source file: mills3.txt Date: Tue, 21 Oct 1997 16:06:02 +0200 Subject: Consonance From: "Andrew L. Kaye" Carl Lumma writes: I like equal-step tunings as much as the next guy. I even like 12. I am always amazed at how good it sounds, and at how powerful it is... Okay, so to you, 12-TET tunings are powerful (and this is cause for amazement, presumably because of the high integer ratios it employs) Carl Lumma writes: Consonance is a factor of the size the number in an intervals ratio. In a sense, yes, because the interval itself is a factor of the sizes of the numbers in the ratio. But in another sense, no: the Random House Dictionary and the New Harvard Dictionary of Music agree that consonance is a factor of cultural conventions and the "mind of the beholder" (or the musical equivalent of that) Carl Lumma writes: An interval 16 cents flat of the sublime 6/5 has frequency ratio 19723/16585. This, of course, is our quite dissonant 12et minor third. So, 6/5 is sublime, and 19723/16585 is quite dissonant, yet powerful. Carl Lumma writes: An interval 18 cents flat of the 6/5 bears ratio 19/16. It is a very consonant minor third found in the duple 16-32 of the harmonic series... And 19/16 is very consonant. Colleagues of the tuning list, the evidence suggests that musical beauty is in the ear of the hearer. I see many claims that low integer ratios produce more "natural" and "perfect" harmonies, but little proof that people actually respond this way. This makes the tuning list sometimes read like some medieval treatise on the nature of God. Why be amazed then, that the Devil incarnate, 12TET, wields such power? SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Dictionary Devils PostedDate: 21-10-97 18:17:44 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: 21-10-97 18:17:01-21-10-97 18:17:02,21-10-97 17:17:40-21-10-97 17:17:40 DeliveredDate: 21-10-97 17:17:40 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 C1256537.00596E38; Tue, 21 Oct 1997 18:16:49 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA22998; Tue, 21 Oct 1997 18:17:44 +0200 Date: Tue, 21 Oct 1997 18:17:44 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA22996 Received: (qmail 15842 invoked from network); 21 Oct 1997 09:17:40 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 21 Oct 1997 09:17:40 -0700 Message-Id: <19971021161926484.AAA261@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu