source file: mills2.txt Date: Sun, 16 Mar 1997 21:55:11 -0800 Subject: 4:5:6:7 and Dominant 7th From: Harold Fortuin In response to Andrew Milne and others: My ears & experience tell me that the 12-ET dominant 7th (major-minor 7th) chord is a representation of 4:5:6:7. In my tonal compositions in 19, 22, and 31-ET, I have deliberately made use of the best match to 4:5:6:7 as a dominant 7th, and contrast it with other 7th chords, such as 10:12:15:18 (minor-minor 7th) and 8:10:12:15 (major-major 7th). The resulting voice-leading of 10:12:15:18 followed by 4:5:6:7, with both built on the same tonic, is naturally microtonal, and very acceptable to my ears. I also find the voice-leading of 4:3 to 7:4 of V to 5:4 perfectly valid. My evolving theory of >12-ET tonality treats 7:4 built on scale degree 5 as a necessary "chromatic" inflection of scale degree 4, comparable to the raising of the 3rd of the V7 chord in minor keys in standard 12-ET practice. I do not consider 9:5 or 16:9 to be proper 7ths for 4:5:6 in >12-ET practice--they should be treated as passing tones, and not be fused onto 4:5:6 when a better 7:4 match is available. Those of you who write in >12-Ets simply for purer 3 and 5 limit intervals will naturally object--but understand that my rationale for using >12-ETs is to extend traditional harmonic practice through the additional simple 7 and 11-limit intervals available in >12-ETs. Those of you that have a cassette of my music might wish to add their evaluation of this practice. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 17 Mar 1997 06:56 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01208; Mon, 17 Mar 1997 06:56:54 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01216 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id VAA26746; Sun, 16 Mar 1997 21:55:27 -0800 Date: Sun, 16 Mar 1997 21:55:27 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu