source file: mills2.txt Date: Fri, 23 May 1997 23:00:01 +0200 Subject: intemperate music From: "Collins, Gordon" To get back to the subject that I really wanted to bring up... Bill Alves wrote (in response to something else, but providing a good starting point): >In my definition of modes in the European tradition, they include at least >the following defining characteristics: > >1) A tuning system, though it may be somewhat flexible as long as the >general pattern of intervals (below) remains recognizable. While there has been a fairly strict intonational standard at most times and places, "somewhat flexible" here is a considerable understatement. The distinction between n-limit JI, x-comma meantone, well-temperament, and 12TET is *totally irrelevant* to the definition of modes and scales! Look at a music theory book and its description of musical resources. Where is there any discussion of pitch or tuning? It just doesn't matter. The only thing that rules out applying JI or meantone is the circle of fifths with its enharmonic equivalence of notes. It also is not sufficient to define "pitch areas" for the notes. There are Renaissance motets in which, depending on one's interpretation of _musica ficta_ rules, the range of pitches used for F overlaps that used for E *within the same piece*. This is not just due to comma shifts, but due to _ficta_ inflections. >2) A subset of pitches from that tuning system, or, put another way, a >pattern of intervals. (In the European tradition this means the diatonic >set.) But the notes of the modes were not taken from a larger set. They WERE all the defined notes. Others were *added* to the set as necessary for polyphony. They were initially considered as intonational inflections, only later being accepted as separate notes in their own right as sharps and flats. I agree with Daniel that modes and scales can only be defined in terms of whole tones and "half" tones, as a pattern of approximate intervals. I don't think that those patterns can be described as pitches selected from a predefined tuning system. >Number of pitches in the tuning system/number of pitches in the >subset/number of commonly used auxiliary tones. > >[qualification snipped] > >Thus traditional diatonic modes are: > >12/7/0 In light of the above, the original modes would actually be: 7/7/0 Guido's system formally allowed for: 8/7/0 and the whole system with _musica ficta_ would be: infinite/7/infinite as there was no predefined set of available frequencies, and no upper limit on available auxiliary (_ficta_) pitches. Reducing this to 12 requires accepting enharmonic equivalence, closing the circle of fifths. That idea strikes me as one of the most pivotal notions in the history of Western music, yet as far as I can tell, it grew gradually over centuries and without much comment, only becoming fully accepted in the 18th century. Only then could 12TET, long understood, be applied. It was far from being the foundation. Gordon Collins Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 24 May 1997 06:40 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09120; Sat, 24 May 1997 06:40:05 +0200 Date: Sat, 24 May 1997 06:40:05 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA09119 Received: (qmail 17705 invoked from network); 24 May 1997 04:40:02 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 May 1997 04:40:02 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu