Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace.1 A recent article in The Physics Teacher aptly demonstrated the use of MacScope2 in just such a manner as a way to teach Fourier analysis.3 A logical continuation of this project is to use MacScope not just to analyze the Fourier composition of musical tones but also musical intervals.
REFERENCES
1.
Both Vernier Software, http://www.vernier.com, and Pasco-Data Studio, http://www.pasco.com, feature software and hardware for this purpose.
2.
Download MacScope and directions for its use, free, at http://www.Physics2000.com. Despite the name, both Macintosh and PC versions are available.
3.
E.
Huggins
, “Teaching Fourier analysis in introductory physics
,” Phys. Teach.
45
, 26
–29
(Jan. 2007
).4.
T.D. Rossing, F.R. Moore, and P.A. Wheeler, The Science of Sound, 3rd ed. (Addison-Wesley, San Francisco, 2002), p. 95.
5.
J.G. Roederer, The Physics and Psychophysics of Music—An Introduction, 3rd ed. (Springer-Verlag, NY, 1995), p. 47.
6.
The augmented-fourth or diminished-fifth, also known as the “tritone” in Just intonation, is the ratio 45/32. The reason for the use of 7/5, the “septimal” tritone, can be seen in Fig. 6. See W. A. Sethares, Tuning, Timbre, Spectrum Scale, 2nd ed. (Springer, London, 2005), p.101.
7.
See Partch's 43-tone scale, Ref. 6, p. 62.
8.
M. C.
LoPresto
, “Experimenting with musical intervals
,” Phys. Educ.
38
, 309
–315
(July 2003
).9.
Ref. 5, p. 166.
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© 2008 American Association of Physics Teachers.
2008
American Association of Physics Teachers
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