source file: mills2.txt Date: Tue, 29 Apr 1997 17:31:00 -0700 Subject: Post: Reply to Paul Rapoport on srutis a From: PAULE Paul R, I would like to see your acquaintance's work on srutis. I have recently scoured the entire Harvard music library for every speculation and shred of evidence on their tuning, for my paper on 22-tone temperament. I was pleased to find some of my original speculations, such as the tempered tuning of the sruti representing kakali-ni in sa-grama and antara-ga in ma-grama, to be repeated by several authors and evidenced in the construction of ancient instruments. I would be pleased to offer comments on your acquaintance's paper. I did not respond originally because I figured someone would be more of an expert in this area than I. Paul Erlich 145 College Ave #2 Somerville, MA 02144 Now for the other issue: >If only the 81:80 is a syntonic comma, then only the 3:2 is a (perfect) >fifth. We don't restrict the latter that way; there's no reason I can see >to restrict the former either. But of course it's necessary to specify >whether you mean just (as in 81:80) or not. The context usually >determines; in any ET, it's obvious. NO, IT'S NOT OBVIOUS AT ALL! In any ET, we would agree that the perfect fifth is the closest approximation to the 3:2. We would also agree that the syntonic comma is NOT necessarily the closest approximation to the 81:80 -- for example, in 22-tET the closest step size to an 81:80 is 0 steps, and yet we would both call 1 step the syntonic comma. Why? Because the syntonic comma is defined as interval obtained by tuning several successive CONSONANT intervals. The two important definitions are as follows: (1) Tune up three perfect fourths, down an octave, and down a minor third. You are now a syntonic comma lower than where you began. In 22-tET, this is 1 step. (2) Tune up four perfect fifths, down two octaves, and down a major third. You are now a syntonic comma higher than where you began. In 22-tET, this is 1 step. So the syntonic comma is 1 step in 22-tET, even though 0 steps would be closer in size to the JI syntonic comma. This situation would never occur for a basic consonace like the perfect fifth. Thus the "pseudo" terminology is warranted. Now there are tunings where (1) and (2) give different answers! For example, in 21-tET, definition (1) gives a syntonic comma of 0 steps, while definition (2) gives an syntonic comma of -1 (that's minus 1) steps. Another example is 20-tET, where definition (1) gives a syntonic comma of 1 step, while definition (2) gives a syntonic comma of 2 steps. So I would argue that if an ET is not consistent within the 5-limit, the syntonic comma is undefined in that tuning. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 30 Apr 1997 02:34 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00941; Wed, 30 Apr 1997 02:34:51 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA00935 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id RAA13583; Tue, 29 Apr 1997 17:33:09 -0700 Date: Tue, 29 Apr 1997 17:33:09 -0700 Message-Id: <199704292150.RAA30852@phyleus.interlinx.qc.ca> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu