source file: mills3.txt Date: Wed, 17 Dec 1997 05:20:45 +0100 Subject: Melodic Limen or Threshold From: Gregg Gibson I wish to elaborate yet again on the question of the melodic limen or threshold. I shall have plenty of new things to say, so no one will be bored. When a note of a melody is raised or lowered by as much as 30 cents or so - not coincidentally about half the melodic limen - the typical careful listener begins to perceive that note as somehow vaguely changed, as 'colored' or 'shaded', but the melody itself remains unchanged. The exact value depends slightly on whether the particular interval in question is consonant or dissonant with the tonic, as well as on other factors, notably the timbre of the instrument. It is well-known that certain instruments producing a rich array of partials produce a more clear conception of definite pitch in the minds of listeners than other instruments of a harsher or more noiselike character. According to Benade's hypothesis, which common experience certainly supports, the mind can, even in monody, apparently perceive consonances more exactly than dissonances. As we sharp or flat the note by more than 30 cents or so, we begin to convince an ever larger percentage of listeners that the note has not merely been 'shaded' or 'colored' but essentially changed, and the melody itself essentially altered. Those who imagine that audiences can be taught to be more perceptive to the point of changing markedly the point at which they consider the melody to be essentially changed, certainly delude themselves; even peoples who treasure enharmonic melody above all, such as the Arabs and Indians, never require such superhuman hypersensitivity of their audiences. But even were it possible to acquire such godlike powers of discrimination, we would only reduce music into a different art-form, with quite a different mission, namely spoken speech. By the time we have sharped or flatted a given note within a melody by about 60 cents, we have - under typical musical conditions of confusion, distraction and excitement - eliminated virtually all doubt in virtually all listeners that the melody has been changed. To respect these limits on human aural acuity is to produce music that may be good; to violate these limits is to ensure that music will be in bad taste. Not coincidentally perhaps, it so happens that singers cannot be trained to reliably sing intervals closer than about 60 cents. That, for example, the Greek theorists chose 56 cents and even slightly closer intervals to tune instruments enharmonically, suggests at most that there is sometimes a regrettable tendency to tune instruments so as to produce slightly narrower intervals than what singers can comfortably sing. Snobbery is a universal human trait, and rarely produces anything very admirable. Note also that there are real limits on a singer's ability to reliably sing a long sequence even of 1/3 tones. A melody with four or five 1/3 tones in a row, even if it could be sung, which is doubtful, would probably be apt only for some strange special effect. One of the delightful paradoxes of the 19-tone equal is that, even though it has a wider, slightly more readily-sung diatonic semitone than the 12-tone equal (126.6 cents versus 100 cents) nevertheless the 19 system has a far wider variety of chromatic modes, because its tuning degree is narrower (63.3 cents versus 100 cents). Returning however to my immediate subject: it is easy to confuse our ears' ability to perceive a minute change in pitch of a given note sounded successively, with our far less accurate ability to perceive a note's having been changed in pitch _in a given melody_, where we have nothing to compare that note to, except the tonic and the other notes of the melody. I wish to emphasize that the melodic limen seems to be affected but very little by cultural environment. The modern Arabs are a good example. Under both native pythagorean and heavy Western influence, the modern Arab theorists have adopted 24-tone equal temperament to describe their native melody. (They have also copied the 53-tone equal from the West, which from their point of view at least gives an approximation to the 1/3 tone.) The typical Westerner finds 24-tone equal less notionally threatening to his theoretico-musical worldview than 19-tone equal or some other system, and the Arabs have been greatly influenced by the modern West, even in such intimate matters as sexual mores and the like. Nevertheless, beginning as long ago as Villoteau (1809), whenever Arab singers are studied, the evidence is quite impressive that they use, in enharmonic melody, a range of close intervals much better described by a 1/3 tone than by a 1/4 tone. Various Westerners, beginning with Ellis (a person not known for a particularly open mind), have attacked these results in all sorts of ingenious ways. But the fact is that singers of whatever culture find melodic intervals as close as 50 cents very difficult to sing, and tend to substitute a somewhat wider interval. This is not a very pleasing subject to the typical modern Western musician, who usually finds even the idea of a melodic 1/4 tone, much less a melodic 1/3 tone, alien to his habits of theoretical thought, and this in spite of the fact that our _own_ popular singers deliberately use 1/3 tones all the time, at least since the 60's ? but so far as I can discover, do not use 1/4 tones except by accident. In short, so strong is the insidious hold of the 12-tone equal on the modern academic Western musician, that he would rather pretend that the Arabs use the mythical vocal 1/4 tone, because this seems to be more in theoretical conformity with the 12-tone equal, than admit that they use something much closer to the 1/3 tone, which anyone can sing, but which leads directly outside 12-tone equal to 19-tone equal temperament. There really do seem to now exist certain Western musicians whose ear-training at the piano has succeeded so well, alas, that they prefer the 12-tone equal even to just intervals. But such are not the musicians that screaming crowds try to tear to pieces in a frenzy of adulation. It is the rock vocalists, who, at least incipiently, use the tonality of the 1/3 tone, who enjoy _that_ godlike destiny, which Haydn, Mozart and Beethoven in their day likewise enjoyed. And this is very ironic, you know, because the music of a Haydn even now might have a far greater popular following than it does have, were it played not in 12-tone equal, nor yet in what Haydn used to compose at his keyboard (a selection from 55-tone equal, it appears) but in the tonality which the rock vocalists are steadily making ever dearer to the masses - that of the 19-tone equal. And as it happens, the 19 system is far closer in harmonic effect to what most of the classical composers used (at least down to Beethoven), than is the 12 system. Beethoven, by the way, played in 19-tone equal is a treat indeed. SMTPOriginator: tuning@eartha.mills.edu From: "Bob Lee" Subject: 19tet vs. meantone? PostedDate: 17-12-97 07:23:39 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: 17-12-97 07:21:38-17-12-97 07:21:39,17-12-97 07:21:17-17-12-97 07:21:17 DeliveredDate: 17-12-97 07:21:17 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256570.0022ED41; Wed, 17 Dec 1997 07:23:25 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17457; Wed, 17 Dec 1997 07:23:39 +0100 Date: Wed, 17 Dec 1997 07:23:39 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17682 Received: (qmail 6600 invoked from network); 16 Dec 1997 22:23:35 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Dec 1997 22:23:35 -0800 Message-Id: <01bd0ab3$f8e7b380$b25e04c7@default> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu