source file: mills3.txt Date: Tue, 9 Dec 1997 01:44:47 +0100 Subject: More on the 19-tone Equal Temperament From: Gregg Gibson My comments on the intervals of 19-tone equal at the limit of human perception seem to have provoked some disbelief. I am indeed serious. Of course anyone can distinguish between tones as little as 5-10 cents apart in successive hearings. But if one substitutes one such tone for the other in a given melody, not one person in a thousand will identify that _melody_ as different. This is what I mean. I can make myself no plainer. I grant that melodies wherein one substitutes one of the degrees of the 22-tone or 24-tone equal for an adjacent degree, do occasionally (not usually) produce a change in melody if one of the degrees is highly consonant. Adjacent degrees of the 31- and 34-tone equal _never_ produce such a change in melody to my ears. Naturally there may be exceptional individuals with more acute powers of discrimination, though I doubt it. But music is written for the many, not the few. 55-60 cents as the limen of intervallic perception is well-established in the literature. Pratt for example in his Meaning of Music, as I recall, found a value "just wider than a quarter-tone", and Seashore & Jenner found a value between 53 and 61 cents. Naturally no one should accept these results without making trial for himself. I find however that my own ears are fully in agreement with these results. There is nowadays a disposition to be suspicious of anyone who ventures to condemn _any_ system of tuning. The presumption seems to be that everything is good for something. The advocates of the 12-tone equal have often been willing to use any argument to defend their chosen system (e.g. the egregious Barbour, who ventured to write a book on tuning, having never heard any tuning system other than the 12-tone equal) and this perhaps, by a kind of reaction in favor of experimentation, has induced many to doubt that any standard tuning system should exist. This is emphatically not the attitude of the great artists of the past, whose work depends as much on calculated limits as on absolute freedoom. Nor was this the attitude of musical theorists of the past, who tended rather to automatically dismiss all tunings that did not conform to quite specific and demanding requirements. And I am far from certain that their attitude was merely benighted. A temperament which results in continual whining dissonances in place of consonances may interest a few, but will never displace the 12-tone equal, nor should it. Music which innovates too radically is somewhat in the case of poetry which should adopt so many new words that the sense is obscured. I have observed that rock singers use a great many third tones; there is seldom a popular melody nowadays without them. This perhaps is what makes rock melody so much more pleasing to the masses than the 12-tone melodies of the last century, which are now almost wholly disregarded. I suspect that if 12-tone equal is ever dethroned, it will be by rock instrumentalists wishing to reproduce the subtler, necessarily 19-tone melodies of their vocalists. All tuning systems which are not mere noise, reduce approximately either to the 12-tone or the 19-tone equal, melodically considered. This follows inescapably from the principle of the melodic limen. 31-tone equal for example reduces melodically to the 12-tone equal (with a few exceptions where the augmented tone occurs, where it has rather a flavor of the 19-equal), because the adjacent degrees of the 31-tone equal are confounded in melody. 17- and 22-tone equal do possess a certain melodic independance, but are so seething with sour dissonances that they are really not worth discussing. I have used tree diagrams to examine all the possible heptatonic modes of the 19-tone equal that have a modicum of consonant intervals and chords, hence the four new modal genera, which I have previously suggested might profitably be added to the diatonic. In harmony these 28 new modes constitute what may be called the chromatic music, whose existence has been hitherto intuited, but never plainly defined. It is fascinating that Francisco Salinas in the 16th century in his De Musica observed that the 1/3 comma mesotonic (virtually equivalent to the 19-tone equal) would alone permit the realization of the enharmonic genus of the ancients. This is indeed the case, of which more later. SMTPOriginator: tuning@eartha.mills.edu From: Aline Surman Subject: lutes again PostedDate: 09-12-97 03:17:08 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: 09-12-97 03:15:21-09-12-97 03:15:22,09-12-97 03:15:09-09-12-97 03:15:10 DeliveredDate: 09-12-97 03:15:10 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 C1256568.000C6010; Tue, 9 Dec 1997 03:15:10 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10202; Tue, 9 Dec 1997 03:17:08 +0100 Date: Tue, 9 Dec 1997 03:17:08 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA10198 Received: (qmail 9133 invoked from network); 8 Dec 1997 18:17:06 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 8 Dec 1997 18:17:06 -0800 Message-Id: <348CB3A9.6D90@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu