Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!ncar!husc6!brauer!elkies From: elkies@brauer.harvard.edu (Noam Elkies) Newsgroups: comp.music Subject: tunings, cont'd Keywords: Intonation systems, octaves, tuning systems Message-ID: <3288@husc6.harvard.edu> Date: 29 Nov 89 20:24:28 GMT References: <3068@husc6.harvard.edu> <6335@merlin.usc.edu> <3113@husc6.harvard.edu> <6460@merlin.usc.edu> <3194@husc6.harvard.edu> <6540@merlin.usc.edu> <3246@husc6.harvard.edu> <6676@merlin.usc.edu> Sender: news@husc6.harvard.edu Reply-To: elkies@brauer.harvard.edu (Noam Elkies) Organization: Harvard Math Department Lines: 53 In article <6676@merlin.usc.edu> alves@aludra.usc.edu (Bill Alves) writes: : [I wrote:] :> [Bill wrote:] :>:I have looked at the spectra of dozens of common and uncommon instruments, :>:and the vast majority are perfectly harmonic within the resolution of my :>:system (about 6 Hz). :> :>6 Hz!? That's about 16 cents at A-440, enough to make the just and tempered :>third indistinguishable. Aren't more precise measurements available? Even :>much smaller deviations would have significant consequences for an intonation :>system based on overtone matching. :> :OK, I'll admit that 6Hz can be a significant difference at higher frequencies, [Presumably this should read "at lower frequencies" or "even at higher frequencies"?] :but not enough for a percussion instrument to look harmonic by mistake. The :distinction between harmonic (winds, strings) and inharmonic (most percussion) :is important, even if the ideal harmonic spectrum never exists in nature. Agreed. : [...] Also, I never looked at these spectra :explicitly for their inharmonicity. Your question as to whether these devia- :tions would or should influence the tuning system is interesting, but I don't :have the answer. Well, if you care about consonance and define it by the absence of audible beats then I'd expect that you would be quite concerned about even subtle inharmonicities; 6Hz difference at any frequency translates, of course, to a very noticeable 6 beats/sec. Conversely, you may be able to locate to within at most ~1Hz any overtone strong enough to generate beats by simply beating it against a sinusoidal test-tone of known frequency. :>:The vibraphone and marimba (after the initial attack) are not :>:only harmonic but almost sinusoidal. :> :>So indistinguishable after the initial attack? Interesting---I'll have to :>remember this! :> :Not at all. First of all, the attack is a vital part of what we hear as the :timbre and is hard to separate from the rest of the sound. Secondly, I should :qualify my use of "almost" by saying that very small deviations (low ampli- :tude partials) from the sinusoidal can be very important to the timbre; i.e. :by "almost" I didn't mean "indistinguishable." I guess I misunderstood. By the way, it is sometimes possible to separate the perception of the "rest of the sound" from the initial attack, as has been demonstrated (on the piano) by Bartok a long time back. --Noam D. Elkies (elkies@zariski.harvard.edu) Department of Mathematics, Harvard University Brought to you by Super Global Mega Corp .com