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

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 |
| page recently, you haven't missed much..." |
+------------------------------------------------------+

On Mon, 11 May 1998, John Chalmers wrote:
> The scale Pauls Hahn and Erlich posted in TD 1412 is precisely the
> "Triple Just" scale that Bill Flavell has been promoting on the
> rec.music.theory USENET newsgroup. Flavell derived his scale by
> combining just major scales on 1/1, 4/3 and 5/3.

Well, I should hope it is--I derived my diagram from the frequencies
Bill posted to this list.

(Just for clarity's sake, Bill's scale is _not_ the same as the
following.)

> * * * * *
>
> * * * * * * *
>
> * * * * * * *
>
> * * * * *
>
> The first of these is the same as Paul Hahn's scale, the second is the
> inversion.

This seems to have been a bit garbled in transmission--John, I assume
you mean for the second scale to look like this (are you using a
fixed-width font?):

* * *

* * * *

* * *

* *

Marion posted these to the list some time back, as I recall.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>