source file: mills3.txt Date: Wed, 17 Dec 1997 02:38:44 +0100 Subject: Septimal Intervals From: Gregg Gibson The perfect fifth 3:2 is comprised of the minor third 6:5 and major third 5:4. This in turn means that the consonant chords of the 3-limit and those of the 5-limit are congruent, that is to say, they can exist together without producing dissonant intervals. But when we reach the septimals, we find that the perfect fifth 3:2 is comprised of 7:6 and the undoubtedly dissonant 9:7. The other possible septimal bisection of the fifth, 8:7 and 21:16, also includes an undoubted dissonance (21:16) although the closeness of 8:7 makes it too, undoubtedly dissonant. Now a chord with one dissonant interval, is dissonant. Someone may try to deny this, but I am afraid he will fail. There do exist a few septimal triads that seem to escape this argument, e.g. 5:6:7, 4:5:7, 4:6:7. But a few triads do not begin to compare with the richness and variety of the harmonies of the senario. If follows that the septimals, even if one admits them to be weakly consonant - which I do _not_ - certainly give rise, for the most part, to undoubtedly dissonant chords. They have only the most tenuous relation with the harmony of the senario, which on the contrary, forms a closed, well-ordered system. All this was observed centuries ago. Mersenne is full of highly ingenious arguments regarding the septimals - nihil sub sole novum. The Renaissance and Baroque were much occupied with debating whether the septimals might ever be used as consonances, and were much more acquainted with the septimals than the average modern. They concluded, I would say quite reasonably, that the septimals make charming, effective dissonances of a peculiar and valuable kind - but very poor consonances. In former centuries musical theory was an honored and well-rewarded study, and so we should not be surprised if most of what we now think terribly modern questions, are actually very ancient questions. Nor does the accident of being dead make a man necessarily wrong. There is a disposition to assume that because one calls an interval dissonant, one hates it, and wishes to banish it from music. One can trace this assumption to the early Renaissance, during which a certain school of composition did actually try to rid music of all dissonant chords, which were felt to make impossible any attempt to join different melodies harmonically. So today, some people still take it as a personal insult if an interval they fancy is called dissonant, and - very absurdly - try to make consonance and dissonance purely relative ideas with no basis in physics. It is as if everyone were convinced red were the only beautiful color, and were mortally offended if anyone dared to call a green shirt anything but red. But the shirt would still be _green_. But I - just as about 99% of all the Western musical theorists who have ever lived - do really hate and wish to banish a certain narrow class of dissonances - those which are so close to consonances that they beat badly, but yet are melodically confounded with the consonances. These are called mistuned consonances, and anyone who really loves these intervals does really deserve to be insulted, for if these intervals are accepted they will drain instrumental music of most of its expressive power. We find a perfect analogy in modern poetry, where not merely rhyme, but even metre - nay, even clear sense and ordinary grammar - is felt by a certain kind of poet to be too constricting on his power to express his emotions and ideas. And what has been the result? In the mouths of such personnages, language itself becomes more irrelevant to culture than the worst babblings of the Christian or Muslim Fundamentalists. Poetry is now perfectly irrelevant to modern literature, which is dominated by the most miserable, low, fourth-grader prose. But that prose can at least be understood, and is _genuine_ language, and so the people take it to their hearts. Were a true poet to appear today, using metre and even rhyme in the service of easily noble or pathetic thoughts and emotions, he would seem a veritable monster, and would probably be regarded as a madman. But to return to music ? singers will never be corrupted by the lunacy of deliberately using badly mistuned consonances, for they will never be able to sing them, unless perhaps one could induce some hopelessly tone-deaf people to become singers. In an age where a composer - personally he was a charming fellow, I believe - can write a piece consisting entirely of _silence_, why not a new music exclusively for the tone-deaf? SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: Melodic Limen or Threshold PostedDate: 17-12-97 05:20:45 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 05:18:44-17-12-97 05:18:44,17-12-97 05:18:23-17-12-97 05:18:24 DeliveredDate: 17-12-97 05:18:24 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 C1256570.0017AD32; Wed, 17 Dec 1997 05:20:33 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17592; Wed, 17 Dec 1997 05:20:45 +0100 Date: Wed, 17 Dec 1997 05:20:45 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17587 Received: (qmail 28840 invoked from network); 16 Dec 1997 20:20:41 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Dec 1997 20:20:41 -0800 Message-Id: <3497B536.585A@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu