From: sumrn@dssv01.crd.ge.com (Robert N. Sum)
Newsgroups: alt.guitar
Subject: Re: Note Frequencies needed
Keywords: frequency, note, hertz
Date: 18 Dec 92 13:53:44 GMT
Reply-To: sumrn@crd.ge.com
Followup-To: alt.guitar
Organization: GE R&D, DICE Program

In the recent discussion on frequencies, I missed the bit about
overtones and "undertones," so here's what little I know about those:

  Most all sound producing things emit a variety frequencies at the same
time.  In all but extremely unusual cases, one hears the lowest frequency
as the pitch of the sound with the blend of the overtones giving the sound
its timbre (what makes a guitar different from a violin from a clarinet ...).

  For most stringed, wind, and some (but not all) percussion instruments,
overtones are simply integer multiples of the lowest frequency.  (Your physics
book can help explain why.)  So, using our A440 example, the overtones are
880, 1320, 1760, 2200, 2640, 3080, 3520, ....  Now, it so happens that the
way western music is constructed, many of these happen to be rather important
notes with respect to the lowest note.  (Note, however, these frequencies do
not match the equal temperament frequencies.  As I mentioned in the last
posting, equal temperament is a compromise.)  Adding the names and realizing
that each A is up the next octave we have the notes

A     A    E     A     C#    E     G*    A
440   880  1320  1760  2200  2640  3080  3520

which are all part of the A major or, if you include the G, an A7 chord.
The reason for the * is that the G is fairly far out of tune with respect
to equal temperament whereas the others are pretty good.

Nomenclature:  There are many terms for these things and I sometimes get them
confused.  In any case, the lowest pitch is called the fundamental frequency
(or just the fundamental).  Then you can use either harmonic or overtone to
describe remaining ones e.g., E1320 is the second harmonic.  There are some
people who refer to these as partials.  In that case, the numbers are moved
over by one because the fundamental is the first partial.

  I have not heard the use of "undertone" before, but one might apply this term
to the phantom sounds that are heard when instruments' pitches blend to
give the
impression that a lower note is being played, but it really is not. 
This effect
is actually how some ensembles of wind and string players can tell they've
gotten a particular chord in tune.  The simplest of these phantom notes to
produce is the octave below the lowest note with instruments playing notes that
are a fifth apart. For example, if one player plays the A880 above and another
player the E1320, then when they are exactly in tune, your ear may hear
the A440
even though there is no one playing it!

  I have had the pleasure of being in a symphonic band when about 70 people
locked in a chord (a bit more complex than two notes) in this way and the sound
was mind blowing!!!  (We were not playing particularly loudly, either!)

  Hope this helps,

    Bob
==
  sumrn@crd.ge.com

  Robert Sum
  G.E. Corp. R. & D.
  P.O. Box 8, Rm. KW-C287
  Schenectady, NY 12301

  Tel. (518) 387-7696

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