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Music Analysis/Synthesis by Optimized Multiple Wavetable Interpolation: Results in Detail Open Access


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Mohr, Jonathan
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optimized multiple wavetable interpolation
recorded sound
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Computing Science Technical Report
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Technical report TR02-19. Music analysis/synthesis is a general process in which a recorded sound is analyzed in such a way that a musician can modify the analysis data and synthesize an altered sound from the modified data. Multiple wavetable interpolation is a form of music analysis/synthesis. The algorithm involves three basic steps: 1) The recorded sound is reduced to a set of breakpoints by piecewise linear approximation of the spectral envelopes of its harmonics; 2) the spectrum at each breakpoint is matched by determining weightings for a small number of wavetables; and 3) the sound is resynthesized using multiple wavetable additive synthesis by interpolating between the weightings for each wavetable at consecutive breakpoints. Optimized multiple wavetable interpolation is a new music analysis/- synthesis method introduced in the author's doctoral thesis that generalizes and optimizes multiple wavetable interpolation. The method uses a clustering algorithm to select a bank of wavetables such that the wavetables will be useful in matching the breakpoint spectra of a wide variety of harmonic tones played by various instruments. The breakpoint-matching algorithm selects subsets of the wavetables in the wavetable bank which best match each breakpoint spectrum, subject to the constraint that a wavetable which ceases to be used at a given breakpoint must be faded out by the next breakpoint and one which comes into use must be faded in. The algorithm introduces the use of the single-source acyclic weighted shortest path algorithm to choose breakpoint matches in a globally optimal way. The output of the algorithm is a sequence of N-tuples of pairs of wavetable indices and weights which can serve as a control stream for a hardware or software synthesizer. The method was tested on 198 tones played by sixteen different instruments at pitches which spanned the range from A1 to B6 at intervals of a minor third. The tones were grouped by pitch into five subranges so that a greater number of harmonics could be retained for the lower tones to provide greater fidelity on resynthesis without introducing artefacts by exceeding the limit of the Nyquist frequency. A separate wavetable bank was selected for each group of tones. This technical report serves as a supplement to the thesis, providing tables of results of the application of the breakpoint-matching algorithm to all five groups of tones.
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