OK, I'm ready to argue against my own post. Steve Haflich is right to
question the FFT I used in Audacity. I did extend the length (8192), but
this simply pads the windowed signal. There are also various windowing
methods (I used Hanning), all of which can cause some error in the
spectrum. Looking more carefully at my numbers (not repeated here), 5 cents
difference in the lowest frequency (353 Hz) gives a difference of only 1 Hz,
certainly within the error of my measurements. Therefore I think we can
conclude that I simply played the same note 5-10 cents flat the second
time. Steve Freides is also right that the higher harmonics are all lower
for the farther note, but I don't see any systematic change other than that
the overall volume was less farther away.
This morning I tried two other tests. First I used the synthesized pitch
from my tuner with the same experiment, measured 2 meters away and again
about 8 meters away. There were several overtones recorded in each case and
both sets give exactly the same frequencies. Next I played a middle C on an
electronic keyboard using the midi "French Horn" setting (I'm biased). I
recorded the sound in the same room, then carried the recorder to the far
end of the house, again about 8-9 meters away) and recorded the same note.
Again the frequencies are exactly the same (within measurement error). The
amplitudes are smaller for the farther recording. I'm not sure how to
interpret the relative amplitudes. Is the variation from 20-30 dB softer
for the farther recordings enough for us to sense the pitch as flatter?
Here are the numbers:
Middle C on electronic keyboard horn setting:
Near Far
C4 262 Hz 7.2dB 262 Hz -10.2dB
C5 524 Hz 0.1dB 524 Hz -36.5dB
G5 785 Hz -24.3dB 785 Hz -43.2dB
C6 1047 Hz -24.1dB 1047 Hz -49.0dB
E6 1310 Hz -20.6dB 1309 Hz -46.3dB
G6 1571 Hz -33.0 dB 1570 Hz -64.6dB
A#6 1833 Hz -37.9dB 1833 Hz -65.2dB
C7 2094 Hz -40.6dB 2094 Hz -68.2dB (in noise)
--
Jeffrey S. Barker
Assoc. Prof. of Geophysics, Binghamton University
Faculty Master, Dickinson Community
(607) 777-2522 (Geology) (607) 777-2826 (Dickinson)
http://bingweb.binghamton.edu/~jbarker/
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