source file: mills3.txt Date: Tue, 25 Nov 1997 10:08:20 +0100 Subject: To Paul Erlich From: Daniel Wolf Shohe Tanaka's dissertation _Studien im Gebiete der reinen Stimmung_ is i= n volume 6 (1890) of the Vierteljarhsschrift fu''r Musikwissenschaft. My translation of the full text is in revision; a rough translation of a sma= ll part of the text was made for Larry Hansen some years ago and was publish= ed (a surprise to me) in an issue of Xenharmonikon (for what it is, the translation is okay but the layout is lousy). = Tanaka's graphing techniques develop those of Hauptmann and von Oettingen= ; only Wilson's development of graphing techniques for additional dimension= s and Tenney's observations about the logarithmic distances illustrated by graphs represent major music-theoretical advance s on work of the nineteenth century, although it may be added that none of these technique= s, from a mathematical standpoint, are anything other than obvious. I stand by my comments on Balzano's work. He gave a presentation in Santa= Cruz in 1982 and said specifically that 20 was chosen because he was working with group characteristics and 20 was a reasonably small number with the same number of factors as 12. Indeed, it could be said that he w= as looking for an alternative tuning with which he might confirm some hypotheses regarding 12. However, once he started work with 20, he became= quite pleased with the tuning (Balzano has perfect pitch memory and rapid= ly had command over the set of 20). My disparaging comments about Richter Herf and his _Ekmelische Musik_ are= a private aesthetic opinion. Austria's history is full of minor cultural figures with minor followings. I'd rate him and his group as both smaller= and considerably less important than Hauer and his group. Ezra Sims is a rough contemporary, a clearer thinker and a far better composer, so let's= let Ezra take the 72-tone chair. (If we want to argue on the basis of priority, then Bosanquet gets all multiples of 12, followed by Carrillo).= As to Partch's tuning on the harmonium: The voicing of a harmonium reed c= an retune individual partials; his tuning was close but not exact by any means. (I am working at present with aluminum rods fixed at one end. An ideal rod should yield three first partials in the ratios of 1 : 6.27 : 17.55; I have yet to meet such a rod, but have found that with a little filing in the right places I can tune the partials close to 1 : 8 : 16 = SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: RE: next step in tunings PostedDate: 25-11-97 10:17:46 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: 25-11-97 10:16:16-25-11-97 10:16:16,25-11-97 10:16:18-25-11-97 10:16:18 DeliveredDate: 25-11-97 10:16:18 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 C125655A.0032EA0A; Tue, 25 Nov 1997 10:16:07 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00471; Tue, 25 Nov 1997 10:17:46 +0100 Date: Tue, 25 Nov 1997 10:17:46 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA00469 Received: (qmail 2539 invoked from network); 24 Nov 1997 14:11:02 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 Nov 1997 14:11:02 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu