at school, if you can work with fractions, and use a calculator
you can learn the theory.

-- G.
http://www.angelfire.com/music/harmonica/harptechtips.html