source file: mills2.txt Date: Thu, 2 Jan 1997 13:40:47 -0800 Subject: RE: mod groups & rhythm From: PAULE Gary wrote, >I suspect though that pitch and rhythm are fundamentally different when >it comes to temperament. Tempering pitches is meaningful because our ears >hear in a manner that could perhaps be described as simultaneously in >linear and logarithmic frequency scales. During my month away from the list, I too came up with the idea of rhythmic temperament, and so was pleasantly suprised to find that it had been discussed in my absence. Although Gary's point has some merit, perhaps he is forgetting that logarthmic relationships arise from application of a given multiplicative factor, in this case a ratio, several times. There is nothing in the nature of rhythm that prevents this from having significance. For example, one can, in the course of a piece, reinterpret triplets as quarter-notes, a rhythmic modulation by a factor of 3/2. Repeat this three more times, and you will have accelerated by a factor of 81/16. Now interpret every fifth note as the basic pulse, and you will be at 81/80 of the original tempo. Of course, no one will notice that you have not returned to the original tempo. But what if you had left the original tempo in place through the entire process, in one voice or a drumbeat? You would want to come back to it at the end. The polyrhythms in the middle of the process would be too complex to hear mathematically, anyway, so why not "temper" them, so that the 81/80 becomes a 1/1? Each time the triplets are introduced, they could be played a tiny bit too slow, the exact amount of tempering being identical to that of meantone tuning. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 2 Jan 1997 22:52 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00891; Thu, 2 Jan 1997 22:55:22 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA00889 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id NAA12389; Thu, 2 Jan 1997 13:55:19 -0800 Date: Thu, 2 Jan 1997 13:55:19 -0800 Message-Id: <199701021653_MC2-E36-6524@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu