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In this workshop video, we implement pitch tracking in digital audio from scratch! We first go through a classical algorithm called YIN, and then we show how to improve it using a Hidden Markov Model, upgrading it to a version called probabalistic YIN. Finally, we show some applications, including making singing bells, creating an autotuner like Cher, and changing a song so that it's the same note the whole time. This is a long video, but it's worth it! Jupyter notebook code here: https://ctraliedotcom.github.io/pYIN/... (longer notes coming soon!) Table of contents: 00:00 Intro Sequence 00:16 Motivation 05:10 Repetitions in pitched waveforms 09:19 Autocorrelation concept 11:22 Frequencies, notes, octave errors 16:31 Mathematical definition of autocorrelation 20:04 Speeding up autocorrelation with the FFT 25:50 Framing 30:24 Basic YIN And Computation 40:02 Normalized YIN 42:45 Basic fundamental frequency system and sonification 50:12 Refinement with parabolic interpolation 57:44 Preparing all YIN estimates for probabalistic YIN 1:05:22 Introducing probabalistic YIN and HMMs 1:10:36 State space 1:15:17 Transition model 1:19:48 Unrolling state transitions over time 1:21:06 Unvoiced states 1:27:42 Observation model 1:32:13 Coding up probabalistic YIN! 2:00:02 Debugging probabalistic YIN code 2:03:31 Backtracing the optimal frequency trajectory 2:09:27 Probabalistic YIN results 2:14:58 Real time (causal) probabalistic YIN 2:19:20 Research notes 2:22:33 FM synthesis sonification 2:28:13 Making an autotuner! 2:39:19 Everything the same note (lol) 2:43:31 Outro Special thank you to Brendan Sellers (mrbrendansellers on Instagram) for letting me use his vocals! ------------------ Errata I had a slight typo in my parabolic interpolation. The a coefficient can be negative, so to prevent divide by 0, I should simply say a[a == 0] = 1 ------------------ References [1] De Cheveigné, Alain, and Hideki Kawahara. "YIN, a fundamental frequency estimator for speech and music." The Journal of the Acoustical Society of America 111.4 (2002): 1917-1930. [2] Mauch, Matthias, and Simon Dixon. "pYIN: A fundamental frequency estimator using probabilistic threshold distributions." 2014 ieee international conference on acoustics, speech and signal processing (icassp). IEEE, 2014. [3] Georgieva, Elena, Pablo Ripollés, and Brian McFee. "The Changing Sound of Music: An Exploratory Corpus Study of Vocal Trends Over Time." Proceedings of the International Society for Music Information Retrieval Conference. International Society for Music Information Retrieval, 2024. [4] Ellis, Daniel PW. "Beat tracking by dynamic programming." Journal of New Music Research 36.1 (2007): 51-60.