source file: mills2.txt Date: Thu, 6 Mar 1997 21:21:30 -0800 Subject: Re: New Paper From: "Asmussen, Robert" Dear Mr. Tomes, Thank you for your comments regarding my paper. I have in turn been reading your paper on just intonation, which is located at: http://www.kcbbs.gen.nz/users/rtomes/aji-main.htm I think you have many fine ideas, such as translating passages of traditionally notated music with variable pitch sets. I will take more time later to delve into the details. I have devised a mechanism similar to the keyboard system in your paper. In my translator, a Csound orchestra stores variable pitch sets (12 members each) in wave tables, then looks them up as they are needed according to values stored in the score. For the purposes of pedagogy, especially at the introductory level, I try to avoid references to traditional tuning systems. Doing so eliminates the unnecessary step of translating from a limited, fixed system into an unlimited one. For this reason, I left comparisons and translations between equal temperament and just intonation out of the most recent version of my paper. As to some specific details, I believe you are incorporating intervals in your Mozart example that are not in keeping with the classical style. For example, you use octave equivalents of 7/4 as some of your frequency ratios. I challenge you or anyone to create a dominant seventh chord, using the number seven as a multiple in the denominator of the chord’s seventh, that would not sound out of place in a piece of chamber music by Mozart. I would suggest giving it the acid test, which would be to make a WAV sound file of your Mozart score using Csound. With the tempo nice and slow, try 7/4, then 16/9 as the relative frequency for the seventh of your dominant chord. Under such conditions, nearly everyone would agree the ratio 16/9 is a much better selection for music of this period. I cannot provide an airtight proof of why this is the case, but my ear and 30+ years experience as a musician tell me it is so. I can point out that from the major scale provided by Helmholtz in his book, “Sensations of a Tone”, the relationship of 16/9 for the seventh of a dominant seventh chord may be inferred. You state, ”Some intervals such as a minor sixth may be interpreted as 7/4, 16/9 or 9/8 depending on circumstances.” Without going into the potential merits of your statistical approach to pitch selection, I must point out that 7/4 is approximately a minor seventh; 16/9 is an in-tune minor seventh; and 9/8 is a major second. Certainly none of these ratios is a minor sixth. I assume this is just a grammatical error. When I stated in my paper that pieces of traditional tonal music could not be translated without modification from traditional notation into integer ratios, I could have elaborated further with the following two points: 1. Often, such as when employing chromatic scales, the composer is simply filling in the space from point A to point B with notes. Such passages do not need to be translated, nor often can they be, into ratios. One might even argue that such passages are not really music, but rather more like dust on a mirror. 2. Composers of the past wrote their music using limited instruments and tuning systems that were available at the time. We should not expect to translate their imperfect creations into a purely mathematical framework; in fact, we should be surprised when it is possible to do so. In my paper, I have included one such surprise, complete with a WAV sound file generated in Csound. This entire two-part invention, a lovely gem by Bach, can be tuned according to the principles given 130 years ago by Hermann Helmholtz. The Csound orchestra, score and WAV file are located at: http://www.terraworld.net/users/r/robert/htmlpap7.htm In the Csound score for this two-part invention, every interval is provided in the last two parameter fields, columns 5 and 6. The bars are numbered clearly to facilitate comparison with an actual score. Regarding the problems you are having with the graphics in my paper, would you please contact me if you experience additional difficulties? I have reloaded all ten HTML files off my server quite easily using only 8 megs of RAM while running a minimum of applications and windows. I look forward to studying your paper, as well as examining your many other papers, in greater detail. Best regards, Robert Asmussen P.S. For those seeking information about Csound, a good starting point is: http://ccrma-www.stanford.edu/~tkunze/Csound/title.html Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 7 Mar 1997 23:58 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09033; Fri, 7 Mar 1997 23:58:38 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA08926 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id OAA07256; Fri, 7 Mar 1997 14:56:07 -0800 Date: Fri, 7 Mar 1997 14:56:07 -0800 Message-Id: <199703071521.HAA22318@ella.mills.edu> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu