source file: m1412.txt
Date: Mon, 11 May 1998 02:52:30 -0700 (PDT)

Subject: Re: Jon Catler's desc. of undertones (digest 1411 topic 6)

From: Mark Nowitzky <nowitzky@pacificnet.net>

First, Jon Catler, quoted by Johnny Reinhard, wrote
>>> "The difference between the frequencies of the
>>> two notes being sounded produces a third note
>>> below the range of the first two, called a difference
>>> tone.  By playing through a _descending_ harmonic
>>> series with two notes and keeping a "B" on top, we
>>> can see that the difference tone line creates an
>>> _ascending_ minor scale that corresponds exactly to the
>>> Undertone Series created earlier from mirror-imaging.

Then Paul Erlich wrote:
>> The wording here is unclear -- anyone know what Jon
>> meant by "playing through a _descending_ harmonic series
>> with two notes and keeping a "B" on top"? Judging from
>> the results, he probably meant something like "playing
>> through a series of superparticular ratios, with the upper
>> note fixed at "B", and the lower note descending."

Then Joseph Monzo wrote:
>This is exactly what he meant.  I believe this passage
>refers to the part we just heard last night in "Sleeping
>Beauty" where Jon does this on his JI electric guitar.

Maybe I'm misinterpreting the above, but I cannot get it to work.  Here's
one my feeble attempts (note names are sometimes approximate):

lower tone freq  upper tone freq  difference    name
---------- ----  ---------- ----  ----------  ---------
       C    264       B      495     231      Bb
      Bb    231       B      495     264       C
     G      198       B      495     297        D
    E       165       B      495     330         E
   C        132       B      495     363          F#
  G          99       B      495     396           G
 C           66       B      495     429            A
C            33       B      495     462             Bb

The above does not result in a minor scale.  It kind of starts out like a
whole tone scale, and the intervals get slightly smaller and smaller.

Can anyone show an example with actual note names and/or frequencies?  Thanks,
--Mark

P.S.:  I do remember an demonstration long ago of "difference tones", where
the resultant tones played the tune "Yankee Doodle".  What's scary is that
just after I thought of it, while writing this email, a commercial came on
the radio for a place called "Yankee Doodle's" in Woodland Hills (KROQ, FM
106.7, Los Angeles, California, USA).  What are the odds?  :)
+------------------------------------------------------+
| Mark Nowitzky                                        |
| email:  nowitzky@alum.mit.edu                        |
| www:    http://www.pacificnet.net/~nowitzky          |
|         "If you haven't visited Mark Nowitzky's home |
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+------------------------------------------------------+