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