source file: mills2.txt Date: Mon, 28 Apr 1997 02:05:22 -0700 Subject: Re: syntonic comma in 22-tET From: mr88cet@texas.net (Gary Morrison) >On 22-tET and commas, I have no idea where the pseudo terminology came >from, but the syntonic comma in 22 is just as real as anywhere else. Paul is certainly right that "pseudo" carries some risk in the sense that it suggests that it's not real, and clearly it is. I'm personally open to another prefix. Ivor Darreg is where I heard that term. I don't know if he coined it or got it from somewhere else. >In equal temperament systems, no comma will equal 81:80. If the syntonic >comma is defined as usual, then it is one unit of this tuning, appx. >54.545 cents. Whether one should view the size of a syntonic comma as absolute or relative to a tuning system is a matter of opinion, or perhaps of history. I know of no historical precedent either way, but perhaps Paul does or some others of you do. I believe, however, that a syntonic comma is a specific interval of size equal to an 81:80 frequency ratio, that could be used as a unit of pitch difference, as it is in formulating sizes of meantone fifths. That is a further justification for calling 22TET's reflection of the syntonic situation a pseudocomma - it's size is nowhere near 21.5 cents. But the most important reason to call it something else is that the real syntonic comma produces more pitches per octave's span, but the 22TET syntonic pseudocomma does not. Consider, for example, a I IV ii V V7 I progression, preserving common tones so as to cause your tonic to wander down a comma. You can repeat, or perhaps I should say compound, that progression indefinitely and never arrive at the exact same pitch class as where you started. Whereas 22TET's syntonic psuedocomma never produces more notes per octave's span than the 22 you start out with, so you will land eventually where you started. Realistic applications of that? Well, it's not impossible, in 22TET, to construct a progression starting and ending on the same tonic, but which relies upon a syntonic pseudocomma shift. Perhaps for example, it could pseudocomma shift the tonic down to where an A matches the original Ab, and then "pun" between vi and bVI in a progression that lands you back at the original tonic. That's fundamentally impossible with real syntonic comma shifts. That is, on my opinion and Ivor's, a very fundamental difference, and the most important reason to not call it exactly "syntonic comma". >But even in the key of C you will >sometimes need one E and sometimes the other. True, it need not be a key change, but that's an easy way to show the idea of a pseudocomma in 22TET. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 28 Apr 1997 16:54 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA32520; Mon, 28 Apr 1997 16:54:29 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA32459 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id HAA28334; Mon, 28 Apr 1997 07:51:51 -0700 Date: Mon, 28 Apr 1997 07:51:51 -0700 Message-Id: <199704280525.GAA22164@spectra> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu