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 analysing 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.

Keywords:

• stochastic performance model
• ornaments
• hidden Markov model
• score-performance matching
• score following
• performance analysis

Acknowledgements

The authors are grateful to Ayumu Yamanaka and Tadayuki Hayasaka for useful discussions and their cooperation in piano performance, and Bruno Gingras for providing the evaluation data and giving many helpful suggestions for revisions in the text. The author E.N. wishes to thank Yasuyuki Saito and Tomohiko Nakamura for fruitful discussions.

Notes

1 This is written as ‘grace notes’ in Read (1969). In general, the word ‘grace notes’ means either small notes in scores or ornamental figures notated with these small notes, which are also called short appoggiaturas. We will use the word ‘short appoggiatura’ to mean the ornamental figure and ‘grace note’ to mean a small note in scores in this paper, to avoid confusion.

2 Unlike short appoggiaturas, long appoggiaturas (or simply, appoggiaturas) usually have determinate note values. Typically they are notated with a single grace note (without a slash), and a single short appoggiatura is usually notated with a grace note with a slash.

3 It is true that notational ambiguities with long appoggiaturas or confusion between long and short appoggiaturas sometimes arise, but these require more or less musicological arguments which are out of our scope.

4 By this, we mean that they may differ between performers and also from time to time.

5 In German terminology, accented short appoggiaturas are sometimes called (kurze) Vorschläge and unaccented ones Nachschläge.

6 Copy of the first Artaria edition, Breitkopf & Härtel, Peters, and Schirmer editions can be downloaded from IMSLP Petrucci Music Library http://http://imslp.org.

7 In this paper, the term ‘chord’ will be used in a way which is different from its normal meaning. We define the term in the next sentence.

8 For example, we might take the range of glissando sufficiently wide.

9 The problem of probability flow can be reduced to some extent by using the forward algorithm, but the problem of unreliable estimation still remains.

10 Tempo defined here is inversely proportional to the conventional one, i.e. beat per minute. It is often used in computational models.

Additional information

Funding

This work is supported in part by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science, Nos.23240021 (S.S. and N.O.), 25880029 and 15K16054 (E.N.).