source file: mills3.txt Date: Mon, 1 Dec 1997 23:06:41 +0100 Subject: JI vs. equal temp. From: "Paul H. Erlich" Many of the JI enthusiasts neglect to mention that the language of Common Practice (i.e., Western c. 1600-1900 plus Tin Pan Alley, etc.) music requires the vanishing of the syntonic comma. Some form of temperament (not necessarily equal despite Neil's claim, but any regular or irregular meantone temperament) is therefore required for performances of this music. If one wishes all the chords to be perfectly pure, and one does not make constant slight adjustments to the pitch level of common tones, one will find the pitch of the music wandering, usually descending by several commas. But that does not mean JI music cannot support chord changes. From the latest issue of The Microtome, an interview with Ben Johnston: "I asked myself, suppose in writing some of the really very intense slow movements that he did, Beethoven had not had the tempered scale to work with, but had instead just intonation, what might that music have been? Then I tried to write that piece, as an exercise for myself. It's actually part of a piece--I liked it well enough that I put it into a piece. But at first of course it's just to find out. The richness is one thing, the flexibility is another. The typical Beethoven progression, for example will cause you to drop by a microtonal amount every time the progression repeats itself. What I did was to work it out that the pitch would drop, gradually, until the whole thing drops almost a half step, and then I force it to come back up by working out progressions that would make it do that. That is, of course, quite different from what Beethoven was dealing with. He would have had to deal with that had he been actually using just intonation with the kind of interests that he had." For guitarists, the set of pitches that Ben Johnston needed for this example is quite forbidding, as is any interval less than a comma near the middle of the fretboard. Equal temperaments make sense for guitar music because only then is the same set of pitches available on all strings, and because styles that make use of bending come to grief when one encounters a dog-legged fret. Of course, a fretless guitar alleviates all these problems, but even so one still has to contend with the error of one syntonic comma in tuning the open strings of a guitar to something resembling standard tuning. This will be a problem in any tuning that is not a meantone tuning (12-, 19-, and 31-equal are meantone tunings that happen to be finite). Neil H. has stated that the interval between the G and B strings on his 34-tone guitar is one degree of the tuning larger that the "best" major third, and Jon Catler's D and G strings are one syntonic comma farther apart than a just perfect fourth. My 22-tone guitar also has two adjacent strings separated by a major third augmented by one degree; although this interval is only 1 cent off a just 9:7, it is too low (approx. Eb-G below middle C) to sound consonant by itself. SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Re: TUNING digest 1254 PostedDate: 02-12-97 02:51:00 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: 02-12-97 02:49:22-02-12-97 02:49:22,02-12-97 02:49:16-02-12-97 02:49:17 DeliveredDate: 02-12-97 02:49:17 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 C1256561.0009FF2D; Tue, 2 Dec 1997 02:49:11 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03891; Tue, 2 Dec 1997 02:51:00 +0100 Date: Tue, 2 Dec 1997 02:51:00 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA03889 Received: (qmail 23445 invoked from network); 1 Dec 1997 17:50:53 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 1 Dec 1997 17:50:53 -0800 Message-Id: <19971202015150281.AAA134@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu