source file: mills3.txt Date: Mon, 15 Dec 1997 18:40:20 +0100 Subject: Re: Reply 2 to Graham Breed From: Steven Rezsutek Gregg Gibson Alas, the incommensurability of the thirds and fifths in 22-tone > equal does not arise only when modulation is employed, which I have > always been very careful to note. If, taking C as tonic, we tune by > fifths of 709 cents, we have a G of 709 cents and a B of 1145 > cents.=20 What is `C'? What is 'G'? What is `B'? What is the sound of forcing a seven-sided peg into a ten-sided [for sake of argument] hole? When I first got into tuning, I was locked into the 7 tone diatonic thing, too -- problem was I could never reconsile that with what I wanted to hear. Once I let go of my security blanket and opened up my ears, a whole world opened up around me. I had absolutely no trouble finding a 10 tone scale in 22 by ear,=20 with no theory at all to guide me (until after the fact, that it :). Maybe that makes me special (of full of it), since it's more than the magic 7, but what of it? Lots of people listen to 12 serial rows and to them it is comprehensible [I'm not there yet, myself]. At any rate I make music for myself, and whomever is open enough to listen to what I might have to say. I've no interest whatever in forming a band to please the masses [and I'm not that good=20 yet, anyhow ;-)]. > The idea that a static scale =E0 la just intonation can be employed > melodically so long as one does not modulate, fails to understand > that it is not only in modulation that commensurable consonance is > necessary; the very tissue of melody itself falls apart unless the > consonances are conciliated by temperament. 22-tone equal does not > do this, which is one reason why it is such a poor system. I found this yesterday, while noodling around on my worthless^H^H^H^H 22TET guitar: To make sense of it, you should read Pauls paper on 22. I will say now that I found this aurally, and I have yet to sit down and grind the numbers out. Frankly, numbers don't mean squat if it sounds good, IMHO as a musician. I've been working with Pauls Decatonic Minor modes, notably the=20 Standard Pentachordal form. [I haven't seen the edition of the paper with the graphics, so I'll use the following notation: =09 =09I(10) - Maj decatonic tetrad =09i(10) - min " " =09I-(10) - Maj-Min tetrad =09i+(10) - min-Maj tetrad =09I*(10) - Augmented tetrad. ] What I've found is that the three _consonant_ chords that completly define the mode as suggested by Paul are i, II- and III. =20 I was playing with various patterns of chords like this: i(10) -> v(10) -> i(10) -> IV(10) -> III(10) -> II-(10) -> i when I came up with the following modulation to the subdominant (v): [assume the `(10)' subscript here]: First, firmly establish the sense of tonality: i -> v -> i -> IV -> III -> II- -> i Then, go to the subdom: i -> v -> i -> IV -> III+ -> IV+ -> v (of i) [IX+] -> [X+] -> i (of v) This was every bit as powerful, if not more so, to my ears, as the usual diatonic modulation to the dominant. =20 Now, as soon as I can find an equally cool way to get back again, I'm going to plop a reel on the 8 track and start working on a=20 bass line. ;-) Steve =20 SMTPOriginator: tuning@eartha.mills.edu From: Steven Rezsutek Subject: Correction Re: Reply 2 to Graham Breed PostedDate: 15-12-97 18:57:18 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 15-12-97 18:55:20-15-12-97 18:55:21,15-12-97 18:55:00-15-12-97 18:55:01 DeliveredDate: 15-12-97 18:55:01 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125656E.00626F95; Mon, 15 Dec 1997 18:57:07 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16139; Mon, 15 Dec 1997 18:57:18 +0100 Date: Mon, 15 Dec 1997 18:57:18 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA16137 Received: (qmail 17163 invoked from network); 15 Dec 1997 09:57:14 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 15 Dec 1997 09:57:14 -0800 Message-Id: <199712151753.MAA07535@doghouse.hq.nasa.gov> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu