source file: mills2.txt Date: Sun, 29 Sep 1996 16:07:45 -0700 Subject: Re: Quadratic Prime Just Intonation From: Johnny Reinhard Paul and others have asked me what I mean by "quadratic prime just intonation" and this is now the time. I used this tuning exclusively in a solo trombone work called _Rama_ based on the Arthur C. Clarke & Gentry Lee series of books. I later used it for a section of my string quartet _Cosmic Rays_. Firstly, I'd like to quote a passage of _Rama_ which lead me to the tuning: "What comes first? Do we use models to help us find the truth? Or do we know the truth first, and then develop the mathematics to explain it?" - a lead character Nicole les Jardins Quadratic Primes 41, 43, 47, 53, 61, 71, 83, 97 Each successive number is computed by increasing the difference from the previous number by two, resulting in exactly forty consecutive prome dollars. The sequence of primes ends only when the 41st number in the string turns out to be a non-prime, namely 41 X 41 = 1681. The ratios are: 43/41 = 82 cents 47/43 = 179 cents 53/47 = 193 cents 61/53 = 244 cents 71/61 = 263 cents 83/71 = 271 cents 97/83 = 270 cents and continues to diminish down to 1681/1601 = 84 cents In the _Rama_ books, the alien sentients that rule their lives use quadratic primes as the basis for their computer software. I found in using what at first seem like arcane relationships actually make consonance of all possible combinations. Thats why its just intonation. Johnny Reinhard American Festival of Microtonal Music 318 East 70th Street, Suite 5FW New York, New York 10021 USA (212)517-3550/fax (212) 517-5495 reinhard@ios.com Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 30 Sep 1996 06:28 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05130; Mon, 30 Sep 1996 05:28:58 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA04713 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id VAA16288; Sun, 29 Sep 1996 21:28:55 -0700 Date: Sun, 29 Sep 1996 21:28:55 -0700 Message-Id: <01IA2JG9OEF68Y62BX@delphi.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu