source file: mills2.txt Date: Wed, 28 Aug 1996 15:51:47 -0700 Subject: RE: 7:4 versus... From: PAULE Harold wrote: >--create a pure 4:5:6:7 chord on your synth >--create a 4:5:6 triad, but add a 9/5 on top (9/5 * 4/4) >--create a 10:12:15:18 chord on the same root as each of the previous chords >After you are convinced thatchord #1 is smoother than chord #2[...] Harold, the "classical" dominant seventh chord is a 4:5:6 triad with a 16/9, not a 9/5, on top. While the 4:5:6:7 is unquestionally smoother and more consonant, it is unfamiliar sounding, and Western musicians trained in tonal triadic diatonic practice will initially prefer a 4:5:6 triad with a 16/9. In 41-tet, the three "dominant seventh" chords would be 0 13 24 33 (7/4 on top) 0 13 24 34 (16/9 on top) 0 13 24 35 (9/5 on top) In 12, they are all the same. In 19 and 31, the last two are the same. In 22 and 27, the first two are the same. That's why I went to 41. >Another ear-shock: 22 also has a very good 11/8. Try playing a >4:5:6:7:9:11 chord in 22, and you'll see what I mean. We all know that >in 12, we must omit the major third of this chord (5/4), but notice >how smooth this chord is with good 7/4 and 11/8 approximations! In 12, the closest approximation to this chord, both mathematically and aurally, is C E G Bb D F#. I never heard of omitting the major third of this chord. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 29 Aug 1996 00:52 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04031; Thu, 29 Aug 1996 00:53:14 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA03914 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id PAA16880; Wed, 28 Aug 1996 15:53:13 -0700 Date: Wed, 28 Aug 1996 15:53:13 -0700 Message-Id: <80960828224908/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu