MATH 5 PROJECT INFO (updated 9/22/11) Project choice deadline: Fri Nov 11, but you should discuss way before this. Presentation date: Wed Nov 30, in class. Each of you presents for 10 mins - it's actually very hard to give such a short, clear presentation (eg 5 slides and a quick demo) You may work in groups of 2. Group presentations should include something from each of you in the group. Projects may be purely reading (library) research, purely measurement (experiment) based, or purely computer simulation or mathematical modeling, or purely building a new instrument. However, the best projects combine a bit of two or more of these approaches. The best projects also make clear use of tools and concepts we have learned in class, but also take you (and us, the audience) beyond the lecture material. Don't head *too* far off into foreign territory (or at least discuss with me first!) Suggested topics: * Analyse an existing musical instrument in depth using tools from class, combine with background reading on modes, spectral features, timbre over different pitch ranges, excitation (mouthpieces, bowing), etc * Essay about technology or history of an instrument, ancient or modern. How does the acoustics we have learned constrain the design of a successful musical instrument? * Analyse reverberation time (at various frequencies?), and early echoes, of a room, concert hall, or interesting acoustic space on campus. (Practise rooms, lecture halls, racquetball courts, swimming pool, steam tunnels, ...?) What makes speech or music easy/hard to enjoy there? Modify the acoustic in some way, and measure the effect, compare to Sabine's formula. * Build Chladni plate(s), drums, or bars, and measure their mode shapes, frequencies and decay times, using resonant excitation. Relate them to researched theoretical calculations. * Build Gordon-Webb-Wolpert isospectral drums and check the theorem that they have the same set of natural mode frequencies. * Compose some music, inspired by ideas from the course. Eg, computer-generated music, either using basic functions in Matlab, or with a music synthesizer program. Explain how you brought in mathematical ideas from the course into your piece. * Measure our human hearing response, eg, what is the shortest echo time we can distinguish (does it depend on the type of sound?) Do people who use headphones a lot have worse high-frequency hearing that average? How long does a note need to be before we can distinguish pitch, or what instrument it is? Can we distinguish instruments played backwards? Do a small statistical study of your peers and present your findings. * Meausure how the location of a listener in a room affects (spectrally colors) the sound detected, eg, near a wall, in the corner... Do the same for location of your stereo speakers. Connect this to theory of modes in a room (for the low frequency effects). * Discuss how analog and digital electronics are used to modify sounds. Effects pedals, vocoder, delay loops, auto-tune. How do they work, and can you analyse the before and after using our class tools? How does MP3 compression work, and how does this connect to psychophysics. * Measure how the bell shape affects timbre in a (home-made?) wind or brass instrument. Try different bells, and show how harmonic strengths change. * Build a device to produce unusual sounds of musical or scientific interest, and characterize it using the tools from class. Examples: synthesized sounds, formant machine, something who's timbre or pitch can be controlled in unusual ways... * Dig in more detail into tuning systems, and theories of harmony, and their connection to rational frequency ratios. Why does the augmented 4th sound dissonant alone but yet forms the key to jazz when found within a 7th-chord? * Analyse an aural illusion we didn't discuss in class. Try to reproduce it. Relate to theories of aural perception, masking, psychophysics. Test your peers. * Find other mathematical-musical connections we didn't explore during lecture, eg permutations, Tymoczko's triad chord orbifold, more on Greek history, music of the spheres, Newton's color wheel, approximations for the fret locations of guitars, etc.... (eg see Music and Mathematics, book edited by Fauvel, Flood and Wilson (Oxford, 2003)). * Get ideas from interesting acoustical news stories from the ASA newsletter here: http://asa.aip.org/echoes.html * See previous Fall 2010, 2008 and Spring 2007 websites for successful student projects, and build upon one of these! - Alex