source file: mills2.txt Date: Sat, 14 Dec 1996 11:39:38 -0800 Subject: mod groups & rhythm From: James Kukula Rhythm, or the duration of notes, is structured a lot like pitch. The common musical palette for duration is much more limited than than for pitch. But the ratio of 2/1 is still the fundamental structure, with 3/2 not far behind. One idea that follows from this - tempered rhythm! Instead of triplets being exactly 3/2 speed, one could speed them up or slow them down a touch. This would then permit rhythmic puns. Rhythm has an extra dimension that pitch doesn't - phase. Two steady pulses with the same speed can still differ, they can be offset from each other in time. Really, pitch and pace - pardon my dread ignorance of proper musical terms - are not wholly separate. A steadily repeated click sets up a regular pulse at say 3 beats per second. But speed it up to 24 beats per second and it's a very deep pitch. Somehow as this pulse/pitch transition is traversed, the sensitivity to phase or registration in time is lost. Perhaps that loss of phase is just what the transition is about. Adding phase makes the mathematical structure messier. Pitch intervals do seem to form a group. Moving one interval after another is the same as moving some third interval. With rhythm or pulse, there are two operations. One can shift the pulse in time, or change the speed. Shifting a pulse back and forth in time looks like a group structure - there's a nice inverse. But changing speed is messier. It makes good sense to double the speed of a pulse. But if I halve the speed, then there are two ways to do this - I need to skip every other beat, but do I choose to skip the even or odd beats? So the speed-up operation appears not to have a well-defined inverse. Jim Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 14 Dec 1996 21:34 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04277; Sat, 14 Dec 1996 21:36:24 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA04276 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA29197; Sat, 14 Dec 1996 12:36:21 -0800 Date: Sat, 14 Dec 1996 12:36:21 -0800 Message-Id: <199612141535_MC1-D16-AE95@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu