source file: m1401.txt Date: Fri, 1 May 1998 11:33:17 -0400 (EDT) Subject: Re: Undertone Series From: Johnny Reinhard With permission, I quote Jon Catler from his article Just Intonation in Modern Music (PITCH I:1, Autumn 1986): "There is another, sort of magical way in which the undertone series manifests itself. Whenever two tones are sounded simultaneously, other tones are produced in the human ear that are not actually being played. "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. "In this way, we can see how the overtone series and the undertone series are not separate--in fact, they are inseparable." (Jon Catler, PITCH I:1, p. 5) Johnny Reinhard Director American Festival of Microtonal Music 318 East 70th Street, Suite 5FW New York, New York 10021 USA (212)517-3550/fax (212) 517-5495 reinhard@idt.net http://www.echonyc.com/~jhhl/AFMM