elkies@brauer.harvard.edu (Noam Elkies) (11/30/89)
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 Universitybartho@obs.unige.ch (PAUL BARTHOLDI) (12/01/89)
In article <3288@husc6.harvard.edu>, elkies@brauer.harvard.edu (Noam Elkies) writes: > ... 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 Do you mean musical demo, or textual ? Could you give me (us) some reference on this point by Bartok ? Thanks, Paul Bartholdi, Observatory of Geneva, Switzerland bartho@cgeuge54
alves@aludra.usc.edu (William Alves) (12/02/89)
[Noam writes:] >[I wrote:] >: [...] 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. > Of course. That's the whole point of just tuning systems that I work in. What I meant to say, but perhaps I wasn't clear, was in reference to an earlier issue that you had brought up: have tuning systems in various cultures evolved because of the spectral characteristics of their instruments? That's the ques- tion I don't have the answer for, and I doubt if anyone really does. First, relatively very few world cultures have fixed, standardized tuning systems in practical use. Instruments which have one separate vibrating body for each pitch (keyboard instruments, zithers, mallet instruments) provide the most common need for a tuning system, and often they are not played in ensembles with other instruments of the same type. Even then (as in Indonesia and some parts of Africa) tuning systems are only standardized for a particular or- chestra of instruments. A corollary issue that I would also like to clarify is whether inharmonicity can be considered a kind of "justification" for temperament. Personally, I really don't think so, but my feeling is mostly based on empirical experience working with timbres and tuning systems in a compositional context. Just in- tervals on a piano are significantly different from tempered intervals, even if they are just a few cents off. >: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. > A very early experiment in aural perception utilizing recording technology was one in which an experimenter faded in single notes from various instru- ments on a disc recorder. The subjects frequently mistook an oboe for a flute, a trumpet for a violin, etc. I don't have the exact reference, but I'm sure that someone could point me to it. Inharmonics in the attack are crucial to what we call timbre, a fact that has been exploited in many synthesizers. Bill Alves USC School of Music / Center for Scholarly Technology
elkies@osgood.harvard.edu (Noam Elkies) (12/04/89)
In article <461@obs.unige.ch> bartho@obs.unige.ch (PAUL BARTHOLDI) writes:
'In article <3288@husc6.harvard.edu>, [Iwrote:]
'> ... 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
'
'Do you mean musical demo, or textual ?
'Could you give me (us) some reference on this point by Bartok ?
Musical demo; for instance the end of the second of the Two Roumanian Dances.
A simple variation of that: play a loud cluster, holding the pedal down; return
soundlessly to a subset of the cluster; release the pedal. That subchord will
be perceived without the initial attack. Or, hold a chord silently with the
right hand, and strike the same chord an octave down staccato with the left.
Provided your piano is tuned, you'll hear the upper chord sustained without
an attack (the undamped strings resonate with the octave overtones of the
bottom chord). What happens if you hold down the G an eleventh below middle C
and strike the A#-B-C cluster directly above that G? [Your mileage may vary.]
--Noam D. Elkies (elkies@zariski.harvard.edu)
Dept. of Mathematics, Harvard University