Setting parameters in Librosa's CQT function for an 88-key piano

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I am doing an automatic music recognition project with a deep learning model. For my data preprocessing, I am trying to calculate the Constant Q Transform for polyphonic 88-key piano audio using Python's Librosa library. However, I do not understand what I should set fmin, n_bins, and bins_per_octave to in Librosa's cqt() method to do this. Specifically:

  • What exactly is a bin? Do the upper and lower boundaries of a bin correspond to the frequencies of two consecutive notes? In other words, because an 88-key piano has 7 octaves each with 12 unique notes, should I set n_bins = 7 * 12 = 84 or equivalently bins_per_octave = 7? Or should several bins correspond to a single note interval?
  • Is fmin supposed to be the deepest note on the 88-key piano, i.e. the A note with a frequency of about 27.5 Hz?
  • Why do we need fmin? Is this some sort of reference point, similar to the equation from amplitude to decibels?
  • What are the differences between n_bins and bins_per_octave and which is better to use? For example, this research paper here uses both.
  • When is it appropriate to use Librosa's chroma_cqt method?
signal-processing python
1 Answers

I'm not an expert in CQT, but I can maybe help to answer some of these question. According to this wikipedia page, CQT can be thought of as series of filters on the signal. Each filter isolates some frequency domain of the signal, and then the amplitude of the filtered signal is the amplitude which is output for that frequency.

So to your first question, a bin is a filter which isolates a particular part of the signal in the frequency domain. The upper and lower bound of the filter is a bit unclear to me exactly, but certainly the idea is that each bin is centered at frequencies which I'll describe after this, and the bins ideally wouldn't overlap, but also not lose any data if you attempted to reconstruct the original signal.

For your case, I would set fmin to the lowest note on the piano, like you said, 27.5 hz. Then I would put bins_per_octave at the default (12), since you'd like to match the bins to each note on the piano. Finally, the number of bins would be 88, since you have 88 keys. You won't capture any harmonics of the keys (especially the higher ones), but maybe that's okay for you case.

To explain more about how frequencies are chosen, the idea is to mimic how humans hear frequencies. We are more discerning at lower frequencies, and less so at high frequencies, with a roughly logarithmic response. So the internal formula for each bin's frequency is probably something like:

f_min * 2 ** (i / bins_per_octave)

where i is the bin index and in range [0, n_bins).

I have no idea when chroma_cqt is best used, so hopefully someone else can help with that :)

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