I think the calibration data are important. We are just seeing a picture of a sound with no reference data to compare it to. I would want to pop a couple of waves through to test the equipment, square in, square out, etc. dt
At 09:39 AM 1/2/2009, you wrote: >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
