source file: mills2.txt Date: Thu, 29 May 1997 00:43:20 +0200 Subject: intemperate music From: "Collins, Gordon" Bill Alves wrote: >Well, right now I have my synth tuned in a very interesting 11-limit >lattice, and when I play the white keys from C to C it certainly doesn't >sound like any kind of major scale I would recognize. What you've got there is not a major scale. But a major scale is a major scale is a major scale whether a whole tone is 9/8, 10/9, (5/4)^(1/2), 2^(1/6), or something in between. Or whether the scale is 1/1 9/8 44/35 4/3 3/2 176/105 66/35 2/1. This is 11-limit according to at least one definition I've seen (yet another terminology problem plaguing this list). (Actually, I haven't had a chance to listen to this one, but all the ratios are within the ranges bounded by 5-limit JI and 12TET for the corresponding notes.) >This is one real problem with most theory books (by which I assume you >primarily mean harmony books) but I won't get into that. The reason that >they don't go into it is because 12TET is assumed as a standard now. They >don't go into a lot of the "why's," not because they aren't important, but >just because they want to take a lot of things as given in order to get on >to the business of augmented sixth chord arcana. However, in many theory >books of pre-12TET period, tuning is discussed as a prerequisite to the >study of harmony. The point is, those augmented sixth chord arcana are more important *to understanding the music* than are the details of the tuning. In an era when everyone tuned their own way, composers did not specify tuning instructions with their music. That's why you see raging debates about J. S. Bach's desires for the WTC. Rameau, for instance, wrote his Treatise on Harmony when JI was not in use. Yet he gave integer ratios for the various intervals - not one, but *two* ratios for most of them. He then went on to say that the (syntonic) comma is inaudible and proceeded to ignore the difference in the rest of his Treatise. Later (if I recall correctly) he advocated ET without, presumably, any effect on his theories. It is clear that the ratios themselves were merely an explanation for the origin of consonance and dissonance. Modern players don't play in 12TET *per se*, they play *in tune* with each other. Most of the time that results in 12TET because a piano is being used. But a good choir will experience comma shifts when a capella and if string players are playing along with a 1/4CMT harpsichord, they'll match it without thinking about it. >Yes, perhaps accepting enharmonic equivalence was >an important step in European music. Personally, I think it was a step >conceptually taken long before the 18th century and the use of 12TET [....] The idea was certainly considered earlier, but the persistence of non-circulating tunings and of split-key keyboards through the 17th century prove that it was not accepted until then. >[T]he ability to [hear a diatonic scale] in a system is part of what I >meant by "recognizably diatonic" when refering to the flexibility of >tuning systems in defining modes. Your idea of "recognizably diatonic" is interesting, and deserves quantification. As in, "What is the ideal and how far from it can a scale be to be recognized as diatonic?" But treating 3-limit JI and 12TET as variations within the same tuning system.... Well, I have the definite impression that most list contributors consider them to be fundamentally different. Gordon Collins From: SMTP%"tuning@eartha.mills.edu" 29-MAY-1997 00:55:26.10 To: manuel.op.de.coul@ezh.nl CC: Subj: modes vs keys (was: JI modes) Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 29 May 1997 00:55 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03260; Thu, 29 May 1997 00:55:23 +0200 Date: Thu, 29 May 1997 00:55:23 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA03258 Received: (qmail 2353 invoked from network); 28 May 1997 22:55:18 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 28 May 1997 22:55:18 -0000 Message-Id: <338C294D@fsdsmtpgw.fsd.jhuapl.edu> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu