Path: utzoo!attcan!uunet!aplcen!samsung!usc!merlin.usc.edu!aludra.usc.edu!alves From: alves@aludra.usc.edu (William Alves) Newsgroups: comp.music Subject: Re: New tunings Keywords: Intonation systems, octaves, tuning systems Message-ID: <6676@merlin.usc.edu> Date: 25 Nov 89 06:28:30 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> Sender: news@merlin.usc.edu Reply-To: alves@aludra.usc.edu (Bill Alves) Organization: University of Southern California, Los Angeles, CA Lines: 64 In article <3246@husc6.harvard.edu> elkies@walsh.harvard.edu (Noam Elkies) writes: >In article <6540@merlin.usc.edu> alves@aludra.usc.edu (Bill Alves) writes: >:[account of a certain composer with perfect pitch who would wince at just >:intervals] > >Ah. His problem is that "perfect" pitch is (no pun intended) relative--- >presumably anybody's pitch is "perfect" enough to tell when a familiar piece >is played an octave up or down, and I doubt anyone can reliably pin down a >pitch played out of the blue to within say 5 cents. So we compensate by >digitizing pitch perception so an interval of (say) 782.5 cents is heard >as a quite flat minor sixth rather than 775+-15 cents. Then it transpires >that the digitization error completely obscured a near-perfect 11/7 interval.. > Perfect pitch is indeed relative, and I would be interested to find out exactly what the tolerances for different people are. This particular compo- ser has pretty darn good perfect pitch, and I've only met a few people I could say that about. That aside, I think it's important to add that one doesn't have to have dead-on perfect pitch to hear differences of 5 cents within a sonority. Then the presence or absence of beats will tell you if the interval is far from a just ratio. I am convinced that even for those not trained to notice the beats or when the beats are obscured by a greater number of simultaneous pitches, the small differences are still very impor- tant to the sonority, if at only a subliminal level. >: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, 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. At what point should a spectrum be considered "inharmonic"? I don't know. The point was that harmonicity (apart from "small" deviations) is a common pheno- menon. One doesn't need a spectrum analyzer to tell you that. (By the way, the program that I've been using has a maximum FFT window length of 8192 samples. At a 50 kHz sampling rate, which gives a window time of about .17 seconds, that's the resolution you get. Of course the only reasons that that's a limi- tation is that I haven't programmed one myself yet or found another program. Anyway, it's better that DigiDesign's Sound Designer, which has a resolution of...is it 96 Hz? Something like that.) 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. >: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 "indistinquishable." Bill Alves USC School of Music / Center for Scholarly Techology