I feel that we are now in a position in time where it is possible for each of us to indulge in whatever musical specialty we may feel a passion for, without holding back the course of musical evolution in other realms. Ivor was indeed pressed for time. But thanks to his work, (and the internet) we are now able to communicate with each other about a multitude of subjects, in as much detail as we choose. Each post from each person contributes to the whole from which each of us may glean whatever may be of value to us. Though I have been primarily interested in higher harmonics in the past, and now in an expanded version of Partch's tonality diamond, I find the discourse on other systems to be stimulating. The whole of knowledge is a better resource than any militant subset (at least for me). Specialized systems like 88cet might never be documented at all if it weren't for Garys enthusiasm. Marions exploration of the subharmonic series is profound. Even though Charles Lucie's ideas are hard to accept as the perfect system, I find his perspective fascinating. Now, Brian is challenging everything that comes before him, and presenting evidence for his objections. We all win! Ivor was one of the most open minded people I ever met. He was allways in favor of exploration. He encouraged work in any new field, and applauded all developments, no matter how unusual they were. In his kinder moments, he even acknowledged 12 tet as useful for certain purposes. I guess I'm rambling. But my point is: I'm glad to be in a position to communicate directly with such a diverse group of astute colleagues, and to have access to so much valuable information. For those of you who think that I'm not being militant enough on the side of just intonation, I would like to point out something that Easly Blackwood once said: "There is no such thing as just intonation. All you can do is approximate a ratio by some standard of precision. It all depends on the tolorance that you are willing to accept". I think that the same thing could be said about equal temperaments, as well. This all comes to a head with David Canright's early work in which he showed that any equal tempered scale could be described as an array of just ratios when sufficiently high numbers are accepted in the ratios. I find limits on just intonation components to be useful for compositional purposes as well as necessary for instrument construction, but I cannot imagine why I would ever say "No music should be made using intervals beyond the x limit". Unless I was concerned about the playability of that music by someone other than it's creator. But even that should not stop anyone from exploring the interest in their heart. Go, Xenharmonikers!
Denny Genovese
Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 18 Oct 1995 18:26 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA13964; Wed, 18 Oct 1995 09:26:13 -0700 Date: Wed, 18 Oct 1995 09:26:13 -0700 Message-Id: <199510181624.JAA13795@eartha.mills.edu> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
"John H. Chalmers" writes: > See also Neubauer , Otto (?, Neuberger, etc.) The Exact Sciences in > Antiquity. Sorry I don't have a better reference to this book.
That would be Otto Neugebauer, who I believe founded the Brown department of the History of Mathematics.
AUTHOR Neugebauer, O. (Otto), 1899- TITLE The exact sciences in antiquity. EDITION 2d ed. PUBLISHED New York, Harper & Brothers [1962] DESCRIPT'N vii,240 p. illus., facsims. 21 cm. SERIES Harper Torchbooks, TB 552. NOTE Includes bibliographical references and index. LC SUBJECT Mathematics, Ancient. Astronomy, Ancient. LCCN 57012342. RLIN/OCLC RIBG0626061-B.
Enjoy!
---josh
Joshua Brandon Holden Brown Math Department holden@math.brown.edu "It's never too late to have a happy childhood!" ---Cutter John YAZ/socrates
Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 20 Oct 1995 16:58 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id HAA10033; Fri, 20 Oct 1995 07:57:41 -0700 Date: Fri, 20 Oct 1995 07:57:41 -0700 Message-Id: <9510200755.aa14515@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu