Math 5: Resources - SPRING 2007

Theory: General references

• My list of ERRATA for our textbook, G. Loy, Musimathics, Volume 1 (2006). Author's website.
• On reserve at the library:
  • Arthur Benade, Fundamentals of Musical Acoustics, (Dover edition, 1990), is a beautiful, non-mathematical introduction at about our level (in fact with less math than we'll do). Benade was a renowned researcher of the workings of instruments.
  • Fletcher, The Physics of Musical Instruments (1991), wonderful investigations into details of instrument acoustics, is more mathematically sophisticated than our course. Fletcher is known for his original research in this area.
  • Rossing, Moore and Wheeler, The Science of Sound, 3rd Ed. (2002). (I think 2nd Ed. is also on reserve). This massive book introduces many of the concepts of our course, at our level, with a engineering/physics rather than math spin. It tends to be encyclopedic, with a lot of sometimes tedious or incomprehensible data and graphs on particular instruments, while missing the elegant universal themes.
• Music: A Mathematical Offering by David J. Benson (Cambridge University Press, 2007), a freely-available 10MB PDF file. This is a wonderful study, with beautiful and deep musical-math connections, and almost-obsessive detail about e.g. tuning systems, Fourier methods, world-music instruments, symmetry, etc. It is at the advanced undergrad math major level, but don't be scared to dig in!
• Basic Physics of Sound course by Rick Van Kooten at Indiana.
• Wave and sound applets from Indiana University Southeast.
• Internet Searching Guide: links on assessing web sources and searching, by our library staff.
• General notes on exam and study technique (geared mainly towards final exams in intermediate-level math courses).

Mathematics

• Math review with some tools you'll need.
• Trigonometry shown with nice interactive circular motion applets.
• Addition formula for sin derived with rotating vectors.
• Function plotter applet with ok mouse zoom and pan. Another from University of Vienna; another one with mouse pan and axis labels but no mouse zoom; and one that explores a family of graphs by allowing you to slide parameters (eg sin(k*x) for various k), no mouse zoom.
• Fourier series applet finds harmonic content of a waveform you draw by hand.

Instruments

• University of New South Wales (Australia) musical acoustics research group has many pages about acoustics and various instruments.
• Tuning of bells, a wealth of information and recordings on their site.
• Acoustical properties and construction of the tabla, compared to other drums. Some cool re-tuning of resonant frequencies using a non-uniform mass distribution on the tabla surface.
• violin string motion during bowing from +Plus magazine
• My summary of what affects string timbre for this course, fabulous plucked string applet
• Overtone singing and Scientific American article on Tuvan throat singing.

Music Theory and Perception

• Consonance and Dissonance, online graduate level music course notes from Ohio State.
• Ernst Terhardt page with lots of info on pitch perception, consonance, and other scientific auditory research.
• `Just' intonation resources including sound files to compare to equal-tempered tuning.
• Applet to explore tuning systems (including playing music excerpts and intervals), with excellent explanation by Pierre Lewis.
• Applet to play the 23-note Hindu scale (needs you to install JSyn first via your browser)
• Dissonance curves and explanation of Helmholtz theory.
• My matlab code helm_diss which counts numbers of dissonant partials for various intervals.
• Circularity in pitch judgement with Shepard tones (continuously ascending scale); also see applet at Exploratorium and this applet.
• 15th century woodcut showing Pythagoreans with strings of different tensions (note the frequency ratios are given by the square-root of tension, so would not form a just ratio).

Acoustics

• History of the wave theory of sound, excerpt from book by A. D. Pierce (ASA).
• Falstad's ripple-tank simulator, wonderful sandbox for exploring time-domain waves [applet]
• Information on DTMF telephone codes with example recordings, from EE at Notre Dame.
• My summary of what you need to know about the Doppler effect.
• What is a decibel? (shows Flectcher-Munson phon curves)
• Binaural recording such as the Virtual barbershop

Music/sound sources

• DRAM Dartmouth has access to this NYU-based academic music collection (requires Quicktime plugin to listen via web streaming).
• Primate vocalizations from Hauser lab at Harvard.