source file: mills3.txt Date: Fri, 12 Dec 1997 02:22:13 +0100 Subject: 22-tone equal, reply to Ehrlich From: Gregg Gibson My manner of saying that the 22-tone equal does not close the cycle of fifths was too abbreviated and has given rise to misunderstanding. Of course all temperaments are cyclic by definition, in the sense that their fifths return to the same point, with the exception indeed of a few such as 24- & 34-tone equal which consist of two non-communicating, parallel series of fifths. When I say the fifths are non-cyclic, I mean that, although the thirds and sixths are consonant so long as one does not modulate or use certain melodic intervals, nevertheless they give rise to such dissonant thirds and sixths that the cycle of modulation is broken. And not only the cycle of modulation, but of many melodic progressions as well. Your phrase "vanishing of the syntonic comma" is unfortunate. This comma does vanish in the 22-tone equal, but at a value (218 cents) that leads to excruciatingly dissonant 'major thirds' (436 cents), minor thirds (273 cents), major sixths (927 cents) and minor sixths (764 cents) as soon as one modulates more than a few keys. But even if one remains within the same key, many intervals within the tonal fabric become dissonant so long as fifths of 709 cents are preserved. To those who treasure each new whining, commatic dissonance like the goose's golden egg, and hate consonance with a passion, this temperament is indeed a gift from the gods. The major semitone (164 cents) and minor semitone (55 cents) are utterly divergent from western habits, though the former is melodically usable. Another and simpler way of expressing the non-cyclic character of the 22-tone equal is to observe that the three consonant cycles (those of the fifth, major third and minor third with their inversions) are incommensurable. What this really entails is often overlooked. Some theorists simply look at the 327- 382- & 709-cent intervals of 22-tone equal, and conclude that this temperament has good representations of the consonances. In doing this, they forget that as soon as one modulates (or proceeds by any number of melodic phrases that involve the simultaneous use of the 5- and 3- limits) one obtains highly dissonant thirds, so long as the fifths are held consonant. This is doubtless obvious to many theorists, but not to all. Mandelbaum, for example, a person of no inconsiderable theoretical attainments, fell into this trap. It is meaningless to call a temperament non-cyclic in the sense that one calls the just or pythagorean intonations non-cyclic. When I say that a temperament is non-cyclic I mean that the three consonant cycles do not agree with each other, and that the cycle of fifths does not close in such a way to permit cyclic modulation, or indeed any but the most constrained melodic progressions. 17- 22- 29- 41- & 53-tone equal all fall into this category. Our age is accustomed to very cavalierly dismiss every shred of musical theory left to us by our ancestors - or else to blindly worship the past. An academic minority is eager to deny every principle that the past held dear - while the popular majority tends rather to preserve certain musical elements in simplified form, while accepting many non-Western melodic elements. The same people who detest the very idea of consonance, without quite knowing why, are very often the same people who blindly worship Beethoven or Mozart. Those who are truly "freemen in thought" are respectful of the past at the same time that they searchingly question it. Indian singers - see Levy: Intonation in North Indian Music - do not seem to use the 22-tone equal at all. They certainly do not sing 436-cent major thirds, which occur repeatedly in the melodic texture of 22-tone equal, unless very flat fifths of 655 cents are employed. Of course the centre of 22-tone equal in India is nowadays supposed to be the South. Tuning now to a different issue, you appear to assume that because the historic Arab theorists - most of them more concerned to interpret ancient Greek theory than the practice of their own musicians - prescribe or record a tuning, all are Neanderthals who do not fall down before this tuning in awe. I certainly do not hold Arabic music in contempt. I have devoted much attention to the subject. Gamelan scales by the way can be very satisfactorily reproduced in 19-tone equal. I am aware of the cents in a (12-tone equal) tone. Difference of opinion need not give rise to random unpleasantness. Certainly I mean no offence to anyone in stating what I am convinced are facts. I had much rather be called a 'popularist' than an elitist. Your attempt to equate pitch variation in the articulation of spoken words with musical melody deserves careful consideration. Why, however, would anyone wish to replace (or confuse) melody, which is reproducible, and which is ideally meant to _heighten _ the effect of language or poetry, with the articulation of spoken language, which is nonreproducible, and a wholly different art besides. There have been attempts in this direction, not all of them flat failures. Popular singers occasionally lapse into spoken language for effect. But if this becomes usual it is in very bad taste. I do not deny that non-Western traditions use intervals different from those commonly used in the West. Thank God that they do! I do however categorically deny that any singers whatever (allowance made for the occasional alien with 31-tone equal ears) can reliably reproduce intervals narrower than 55-60 cents in melody. Those who imagine I am insulting non-Western musical traditions in making an observation of fact, misinterpret my motives. I am a great admirer of Indian music and culture, for example. In the actual world these musical traditions are under assault by the overwhelmingly dominant 12-tone equal temperament (instrumentally considered.) Meanwhile, paradoxically enough, our own popular music - vocal rock music - is busily assimilating as much non-Western melos as it can. But it is _not_ assimilating vocal melodic intervals less than about 60 cents in width, for the excellent and quite matter-of-fact reason that singers cannot deliberately reproduce or remember such intervals. It is easy to say: "oh yes they can," and I have no objection if someone wishes to attempt to prove the contrary. The evidence is very much against this, however. There are not a few advocates of 12-tone equal who have managed to convince themselves that the melodic limen is in the region of an equal semitone, which I also deny. There does seem to be an elitest attitude abroad that one demonstrates one's own musical superiority by hearing - or asserting that one hears - extraordinarily minute intervals as essential melodic changes. One is reminded of the bright young student who 'proved' that Helmholtz had preferred just intervals to 12-tone equal ones only because he suffered from a disease of the inner ear, that made his aural faculty preternaturally sensitive! Or again, I am reminded of the Greek theorists made fun of by Aristoxenos - very estimable persons, no doubt - who cared nothing for living or practical music, but who occupied themselves with ceaseless attempts to distinguish ever narrower intervals. Meanwhile, around them even the enharmonic was abandoned, perhaps for want of any such firm theoretical basis as the 19-tone equal might have provided them. Music is primarily a creative, not an exhibitionist art. SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: More on 22-tone equal PostedDate: 12-12-97 07:00:58 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: 12-12-97 06:59:06-12-12-97 06:59:07,12-12-97 06:58:51-12-12-97 06:58:51 DeliveredDate: 12-12-97 06:58:51 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 C125656B.0020DC83; Fri, 12 Dec 1997 07:00:52 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13441; Fri, 12 Dec 1997 07:00:58 +0100 Date: Fri, 12 Dec 1997 07:00:58 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA13447 Received: (qmail 8600 invoked from network); 11 Dec 1997 22:00:52 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 11 Dec 1997 22:00:52 -0800 Message-Id: <3491353D.D5B@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu