source file: mills2.txt Date: Thu, 16 Jan 1997 10:05:41 -0800 Subject: Reply to Pat Missin From: PAULE >Suppose you had a minor triad 10/12/15 - what major sixth would you add to >make a minor 6th chord? The same minor triad can also be represented as 1/6:1/5:1/4. I've done this experiment millions of times, blindfolded, and with a sustaining tone on my synthesizer, using headphones, I always get 10:12:15:17. It would have been nicer theoretically if I got 1/6:1/5:1/4:2/7, but no, 10:12:15:17 sounds right, and 1/6:1/5:1/4:2/7 sounds wrong. Tuning the strings of my acoustic guitar, assuming I already tuned a 10:12:15, I _do_ end up with 1/6:1/5:1/4:2/7. Amazing, but true. From a theoretical standpoint, this chord minimizes beating between overtones, while the 10:12:15:17 exhibits "fusion" or a blending into a single sensation. Approching this latter chord slowly on the synthesizer, one hears beating in the low frequencies gradually coming to a halt. This probably has something to do with eliminating beating between the virtual pitch and the difference tones. The latter are less pronounced on the acoustic guitar, which is however rich in overtones. It is these sorts of experiments that lead me to quarrel with Daniel Wolf about his use of sine waves, which would invariably lead to the 10:12:15:17 solution, and never to the subharmonic one. Incidentally, there is another important tuning of the minor 6th chord, 6:7:9:10, but only in 12-equal is this the "same" chord. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 16 Jan 1997 19:13 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12507; Thu, 16 Jan 1997 11:21:52 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA12445 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id CAA22448; Thu, 16 Jan 1997 02:21:47 -0800 Date: Thu, 16 Jan 1997 02:21:47 -0800 Message-Id: <199701160521_MC2-F5B-3050@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu