By using Fourier analysis to record the complete nuance of a symphony and recording it on to an oscilloscope, what type of curve will a typical symphony look like?

edmund80

A single wave form, specifically one that has a similarity of amplitude of signals when observed over different time scales. The similarities were strong, but not identical between the tested pieces of music in the study below. "Both Beethoven’s 3rd Symphony, 1st movement and Bach’s Fuge in c-minor show strong similarities down to three-second sections. The examples of three-second sections were choosen randomly from the experimental series." "In Music for Mallet Instruments by Steve Reich, we can still see the self similarity at as little as 0.03 sec. Reich’s music, usually described as minimalist, is characterized by a slowly varying sound continuum, and so it is unsurprising that the musical properties and the results of the Fourier analysis do not contradict each other. Conversely, in Aventures by Ligeti, differences in the spectrum are already obvious by a quarter of the piece (around 2:55 min) and are strongly amplified by an eighth of the piece. Within this piece extremes such as long breaks and passages with many notes, silences and fortissimos clash. These examples suggest that the fractal property of a piece of music should be acoustically perceptible." http://209.85.173.132/search?q=cache:TjYBzbkDatMJ:www.leeds.ac.uk/music/studio/rrs/esrrs1997_02a.doc+Fractal+Characteristics+of+the+Fourier+Spectra+of+Recordings+of+Musical+Compositions&hl=en&ct=clnk&cd=1&gl=us&client=firefox-a The mathematical result that describes how a wave can be split up into a sum of sine waves is called Fourier's theorem. Given enough pure sine waves, like those generated by a tuning fork, it is theoretically possible to reproduce Beethoven's Ninth Symphony, even the choral part. http://books.google.com/books?id=MVEOEYgU0-UC&pg=PA122&lpg=PA122&dq=fourier+analysis+of+symphonic+music+%2B+beethoven%27s+ninth+symphony&source=web&ots=X5hVEhObkn&sig=od5O6GWYNqcmfoREjdXLcK3j5v0&hl=en&sa=X&oi=book_result&resnum=2&ct=result#PPA122,M1 Dec 20 08, 10:38 PM