source file: mills2.txt Date: Thu, 16 Jan 1997 02:01:38 -0800 Subject: More on the comma experiment From: Gary Morrison <71670.2576@compuserve.com> Interesting experiment in general, Steve. The most important effect of using V7 instead of V (other than the well-known ones of dominant 7ths vs dominant triads) is that scale degree 4 in addition to 2 becomes a common tone between ii and V7. Try out these subtly different 22TET four-part harmonizations, using a similar progression: 1. Diminished ii (borrowed chord) (there's a pseudocomma error on the b6, but no precedent for that pitch either): 13 9 9 9 7 7 4 4 4 0 0 0 0 0 20 20 16 15 13 13 9 9 0 0 I IV iio V V7 I 2. Scale-degree-2 common tone forced not to be common to avoid pseudocomma-sharp fourth: 13 9 9 9 7 7 3 4 4 0 0 0 0 0 20 20 16 16 13 13 9 9 0 0 I IV ii V V7 I 3. Tonic allowed to wander to preserve all common tones and avoid all pseudocomma errors: 12 9 9 8 7 6 3 3 3 0 0 21 0 21 19 19 16 16 12 12 9 9 0 21 I IV ii V V7 I My personal impressions were these: The diminished and wandering tonic (first and third) cases flow the most smoothly (smoothness being one, but not the only, interesting consideration). The main difference between those two was the obvious one: That the first obviously had the more dissonant diminished ii instead the more typical minor ii, and the third had that wandering-tonic sensation of "???!!! we did everything right but we landed in the wrong place !!!???", right about on the V. The other difference I heard between those two was that the V sounded a little odd in BOTH based upon the small vs. large whole tone in the exposed soprano line. The first one with its large upward whole-tone made that chord seem over all oddly too high-pitched, even though it seemed to have the right harmony, whereas the third one sounded a little flat even though the harmonic effect seemed right. In the second one, the upward movement from 3/22 to 4/22 struck me as too freaky with the already "too-high" effect of the large whole-tone in the soprano. To me the second one was too disconcerting (and discontiguous from ii-V) for that reason. By the way, to actually play these, I finally broke down and stuck masking-tape labels of the numbers above on the keys and then sequenced each part. I have no idea how keyboardists can possible play on stretched keyboards! This woodwind & guitar player is just amazed that anybody can do that! Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 17 Jan 1997 03:24 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19288; Fri, 17 Jan 1997 03:27:51 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA19269 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA24947; Thu, 16 Jan 1997 18:27:48 -0800 Date: Thu, 16 Jan 1997 18:27:48 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu