A Stochastic Temporal Model of Polyphonic MIDI Performance with Ornaments

Abstract

We study indeterminacies in realization of ornaments and how they can be incorporated in a stochastic performance model applicable for music information processing such as score-performance matching. We point out the importance of temporal information, and propose a hidden Markov model which describes it explicitly and represents ornaments with several state types. Following a review of the indeterminacies, they are carefully incorporated into the model through its topology and parameters, and the state construction for quite general polyphonic scores is explained in detail. By analyzing piano performance data, we find significant overlaps in inter-onset-interval distributions of chordal notes, ornaments, and inter-chord events, and the data is used to determine details of the model. The model is applied for score following and offline score-performance matching, yielding highly accurate matching for performances with many ornaments and relatively frequent errors, repeats, and skips.

Rhythm Transcription of Polyphonic Piano Music Based on Merged-Output HMM for Multiple Voices

“…This indicates firstly that a similar (or higher) accuracy can be obtained by using only the pitch information and secondly that a higher accuracy of voice separation does not necessarily lead to a better rhythm recognition accuracy. 4) Influence of the Model Parameters: In our implementation, parameters of the tempo variables (mainly σ v , σ t and λ) were not optimised but adjusted to values measured in a completely different experiment [28]. Since these parameters play important roles of describing 'naturalness' of temporal fluctuations in music performance, we performed experiments to examine their influence.…”

“…This is done by representing a polyphonic score as a linear sequence of chords or, more precisely, note clusters consisting of one or more notes. Such score representation is also familiarly used for music analysis [27] and score-performance matching [28], [29]. Chordal notes can be represented as self-transitions in the score model ( Fig.…”

“…We notate w = (w n ) N +1 n=1 = (r n , g n ) N +1 n=1 . To describe the temporal fluctuations, we introduce a tempo variable, denoted by v n , that describes the local (inverse) tempo for the time interval between the n-th and (n+1)-th note onsets [28], [31]. To represent the variation of tempos, we put a Gaussian Markov process on the logarithm of the tempo variable u n = ln v n as…”

“…In our implementation, they are simply set by hand. The method for determining the other parameters based on a principle of minimal prediction error is discussed in a previous study [28] and will not be repeated here.…”

Automatic music accompaniment allowing errors and arbitrary repeats and jumps

“…States which represent chord, trill, and short appoggiatura in a general sense were introduced in the model, and a state-construction algorithm was derived which can be applied for a quite general polyphonic passage. Detailed discussions on ornaments are given in a paper to appear elsewhere [35].…”