source file: mills3.txt Date: Wed, 10 Dec 1997 01:06:59 +0100 Subject: Reply to Paul Ehrlich From: Gregg Gibson Your point regarding the 3/4 tone of Arabic music is at least debatable; in highly conjunct music the voice and the musical understanding are appreciably more sensitive than in more disjunct music. Nevertheless most researchers have found Arab singers quite unable to reliably reproduce these very narrow intervals, much less anything so esoteric as the neutral third, which usually amounts to nothing more than a slightly inaccurate minor third. You are incorrect that 31-tone equal has more usable melody than 19-tone equal. Between C and D, for example the 31-tone equal has Dbb, C#, Db and Cx ascending. The first of these is melodically confounded with C, the second two are melodically confounded with each other, and the last is confounded with D. The 31-tone equal is in fact a monstrously complex, inefficient way of returning us to our melodic starting-point of 12-tone equal. It is much smoother indeed, but melodically it is a dead-end. There is one exception; as I intimated, the augmented tone in this system does seem to be distinct from the minor third, perhaps because the former is both conjunct and dissonant, while the latter is consonant and at least putatively disjunct. I appreciate that even worthless systems are worthy of extensive study - else how would we know them to be worthless? I also have studied the 22 system. It enjoys extensive advocacy by those who associate it with Indian music, which is certainly worth some attention! The 22-tone equal suffers from two grave defects however, either one of which would be sufficient to condemn it to the category of a curiosity. Its tuning degree is at the outermost limit of what can be reliably distinguished in melody. By this I mean if one flats or sharps a note by 55 cents that note will sometimes be interpreted as having essentially changed the melody, but sometimes not - and more often not. Musicians do not write for exceptionally acute listeners, but for the masses. The second defect of the 22-tone equal involves its failure to close the cycle of fifths. I am aware that some will say to themselves - so what? But a musical system that does not close the cycle of fifths has at a stroke isolated itself from 99% of the music not merely of the western 19th century, but from virtually the whole of the western tradition, and from many other musical traditions as well. Such musical systems, like just intonation, are mere curiosities, and are far more impoverished in usable, aurally distinct resources even than the 12-tone equal. The four scales I gave have consonant triads (major or minor) available on four of their seven degrees. For example: C D E F G Ab B has consonant triads on C, E, F & G, but not on D, Ab or B. I hope this clarifies the matter. Your refer to the 7 and 11 limits. The latter is a mere fantasm of the just intonationists, and is not audible to the ear as anything other than dissonance. The septimal limit is more interesting. But it is dissonant, however this may trouble those who aspire to forever extend the boundaries of consonance, until someday I presume, we shall find everything consonant, and music need trouble itself no longer with any rules or constraints whatever... It will also no longer need to trouble itself with pleasing an audience, for it will have none. Actually however, the 19-tone equal is the _only_ temperament that gives the septimal intervals in such a form that they can be melodically distinguished from adjacent intervals. This is a consequence of the fact that in this system only are the septimal intervals far enough away from adjacent intervals to preserve their own unique melodic character. Your reference to individuals being trained to reliably distinguish melodic intervals as close as 10 cents is the most fantastic piece of information I have ever been privileged to encounter. Presumably such monsters would no longer recognize "Mary Had a Little Lamb" as a single melody, but would distinguish several hundred million essentially different melodies instead! You will forgive me if I remain skeptical of this possibility. SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Misc 3 PostedDate: 10-12-97 01:43:29 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: 10-12-97 01:41:33-10-12-97 01:41:34,10-12-97 01:41:20-10-12-97 01:41:21 DeliveredDate: 10-12-97 01:41:21 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 C1256569.0003CCCD; Wed, 10 Dec 1997 01:41:30 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11107; Wed, 10 Dec 1997 01:43:29 +0100 Date: Wed, 10 Dec 1997 01:43:29 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA11114 Received: (qmail 29147 invoked from network); 9 Dec 1997 16:43:25 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 9 Dec 1997 16:43:25 -0800 Message-Id: <19971210004239812.AAA309@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu