source file: mills3.txt Date: Sun, 21 Dec 1997 20:26:13 +0100 Subject: more melodic lemons From: William Sethares Recently, I suggested several reasons why the Melodic Difference Limen (MDL) should not be used as the sole basis of choosing a tuning system (and these reasons were augmented by mr88cet). Today, I would like to take the stronger position that while MDL does have the *appearence* of a well defined psycho-acoustic term, the idea is actually quite ambiguous. To bring this into focus, consider the following two experiments: Experiment (1): C D E D C Experment (2): C C C D C Suppose first that these notes are given their normal 12-tet meanings. We can explore the MDL in experiment (1) by minutely adjusting the frequencies of the tones. As the extensive previous discussion on this list suggests, very small changes in pitch do not cause a different melody to be perceived, while large changes will cause a different melody to be heard. While the exact values needed to change the melody will undoubtedly differ depending on which note is changed, who is listening, the timbre of the tones, etc., a value of 1/3 tone for a MDL does indeed seems reasonable. [Digression: Say the E note is slowly flattened. The melody with E at 200 cents above D is surely heard as the same as the melody with E 199 cents above D, is the same as the melody 198 cents above D, etc., and thus there is a continuum of minute changes, each of which is judged the same. Yet at the extreme they are judged different. This suggests one interesting kind of "modulation" that is possible in tunings that have very fine pitch gradations... the "same" melody can be "repeated" over and over, yet at the end of the repeats it is a "different" melody. Has anyone explored this compositional idea?] Now consider experiment (2). Say that the D note is 10 cents above the C note. Such a 10 cent difference is clearly audible (no extreme "hypersensitivity" is required - all we're talking about here is the ability to perceive that the pitches are different), and the melody is X X X up X But if the D note was 10 cents *below* the C (if you excuse the notation), then the melody is X X X down X which is indeed a very different melody! Of course, if the D were perceptibly the same as C, the melody would be X X X X X which is different yet again. This highlights the idea that the *contour* of a melody is aurally far more significant than the details of the pitches. The reason the MDL appears large in experiment (1) is because the contour of the melody does not change, but the MDL appears very small in experiment (2) because the contour does change. Thus the MDL is very different depending on the musical context (in this case the contour of the melody) in which it is investigated. Surely, one should not wish to choose a tuning system based on only a small subset of possible melodic contexts. Bill Sethares SMTPOriginator: tuning@eartha.mills.edu From: John Chalmers Subject: Greek musical intervals, Partch PostedDate: 22-12-97 01:55:21 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: 22-12-97 01:53:14-22-12-97 01:53:14,22-12-97 01:52:47-22-12-97 01:52:47 DeliveredDate: 22-12-97 01:52:47 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 C1256575.0004DC45; Mon, 22 Dec 1997 01:55:01 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA23192; Mon, 22 Dec 1997 01:55:21 +0100 Date: Mon, 22 Dec 1997 01:55:21 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA23317 Received: (qmail 17523 invoked from network); 21 Dec 1997 16:55:16 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 21 Dec 1997 16:55:16 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu