Re: [Harp-L] Tuning

[Pat Missin <pat@xxxxxxxxxxxxx>]

Rick Dempster wrote:
> 
>I have noticed, particularly when tuning reeds in the top octave, that I often
>get 'ugly' tones when playing two reeds
>similtaneously, such as 9-10 blow or draw, 8-9 etc. When I listened more
>carefully, I noticed that what I was hearing
>was an overtone in the octave below the notes played.

What you are hearing is a difference tone. For more on this topic, try
this page:

www.patmissin.com/ffaq/q26.html

>When it was the root, the two notes played sounded clear, but when it was
>anything else, the two notes sounded
>distorted. Now I am wondering if listening to that overtone is the right way to
>tune two notes. 

I consider a knowledge of difference tones to be fundamental to good
harmonica tuning. Sadly, as far as I know, none of the published
books, videos, etc. on this subject even mention it.

>The question remains,
>which reed is then the one to be adjusted, and how does it relate to the rest of
>the notes on the harp?
>On the lower notes (ie the first two octaves) the overtone is much deeper and
>harder to hear.

True, but you can learn to hear them with practice. Also, when playing
three or more notes, you can learn to hear the beating when two
difference tones are slightly out of tune with each other.

>Also, if the notes are differing intervals, should the overtone be anything
>other than the octave 

That depends on what notes you are tuning and whether you are tuning
in a temperament or in Just Intonation. One reason why tempered
tunings sound rougher (or more interesting, depending on your personal
point of view) is that all the difference tones in a tempered tuning
are "out of tune" with the notes that are generating them. For more on
this, see these pages:

www.patmissin.com/tunings/tun0.html
www.patmissin.com/tunings/tun3.html

>(so that if I play
>blow 9-10- a 'g' and 'c'- on a 'c' harp the overtone will be a low 'c', 

Yes - on a JI harp, playing holes 9 and 10 blow will give a difference
tone of exactly the same pitch as hole 4 blow. On a harp in 12TET, the
difference tone produced by 9 and 10 blow would be almost 6 cents
sharper than the pitch of 4 blow.

>but if I play 8 & 9 - an 'e' and 'g' what should
>the overtone be?

If you play holes 8 and 9 blow on a perfectly tuned harp in Just
Intonation, the difference tone produced would be exactly one octave
lower than the difference tone produced by holes 9 and 10 blow, ie the
same pitch as that produced by hole 1 blow. On a harp in 12TET, the
difference tone produced by holes 8 and 9 blow would be more than 70
cents sharper than the pitch produced by hole 1 blow.

You didn't ask, but I will add that if you were to play holes 8 and 10
blow on a JI harp, the difference tone produced would be the same
pitch as hole 6 blow. On a harp in 12TET  the difference tone would be
about 21 cents flatter.

>I know I will gradually work this out for myself, but I would like to know if
>anyone else has noticed this and what
>they make of it.

Figuring out what the difference tones should be for any given
interval requires a knowledge of the ratios used in JI, or logarithmic
stuff if you are dealing with tempered tunings. When doing the actual
tuning work, JI intervals are much easier to handle as their
difference tones are always harmonically related to the tones which
generate them.

Given time I could probably draw up a diagram to help you figure out
what the difference tones should be on an ideal JI harp, but it would
require some basic arithmetic to use it. Actually, ~very~ basic
arithmetic, but I know a lot of musicians just glaze over when they
see numbers, so I'm not going to do it unless there really is some
demand for it. As for tempered tunings - you're on your own!

 -- Pat.