source file: mills3.txt Date: Mon, 15 Dec 1997 13:35:04 +0100 Subject: 19 equal and modal genera From: gbreed@cix.compulink.co.uk (Graham Breed) > Bill Alves (quoted by Paul Ehrlich) made a very interesting comment to > the effect that the four chromatic modal genera (scales) comprising 28 > modes, that I have discovered and posted: > > C D E F G A B C > C D E F G Ab B C > C D E F G Ab Bb C > C Db E F Gb A Bb C > > can be played in the 12-tone equal. More importantly, they are all distinct in 12 equal, as are the other 6: C D Eb F G Ab A C C Eb E F G A Bb C C C# E F G G# A C C Eb Fb F G Ab Cb C C C# E F F# G A C C Eb F Gb G Ab Cb C There are also come chords within these scales that work in 12 equal, but not 19 equal. I can find no opposing example. With 12 pitch classes, then, the harmonic vocabulary is enhanced, with no reduction in the number of genera that fulfil Gregg's criteria. This is a strange argument for 19 equal. Gregg's replies are unconvincing: > ... but the resulting modes conflate a number of > aurally distinct modes into single, neutral modes, and lack much of the > distinct melodic character of the 19-tone versions. Which modes cease to be distinct? Of course, the melodic character will be different in different tunings, but that is not to say one is superior to the others. In good old 31 equal, you get the added bonus of septimal chords, consonant or otherwise. The other arguments are all specifically about 12 equal, and not the infinity of meantone temperaments in which the genera also work. To the more general argument: > Hence, 19-tone equal gives rise to a powerful contrast between > consonance and dissonance, both melodically and harmonically speaking. > The effect is to give music a kind of elastic, forward impetus quite > unknown in the 12-tone equal, which has a more static, uncertain > esthetic. This is a good description of 19 equal. I can see the relevance to rock music, but some of us like a bit more subtlety. The consonances are acceptable. but not that good. Minor triads have a uniquely bright sound, which may be a result of the good minor third. The dissonances something to behold. > The prinicipal > temperaments are 12- 19- 31- 43- 50- & 55-tone equal. Gregg's dislike of non-meantone temperaments is well established. As an existentialist, I cannot agree, because I use and will continue to use such temperaments. However, his neglect of non-equal temperaments is so far unjustified. The obvious scale he's overlooking is LucyTuning, whose 54 cent diesis is at the bottom of the melodic limen. As the difference between 19 equal and LucyTuning is well below a melodic limen, melodies will presumably remain distinctive after the transition. Singers should be able to make the distinctions if they are trained with 19 pitch classes. The advantage is that both melodies and harmonies sound a lot better -- but there I go with my opinions again. So, Gregg, how about it? Now, I'd just like to clear this up: > To give some idea of just how immense this universe is - and remember > these are _real_, usable resources, not purely theoretical, aurally > imperceptible variations - compare the number of modes (I here use the > term loosely merely to indicate a collection of seven notes used in a > melody) consisting of 12 notes taken 7 at a time: > > nCr where n = 12 & r = 7 > = 792 > with the number of modes consisting of 19 notes taken 7 at a time: > nCr where n = 19 & r = 7 > = 50,388 Really, you should define modes relative to a tonic, so the numbers get smaller. With 12, you're choosing 6 from 11, which gives 462 modes. 19C6 is 12376. The contrast is still striking. Including all the transpositions, you get 462*12=5544 and 12376*19=235144. SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net (Gary Morrison) Subject: Re: Reply 3 to Graham Breed PostedDate: 15-12-97 15:58:13 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 15:56:17-15-12-97 15:56:19,15-12-97 15:55:59-15-12-97 15:55:59 DeliveredDate: 15-12-97 15:55:59 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.00520AA3; Mon, 15 Dec 1997 15:58:03 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15977; Mon, 15 Dec 1997 15:58:13 +0100 Date: Mon, 15 Dec 1997 15:58:13 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA15986 Received: (qmail 4430 invoked from network); 15 Dec 1997 06:58:04 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 15 Dec 1997 06:58:04 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu