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The EPSRC project GR/L 18273 Low-cost, efficient parallel algorithms for musical electronic learning aids was proposed to research, develop, implement and evaluate monophonic and polyphonic music recognition algorithms for use in computerised interactive musical learning systems. Specifically the aim was to develop real-time algorithms for note recognition in monophonic (task 1) and polyphonic (task 3) music. Further and essentially independent tasks were the development of a real-time tune recognition algorithm (task 2) and of an interactive electronic music tutor for a monophonic instrument (task 4).We are pleased to report that considerable progress has been made, if along lines slightly different from the ones originally outlined in the proposal. Task 1 was completed early in the project and it was shown that this algorithm coped well with monophonic signals. However, the methods suggested in the proposal to extend this method to handle polyphony proved impractical. We were thus forced to return to more fundamental studies of pitch detection algorithms. Substantial theoretical and experimental investigations were carried out into existing algorithms and novel algorithms were developed and implemented that are capable of detecting notes in polyphonic music and which, we believe, represent significant advances over the current state-of-the-art in many aspects. Thus task 3, which was the most difficult fundamental part of the project, was successfully completed.
A two-step approach was adopted which divides the task of note recognition into two subtasks: (A) short-time spectral estimation of the musical signal, resulting in a time-frequency spectrum, and (B) note extraction based on the resulting spectra. Novel approaches have been developed for both the spectral analysis as well as the pattern recognition part of the note identification problem; for the former, the main novelty lies in the use of auto-regressive as opposed to conventional Fourier spectral estimators, for the latter in a combination of data classification methods and a topological approach to note identification which emphasises connectivity patterns in both time and pitch.
The resulting algorithms were coded in Mathematica and successfully tested with digitised recordings of both mono- and polyphonic piano music with up to 3 tones occurring simultaneously. At the time of writing one paper has been published [1], a second one is in preparation which will contain the major part of our results [2], and more technical issues are contained in an as yet unpublished report [3].
References:
[1] T von Schroeter (1998): Frequency Warping with Arbitrary Allpass Maps. IEEE Signal Processing Letters, 6, pp 116-118
[2] T von Schroeter and J Darlington (in preparation): Connectivity in auto-regressive spectra of polyphonic piano music - a topological approach to automated transcription.
[3] T von Schroeter: Auto-regressive spectral line analysis of piano tones, Technical report.