source file: mills3.txt Date: Fri, 10 Oct 1997 19:53:56 +0200 Subject: Another version of 12-tET From: Manuel.Op.de.Coul@ezh.nl To celebrate the 1200th digest, I will present another version of 12-tET: 0: 1/1 0.000000 1: 1662005/1568693 100.0340 2: 1760309/1568693 199.5188 3: 1865285/1568693 299.7998 4: 1975877/1568693 399.5162 5: 2093975/1568693 500.0176 6: 10223/7229 599.9410 7: 2349463/1568693 699.3218 8: 355633/224099 799.5039 9: 2636887/1568693 899.1276 10: 399193/224099 999.5407 11: 2960239/1568693 1099.381 12: 2/1 1200.000 Before you think that I went crazy, I didn't invent this. I just calculated the ratios for the sake of it. This tuning was used in pianos by the English "Best Factory Tuners" in 1840. The idea becomes clear by showing the beat frequencies of 3/2 for the octave above middle C: 0: 0.000: -1.1930 1: 100.034: -1.1930 2: 199.519: -1.1930 3: 299.800: -1.1930 4: 399.516: -1.1930 5: 500.017: -1.1930 6: 599.941: -1.1930 7: 699.322: -1.1930 8: 799.504: -1.1930 9: 899.127: -1.1930 10: 999.540: -1.1930 11: 1099.381: -1.1930 12: 1200.000: -2.3859 Now someone can persuade his piano tuner to set this tuning and let us know if it's an improvement. Reference: Jorgensen, Owen Henry. _Tuning. Containing: The perfection of eighteenth-century temperament, The lost art of nineteenth-century temperament and The science of equal temperament. Complete with instructions for aural and electronic tuning_. Michigan State University Press, East Lansing, 1991. Manuel Op de Coul coul@ezh.nl SMTPOriginator: tuning@eartha.mills.edu From: Manuel.Op.de.Coul@ezh.nl Subject: Re: dynamic JI PostedDate: 10-10-97 20:10:25 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: 10-10-97 20:09:49-10-10-97 20:09:50,10-10-97 20:10:18-10-10-97 20:10:18 DeliveredDate: 10-10-97 20:10:18 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 C125652C.0063C4DA; Fri, 10 Oct 1997 20:09:44 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13528; Fri, 10 Oct 1997 20:10:25 +0200 Date: Fri, 10 Oct 1997 20:10:25 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA13539 Received: (qmail 6077 invoked from network); 10 Oct 1997 11:10:20 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Oct 1997 11:10:20 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu