plomp and levelt

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