source file: mills3.txt Date: Mon, 27 Oct 1997 17:36:49 +0100 Subject: plomp and levelt From: William Sethares David Worrall asked: >In which of these categories does Plomp's Critical Band theory fit? Plomp and Levelt's work fits squarely in the "sensory" consonance definition, and is closely related to Helmholtz' beating theory. To oversimplify a bit, Helmholtz believed that dissonance is caused by the beating of the upper harmonics (partials) of a sound. He claimed that a beat rate of about 32 Hz was the "most dissonant" and dissonance fell off as the rate decreased (much slower rates being perceived more like vibrato) and as the beating rate increased (much higher not being perceived as beating, but as a tone in its own right, like a difference tone). Consonance, according to H., is the absence of dissonance. Plomp and Levelt did a series of listening experiments using sine waves and "naive" subjects to see if Helmholtz was right. Indeed, they found that people tended to judge dissonance as greater or lesser depending on the beating rate. For tones around 500 Hz they found agreement with Helmoltz' 32 Hz figure, but in other frequency ranges, the actual rate of maximum dissonance was somewhat different. Plomp and Levelt's then observed that the rate of beating for maximum dissonance increases with frequency of the tones in exactly the same way as the *critical band* widens with frequency. To see why this is important, you need to know what the critical band is. The basilar membrane is a ribbon-like piece of flabby tissue that flaps around when pressure (sound) waves hit it. Thousands of little hairs mounted on the basilar membrane then vibrate and send messages to the brain, which encode (at least partly) the frequency of the impinging pressure wave. Any given single sine wave excites a small region on the membrane, and the distance in frequency at which two such regions overlap is called the critical band - it varies in frequency and is undoubtedly related to (but not the sole explanation for) the frequency resolving powers of the ear. Thus, by relating the perceived sensory dissonance to the critical band, Plomp and Levelt proposed a kind of biological cause for the sensation of sensory dissonance. This is why their paper was so important and controversial. SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: Uath-72 generalized keyboard PostedDate: 27-10-97 21:19:05 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 27-10-97 21:18:11-27-10-97 21:18:11,27-10-97 20:18:46-27-10-97 20:18:47 DeliveredDate: 27-10-97 20:18:47 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125653D.006F8487; Mon, 27 Oct 1997 21:18:04 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA28960; Mon, 27 Oct 1997 21:19:05 +0100 Date: Mon, 27 Oct 1997 21:19:05 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA28940 Received: (qmail 2576 invoked from network); 27 Oct 1997 12:18:52 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 27 Oct 1997 12:18:52 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu