Also, you would expect a brief transient regime before the string settled into a nominally stable state (overlaid by ongoing decay as energy is gradually lost). During the transient period, I wouldn't expect a Fourier spectrum to be terribly meaningful, or at least it would be more difficult to interpret. That said, I'm not sure how long the transient regime would last, but something like 0.1 sec or so sounds plausible.
Guy -----Original Message----- From: Peter Nightingale [mailto:n...@pobox.com] Sent: Friday, January 02, 2009 4:59 AM To: Herbert Ward Cc: lute@cs.dartmouth.edu Subject: [LUTE] Re: Fourier measurements of lute sound. Herb, I am a little puzzled by what you write. Guessing at what you might be doing, I would say that your fundamental in roughly at 300Hz. Observing a frequency in that range for 0.3 seconds gives you about 100 oscillations. With 100 oscillations, the accuracy of the measured frequency cannot exceed 1%, because you might have failed to account for roughly a cycle. Whatever your do, Fourier transformations included, suffers from this fundamental limitation, and to get better accuracy you need either more time or a higher frequency. In other words, given that 1200 x log_2(101/100) = 17, a measurement of a frequency in the 300Hz range derived from a 0.3 sec. observation cannot produce a result with an error smaller than about 10 cents, which is bigger than the effects you seem to talking about, but maybe I am incorrectly interpreting your email. Peter. On Thu, 1 Jan 2009, Herbert Ward wrote: > > > Using computerized Fourier analysis, I measured spectra > of lute sound, using all strings in courses 1-6, plucked > with good tone. > > Several unexpected features cropped up. > > 1. The pitch of a harmonic often shifts over the duration > of the note, up to 10 cents. > > 2. The volumes of the harmonics often change relative > to each other. Sometimes this can be a strong and > surprising effect, as when the fundamental is basically > absent during the initial 0.3 second, and then assumes > dominance over the harmonics as the note dies away. > > 3. The harmonics' pitches are not consistent with each other, > especially during the initial 0.3 second. For example, > the fundamental can be at -4 cents, and the first harmonic > (an octave above the fundamental) can be at +4 cents. > > These observations provide an ample hypothesis for tuner > instability, but unfortunately suggest no solution. > > > > To get on or off this list see list information at > http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html > the next auto-quote is: True virtue is life under the direction of reason. (Baruch Spinoza) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881
