source file: mills2.txt Date: Sun, 5 Jan 1997 16:39:10 -0800 Subject: Re: mod groups & rhythm From: Matt Nathan [I think I misfiled this and forgot to send it. If I already sent it, please ignore and forgive.] PAULE wrote: > > 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. Check out a book by composer Henry Cowell titled, I think, _New Musical Resources_. He goes into metric modulation, and stacked polyrhythms or rhythmic chords, based on whole numbers. > Of course, no one will notice that you have not returned to the original > tempo. I disagree. Play anything you know to a metronome which is marking 80 beats per minute, then play it again at 81. Notice the difference in feel? I think the audience would as well. I forget which of the mainstream music newsmagazines lists the tempos of the most popular dance tracks in fractions of beats per minute, like mm 125.2, so other musicians, and DJ's, etc. can tune in to the narrow bands of most-fashionable tempos that people are responding to. A tempo difference of 125/124 can apparently affect the popularity of a tune. > 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. The problem with tempered rhythms is in their combination. Tempered triplets say would drift if played against quarter notes; they wouldn't line up at the measure length. If this is what you want, then cool. An irrationally related duration set could give a nice effect of non-groundedness while retaining self consistency. If you want to do a series of metric modulations which end up at the same tempo, without having to temper them, make sure the same numbers which occur in the numerators also occur in the denominators. 2 3 2 1 t * - * - * - * - t 1 2 3 2 To make the progression not retrace the same steps, shuffle the order of numerators or denominators or both (without exchanging numerator with denominator): 2 2 1 3 t * - * - * - * - t 1 3 2 2 I wrote a piece which did something like this for The Martin Dancers here in Los Angeles. It repeated a "rhythmic progression" of meters related by common pulses. Something I wish to do with tempos and with pitch is to write progressions which repeat their link pattern but do not end up at the same place (using whole numbers, not tempered). I think this would sound neat. The simplest example is the "spiral" of continuous 3/2 fifth root motion, but nicer ones must be waiting out there too. Matt Nathan Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 6 Jan 1997 03:55 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02375; Mon, 6 Jan 1997 03:58:22 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA02373 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA01242; Sun, 5 Jan 1997 18:58:19 -0800 Date: Sun, 5 Jan 1997 18:58:19 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu