Klarinet Archive - Posting 000421.txt from 2001/02

From: Kent Krive <kkrive@-----.com>
Subj: [kl] Difference Tones
Date: Mon, 12 Feb 2001 00:29:52 -0500

Dear Difference Tone Combatants,

Not being versed in the more esoteric regions of the physics of sound, I
can relate only empirical evidence that a pitch, in addition to two
different pitches being sounded, may be heard if it is within the range
of hearing of a listener. It seems to me that if it is heard, it must
"exist" to the extent that any other pitch "exists." Exactly where it
"exists" is, of course, the source of confusion and disbelief, as well
as the subject of scientifically supported assertion.

Be that as it may, there is a very practical reason to be aware of
difference tones and how they relate to original tones: In a variety of
cases, a resultant tone will be the same as the tonic or other tone of a
chord and therefore reinforce it. The result is greater projection for a
given amount of energy (more bang for da buck, hey yah? :-)) <sorry, I
attended Escanaba in da Moonlight last night, and am trying
unsuccessfully to forget it.> Back to difference tones...

All of you who teach students and who play at least part of the time
when they play, try this: Have the student play a top-line F (Eb
concert); you play the A (G) above. Listen carefully for a chalameau F
(Eb). If the interval is tuned appropriately, you will hear it. If you
hear, perhaps feel, a "sound presence" other than the two tones being
sounded, but it's not the chalameau F, adjust the A up/down until it is.

What you'll wind up with (if the F (Eb concert) is exactly in tune
according to "A 440."), is a M3 which is 6.175 Hz smaller than an equal
tempered one. The difference tone is an F (Eb concert) two octaves below
- 155.565 Hz, which is the difference between 622.25 Hz and 777.815 Hz.
Cool.

You can expand this activity to include chromatic scales in 2nds, 3rds,
4ths, 5ths, etc. The number of difference tones that will be "audible"
relates directly to the size of the interval being used: Since the
number representing the difference between two pitches a second apart is
small, more of the pitches would be lower than our range of hearing. The
difference between two pitches a fifth apart (with the same lower pitch)
would be a larger number, hence a higher pitch.

To those who feel that this is a waste of a student's lesson time, I
find that students are fascinated with the idea of "other pitches than
those being played" being sounded, and it occupies only a minute or so
more than the playing of the scale by itself. During the "duet" phase of
my lessons, the pleasure inherent in participating in resonant
sonorities, those produced with "secure" intonation, is enhanced by the
awareness of difference tones.

Now, this raises some questions about equal temperament when it comes to
the quest for beautifully static sonorities when working with groups of
wind instruments, and, I guess, strings, as well. We have enough trouble
just trying to achieve perfect octaves, fifths, fourths, etc., that
achieving the correct squeezing to ensure equal half-steps is well-nigh
improbable.

Maybe another thread...?

'nuff said. Kent

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