Pitch recognition of musical notes on a smart phone

Question

With limited resources such as slower CPUs, code size and RAM, how best to detect the pitch of a musical note, similar to what an electronic or software tuner would do?

Should I use:

• Kiss FFT
• FFTW
• Discrete Wavelet Transform
• autocorrelation
• zero crossing analysis
• octave-spaced filters

other?

In a nutshell, what I am trying to do is to recognize a single musical note, two octaves below middle-C to two octaves above, played on any (reasonable) instrument. I'd like to be within 20% of the semitone - in other words, if the user plays too flat or too sharp, I need to distinguish that. However, I will not need the accuracy required for tuning.

Answer 1

If you don't need that much accuracy, an FFT could be sufficient. Window the chunk of audio first so that you get well-defined peaks, then find the first significant peak.

Bin width = sampling rate / FFT size:

Fundamentals range from 20 Hz to 7 kHz, so a sampling rate of 14 kHz would be enough. The next "standard" sampling rate is 22050 Hz.

The FFT size is then determined by the precision you want. FFT output is linear in frequency, while musical tones are logarithmic in frequency, so the worst case precision will be at low frequencies. For 20% of a semitone at 20 Hz, you need a width of 1.2 Hz, which means an FFT length of 18545. The next power of two is 2¹⁵ = 32768. This is 1.5 seconds of data, and takes my laptop's processor 3 ms to calculate.

This won't work with signals that have a "missing fundamental", and finding the "first significant" peak is somewhat difficult (since harmonics are often higher than the fundamental), but you can figure out a way that suits your situation.

Autocorrelation and harmonic product spectrum are better at finding the true fundamental for a wave instead of one of the harmonics, but I don't think they deal as well with inharmonicity, and most instruments like piano or guitar are inharmonic (harmonics are slightly sharp from what they should be). It really depends on your circumstances, though.

Also, you can save even more processor cycles by computing only within a specific frequency band of interest, using the Chirp-Z transform.

I've written up a few different methods in Python for comparison purposes.

Answer 2

If you want to do pitch recognition in realtime (and accurate to within 1/100 of a semi-tone), your only real hope is the zero-crossing approach. And it's a faint hope, sorry to say. Zero-crossing can estimate pitch from just a couple of wavelengths of data, and it can be done with a smartphone's processing power, but it's not especially accurate, as tiny errors in measuring the wavelengths result in large errors in the estimated frequency. Devices like guitar synthesizers (which deduce the pitch from a guitar string with just a couple of wavelengths) work by quantizing the measurements to notes of the scale. This may work for your purposes, but be aware that zero-crossing works great with simple waveforms, but tends to work less and less well with more complex instrument sounds.

In my application (a software synthesizer that runs on smartphones) I use recordings of single instrument notes as the raw material for wavetable synthesis, and in order to produce notes at a particular pitch, I need to know the fundamental pitch of a recording, accurate to within 1/1000 of a semi-tone (I really only need 1/100 accuracy, but I'm OCD about this). The zero-crossing approach is much too inaccurate for this, and FFT-based approaches are either way too inaccurate or way too slow (or both sometimes).

The best approach that I've found in this case is to use autocorrelation. With autocorrelation you basically guess the pitch and then measure the autocorrelation of your sample at that corresponding wavelength. By scanning through the range of plausible pitches (say A = 55 Hz thru A = 880 Hz) by semi-tones, I locate the most-correlated pitch, then do a more finely-grained scan in the neighborhood of that pitch to get a more accurate value.

The approach best for you depends entirely on what you're trying to use this for.

Answer 3

I'm not familiar with all the methods you mention, but what you choose should depend primarily on the nature of your input data. Are you analysing pure tones, or does your input source have multiple notes? Is speech a feature of your input? Are there any limitations on the length of time you have to sample the input? Are you able to trade off some accuracy for speed?

To some extent what you choose also depends on whether you would like to perform your calculations in time or in frequency space. Converting a time series to a frequency representation takes time, but in my experience tends to give better results.

Autocorrelation compares two signals in the time domain. A naive implementation is simple but relatively expensive to compute, as it requires pair-wise differencing between all points in the original and time-shifted signals, followed by differentiation to identify turning points in the autocorrelation function, and then selection of the minimum corresponding to the fundamental frequency. There are alternative methods. For example, Average Magnitude Differencing is a very cheap form of autocorrelation, but accuracy suffers. All autocorrelation techniques run the risk of octave errors, since peaks other than the fundamental exist in the function.

Measuring zero-crossing points is simple and straightforward, but will run into problems if you have multiple waveforms present in the signal.

In frequency-space, techniques based on FFT may be efficient enough for your purposes. One example is the harmonic product spectrum technique, which compares the power spectrum of the signal with downsampled versions at each harmonic, and identifies the pitch by multiplying the spectra together to produce a clear peak.

As ever, there is no substitute for testing and profiling several techniques, to empirically determine what will work best for your problem and constraints.

An answer like this can only scratch the surface of this topic. As well as the earlier links, here are some relevant references for further reading.

• Summary of pitch detection algorithms (Wikipedia)
• Pros and cons of Autocorrelation vs Harmonic Product Spectrum
• A high-level overview of pitch detection methods

Answer 4

In my project danstuner, I took code from Audacity. It essentially took an FFT, then found the peak power by putting a cubic curve on the FFT and finding the peak of that curve. Works pretty well, although I had to guard against octave-jumping.

See Spectrum.cpp.

Answer 5

Zero crossing won't work because a typical sound has harmonics and zero-crossings much more than the base frequency.

Something I experimented with (as a home side project) was this:

1. Sample the sound with ADC at whatever sample rate you need.
2. Detect the levels of the short-term positive and negative peaks of the waveform (sliding window or similar). I.e. an envelope detector.
3. Make a square wave that goes high when the waveform goes within 90% (or so) of the positive envelope, and goes low when the waveform goes within 90% of the negative envelope. I.e. a tracking square wave with hysteresis.
4. Measure the frequency of that square wave with straight-forward count/time calculations, using as many samples as you need to get the required accuracy.

However I found that with inputs from my electronic keyboard, for some instrument sounds it managed to pick up 2× the base frequency (next octave). This was a side project and I never got around to implementing a solution before moving on to other things. But I thought it had promise as being much less CPU load than FFT.