source file: mills2.txt Date: Fri, 15 Nov 1996 11:39:51 -0800 Subject: RE: Reply to Bruce Gilson From: PAULE I wrote, >> My apologies, Bruce; I didn't see the word "melodically," but seeing it now >> I think you are quite correct. Harmonically, though, the situation is quite >> different, if you're talking about anything beyond 3-limit harmony (perfect >> fourths and fifths). Gary wrote, >Uhmmm... Perhaps I'm missing something then. It seems to me that a >diatonic >half-step 1/4 the size of the whole step would sound pretty darned strange >melodically too. It's a little bit disconcerting in 17 as it is. To my ears >anyway. Really? I think diatonic melodies in 17 are quite beautiful. Witness Blackwood's 17-tone etude, for example. By avoiding major triads in structural places, he makes the piece work wondefully. Take a simple melody in a major mode and play it in a tuning where the half-step is 1/4 or 1/3 the size of the whole step (22- and 17-tet, respectively). Sounds great to me! As soon as you add the slightest bit of harmony, say a tonic or dominant drone, YUCK! Actually, minor modes in 22 work pretty well, since the Pythagorean minor triad there closely approximates a 6:7:9. Randy Winchester's 22-tone improvisation works beautifully on this principle. I'm putting some finishing touches on a Xenharmonikon paper right now, and I just happened to note that theorists who derive the diatonic scale from three triads are perpetrating a historico-geographic fallacy. The diatonic scale happens to have lots of good triads in some tunings, but it is a melodic entity first and foremost. Otherwise, why don't we find a 5-note scale that is derived from two triads, or a 4-note scale that is derived from three dyads (perfect fifths) in use anywhere? Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 15 Nov 1996 21:38 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13153; Fri, 15 Nov 1996 21:39:42 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA12083 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA27340; Fri, 15 Nov 1996 12:39:39 -0800 Date: Fri, 15 Nov 1996 12:39:39 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu