Subject: Re: Difference Tones From: Eckard Blumschein <Eckard.Blumschein(at)E-TECHNIK.UNI-MAGDEBURG.DE> Date: Fri, 13 Sep 2002 08:09:26 +0200Since there are also so called first quadratic 2f1-f2 distortion-product otoacoustic emissions being applied in audiology, one is tempted to directly attribute any difference tone alias "terza suoni" or Tartini tone just to the non-linear relationship between electrical and mechanical quantities of the outer hair cells. However, this might be premature. Geoff Wyvill describes in http://www.cs.otago.ac.nz/ProjectList-2002.html why he has "good reason to believe that the tones produced by Helmholtz are subtly different from the Tartini tones associated with resonant strings or pipes and this is why they occur only for certain notes." He argues: "Helmholtz's tones are simply differences of frequencies from two non-resonant sources. Using a computer, we can create the same sound as a string or pipe, but from a speaker that has no particular natural resonant tone. Thus we can reproduce the essential feature of Helmholtz's siren without restricting the tone colour. We can also use Fourier analysis on the computer to detect the tones independently of a human listener. Develop the necessary computer programs and conduct the physical experiments needed to settle these questions." A modification of the Tartini tones is the likewise monaural "Heterodyne Effect". As technicians found out, summation and difference tones will emerge if one passes two pure tones together through a mixer. As examples for f1 and f2 a South africa besed company (http://www.soundharmonics.com/ahata/sh_main.asp) gave 100 and 104 Hz. This is not convincing to me. There are certainly restrictions to the audibility as resolved tones. I do not deal with difference tones. Just being reminicent of Dove 1838, I would like somebody to check in detail to what extent not non-linearity of the cochlear amplifier is the physiological basis for the perception of difference tones. Incidentally, Hpersonic (http://www.acoustics.org/press/133rd/2pea.htmlHSS) technology is using non-linearity of air to transmit a directable audible sound via two ultrasound signals. Eckard http://iesk.et.uni-magdeburg.de/~blumsche/AuditoryFunction.html At 22:34 12.09.2002 +0800, Chen-gia TSAI wrote: >In the CD of Ernst Terhardt's book 'Akustische Kommunikation' (1998, Springer)