Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!cs.utexas.edu!husc6!brauer!elkies From: elkies@brauer.harvard.edu (Noam Elkies) Newsgroups: comp.music Subject: Eliminating the octave [Re: spectral composition] Summary: piano tuners do it Keywords: Intonation systems, octaves, pianos Message-ID: <3007@husc6.harvard.edu> Date: 30 Oct 89 02:09:54 GMT References: <6066@merlin.usc.edu> Sender: news@husc6.harvard.edu Reply-To: elkies@brauer.harvard.edu (Noam Elkies) Organization: Harvard Math Department Lines: 31 [Possibly a repeat post--apologies] In article cornicel@elbereth.rutgers.edu (Cornicello) writes: >Oh, and let's hear it for "just intonation" I would like to see some >alternate tunings listed on this board. How about eliminating the octave? I take it that you mean eliminating the 2:1 octave as the basis of tuning, not eliminating octaves in scores (as some dialects of serial music do). Well, this is standard practice in piano tuning, because the overtones of physical piano wire of positive stiffness grow increasingly sharp to the Pythagorean harmonic series, and each octave is tuned by "beats" so that the first overtone of the bottom note matches the fundamental of the top. This has the effect of narrowing the comma between the perfect and tempered fifth, but widening the comma between the physical third partial and the tempered twelfth. To further confuse matters, for the sake of tone quality the three strings of each course are generally tuned a beat or two apart... But of course all this still amounts to a tuning system anchored on the octave. Before rushing to dethrone the octave, though, consider this: While the initial rationale for octave-based tuning may have been no more than numerology and arbitrary mysticism, such tuning had profound implications for Western music which took ages to work out anywhere near completely. Anybody have a few centuries to spare on a tuning system based on alternating Golden Ratios and the square root of pi? Remember to take out a few decades from composition to creating the new instruments and musical training that this would require. :-) :-) --Noam D. Elkies (elkies@zariski.haravrd.edu) Department of Mathematics, Harvard Univ.