An attempted probabilistic version of the McLeod pitch method, inspired by probabilistic YIN.
Mcleod paper: http://miracle.otago.ac.nz/tartini/papers/A_Smarter_Way_to_Find_Pitch.pdf PYIN paper: https://www.eecs.qmul.ac.uk/~simond/pub/2014/MauchDixon-PYIN-ICASSP2014.pdf
I recently implemented Probabilistic YIN as described in the paper. YIN operates with a constant, threshold, which is up to the implementer to define (I used 0.20, taken from TarsosDSP). In PYIN, threshold is distributed between 0.01 and 1.0, with probabilities computed with some strange beta distributions. The idea is that if a pitch candidate "wins" for multiple values of threshold, the probability that this is the correct pitch increases.
I attempted to apply the same reasoning to the McLeod pitch method. One of the parameters in MPM is the constant k, referred to in the code as Cutoff:
From the key maxima we define a threshold which is equal to the value of the highest maximum, nmax, multiplied by a constant k. We then take the first key maximum which is above this threshold and assign its delay, τ , as the pitch period. The constant, k, has to be large enough to avoid choosing peaks caused by strong harmonics, such as those in Figure 2, but low enough to not choose the unwanted beat or sub-harmonic signals. Choosing an incorrect key maximum causes a pitch error, usually a ’wrong octave’. Pitch is a subjective quantity and impossible to get correct all the time. In special cases, the pitch of a given note will be judged differently by different, expert listeners. We can endeavour to get the pitch agreed by the user/musician as most often as possible. The value of k can be adjusted to achieve this, usually in the range 0.8 to 1.0.
So, 0.8 < k < 1.0. In my regular MPM code, I use k = 0.93. In my attempt of probabilistic MPM, I choose values of k in that range, in steps of 0.01, i.e. 20 total increments, with a uniform probability distribution of probability[20] = 0.05. The total probability sums to 1.0, and each increment between 0.8 and 1.0 has the same probability of being correct.
In one of the test cases, Classical guitar F#4, the probabilistic MPM output multiple candidates:
[ RUN ] PMpmInstrumentTest.Classical_FSharp4_48000
PMpm pitch: 372.387 probability: 0.9
PMpm pitch: 186.137 probability: 0.1
Comparatively, probabilistic YIN gives:
[ RUN ] PYinInstrumentTest.Classical_FSharp4_48000
PYin pitch: 13610.8 probability: 0.305056
PYin pitch: 741.156 probability: 0.104046
PYin pitch: 372.504 probability: 0.52492
PYin pitch: 186.147 probability: 0.030646
PYin pitch: 0.549331 probability: 0.035329