Rhythmic Transcription of MIDI Signals Carmine Casciato MUMT 611 Thursday, February 10, 2005

Uses of Rhythmic Transcription Automatic scoring Improvisation Score following Triggering of audio/visual components Performance Audio classification and retrieval Genre classification Ethnomusicology considerations Sample database management

MIDI Signals Unidirectional message stream at 3.125KHz System Real Time Messages provide Timing Tick message A simplification of acoustic signals No noise, masking effects Easily retrieve note onsets, offsets, velocities, pitches However, no knowledge of acoustic properties of sound

Difficulties in Rhythmic Transcription Expressive performance vs mechanical performance Inexact performance of notes Syncopations Silences Grace notes Robustness of beat tracker Can the tracker recover from incorrect beat induction? Real time implementation (Dixon 2001)

Human Limits of Rhythmic Perception Two note onsets are deemed synchronous when played within 40ms of each other, 70 ms for > two notes Piano and orchestral performances exhibit note onset asynchronicity of 30-50ms Note onset differences of 50ms to 2s give rhythmic information (Dixon 2001)

Evaluation Criteria for Beat Trackers Informally - click track of reported beats added to signal Visually marking the reporting beats Comparing reported vs known, correct beats (Dixon 2001)

Definitions Beat - “perceived pulses which are approximately equally spaced and define the rate at which notes in a piece are played” meterical, score , performance level tempo - beats per minute Inter-onset Intervals (IOI) - time intervals between note onsets (Dixon 2001)

Approaches - Probabilistic Frameworks Cemgil et al (2000) - Bayesian framework, using a tempogram (wavelet) and a 10th order Kalman Filter to estimate tempo, which is a hidden state variable Takeda et al (2002) - Hidden Markov models for fluctuating note lengths and note sequences, estimating both rhythms and tempo Raphael (2002) - tempo and rhythm

Approaches - Oscillators Period and phase that adjusts itself to synchronize to IOI input Dannenberg and Allen (1990) - weighted IOIs and credibility evaluation based on past input Meudic (2002) - real time implementation of Dixon Induce several beats and attempt to propagate them through the signal (agents), then choose the best Pardo (2004) - Oscillator, compared to Cemgil using same corpus

Pardo 2004 - Oscillatory Design Is a Kalman Filter (Cemgil) or oscillator better for online tempo tracking? Performance as time series of weights, W, over T time steps Weight of time step with no note onsets = 0, increased proportional to # of note onsets 100ms is minimum IOI allowed, minimum beat period

Pardo 2004 Uses weighted average of last 20 beat periods, with one parameter varying degrees of smoothing A correction parameter varies how far the period and phase of the next predicted beat is changed according to known information A window size parameter affects how many periods may affect the current prediction Chose 5000 random values of these three parameters, ran each triplet on 99 performances of Cemgil corpora

Cemgil MIDI/Piano Corpora Four pro jazz, four pro classical, three amateur piano players Yesterday and Michelle, fast, slow and normal, captured on a Yamaha Diskclavier Available at www.nici.kun.nl/mmm/

Pardo 2004 - Error Measurement After finding best parameters values for Michelle corpus, applied same values to analysis of Yesterday corpus Compared to Cemgil using that paper’s defined error metric, which takes into account both phase and period errors, to come up with a score

Comparison of Approaches (Pardo 2004) Oscillator somewhat better than tempogram alone, Somewhat worse than tempogram plus Kalman, yet fall within standard deviation (bracketed numbers) of Kalman scores

Other Considerations Stylistic information Musical importance of note Training of tracker Musical importance of note Duration Pitch Velocity

Bibliography Allen, P., and R. Dannenberg. 1990. Tracking musical beats in real time. In Proceedings of the International Computer Music Conference 1990: 140–3. Dixon, S. 2001. Automatic extraction of tempo and beat from expressive performances. Journal of New Music Research 30 (1): 39–58. Meudic, B. 2002. A causal algorithm for beat-tracking. In Proceedings of Conference on Understanding and Creating Music. Pardo, B. 2004. Tempo tracking with a single oscillator. In Proceedings of the International Conference on Music Information Retrieval 2004. Raphael, C. 2002. A hybrid graphical model for rhythmic parsing. Artificial Intelligence 137: 217–38. Takeda, H., T. Nishimoto, and S. Sagayama. 2002. Automatic rhythm transcription from multiphonic MIDI signals. In Proceedings of the International Conference on Music Information Retrieval 2003.