Web Audio tuner

From this API we only use one specific function to access the audio input device, generally the microphone: getUserMedia. Just like with AudioContext, we whould consider the possibility that the API may be prefixed in some browsers or older versions of them.

var isGetUserMediaSupported = function(){
	navigator.getUserMedia = navigator.getUserMedia || navigator.webkitGetUserMedia || navigator.mozGetUserMedia;
	if((navigator.mediaDevices && navigator.mediaDevices.getUserMedia) || navigator.getUserMedia){
			return true;
	}

	return false;
};

if(isGetUserMediaSupported()){
	var getUserMedia = navigator.mediaDevices && navigator.mediaDevices.getUserMedia ?
		navigator.mediaDevices.getUserMedia.bind(navigator.mediaDevices) :
		function (constraints) {
			return new Promise(function (resolve, reject) {
				navigator.getUserMedia(constraints, resolve, reject);
			});
		};

	getUserMedia({audio: true}).then(streamReceived).catch(reportError);
}

There is a variety of methods to detect the pitch of a sound, some work in the frequency domain (like HPS, or Harmonic Product Spectrum), while some others do in the time domain (like Autocorrelation). With such a high sampling rate, we can only fit a small fraction of a second in the buffer used by the AnalyserNode. In these conditions, the latter algorithm usually does a better job than the former, and this is why we chose it for this demo.

Autocorrelation is the process of cross-correlating a signal with a time-delayed version of itself. In other words, we will be comparing a signal at two different points in time. As Wikipedia puts it:

It is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

Given a delay time \(k\) we:

1. Find the value at a time \(t\)
2. Find the value at a time \(t+k\)
3. Multiply those values together
4. Accumulate those products over a series of times (1000 in our code)
5. Divide by the number of samples to get the average

As seen on this page about autocorrelation, the resulting formula would be something like this:

\[ R(k) = \frac{1}{t_{max} - t_{min}} \int_{t_{min}}^{t_{max}}s(t)s(t+k)dt \]

In addition, as you can see in the example, we also normalize the data. Since we are working with an array of bytes (0-255), we subtract 128 and divide by the same value.

Remember that we are working with periodic signals. As you may imagine, the highest correlation will happen once that signal "repeats itself", i.e. that \(bestK\) will match the period (in frames) of the fundamental frequency. In order to get that frequency we just need to divide the sampling rate by that distance \(bestK\).

var findFundamentalFreq = function(buffer, sampleRate) {
	// We use Autocorrelation to find the fundamental frequency.

	// In order to correlate the signal with itself (hence the name of the algorithm), we will check two points 'k' frames away.
	// The autocorrelation index will be the average of these products. At the same time, we normalize the values.
	// Source: http://www.phy.mty.edu/~suits/autocorrelation.html
	// Assuming the sample rate is 48000Hz, a 'k' equal to 1000 would correspond to a 48Hz signal (48000/1000 = 48),
	// while a 'k' equal to 8 would correspond to a 6000Hz one, which is enough to cover most (if not all)
	// the notes we have in the notes.json?_ts=1506034634490 file.
	var n = 1024, bestR = 0, bestK = -1;
	for(var k = 8; k <= 1000;="" k++){="" var="" sum="0;" for(var="" i="0;" <="" n;="" i++){="" +="((buffer[i]" -="" 128)="" *="" ((buffer[i="" k]="" 128);="" }="" r="sum" (n="" k);="" if(r=""> bestR){
			bestR = r;
			bestK = k;
		}

		if(r > 0.9) {
			// Let's assume that this is good enough and stop right here
			break;
		}
	}

	if(bestR > 0.0025) {
		// The period (in frames) of the fundamental frequency is 'bestK'. Getting the frequency from there is trivial.
		var fundamentalFreq = sampleRate / bestK;
		return fundamentalFreq;
	}
	else {
		// We haven't found a good correlation
		return -1;
	}
};

var frameId;
var detectPitch = function () {
	var buffer = new Uint8Array(analyserAudioNode.fftSize);
	// See initializations in the AudioContent and AnalyserNode sections of the demo.
	analyserAudioNode.getByteTimeDomainData(buffer);
	var fundalmentalFreq = findFundamentalFreq(buffer, audioContext.sampleRate);

	if (fundalmentalFreq !== -1) {
		var note = findClosestNote(fundalmentalFreq, notesArray); // See the 'Finding the right note' section.
		var cents = findCentsOffPitch(fundalmentalFreq, note.frequency); // See the 'Calculating the cents off pitch' section.
		updateNote(note.note); // Function that updates the note on the page (see demo source code).
		updateCents(cents); // Function that updates the cents on the page and the gauge control (see demo source code).
	}
	else {
		updateNote('--');
		updateCents(-50);
	}

	frameId = window.requestAnimationFrame(detectPitch);
};

Now that we have the fundamental frequency, we just need to find the note with the closest frequency. Since the notesArray that we showed in previous code snippets is already sorted by this value, we only need to perform a binary search to find it.

// 'notes' is an array of objects like { note: 'A4', frequency: 440 }.
// See initialization in the source code of the demo
var findClosestNote = function(freq, notes) {
	// Use binary search to find the closest note
	var low = -1, high = notes.length;
	while (high - low > 1) {
			var pivot = Math.round((low + high) / 2);
			if (notes[pivot].frequency <= freq)="" {="" low="pivot;" }="" else="" high="pivot;" if(math.abs(notes[high].frequency="" -="" <="Math.abs(notes[low].frequency" freq))="" notes[high]="" is="" closer="" to="" the="" frequency="" we="" found="" return="" notes[high];="" notes[low];="" };<="" code="">

The last step, given the fundalmental frequency that we have found and the frequency of the closest note, we need how far the former one is from the latter. This is done using the following formula.

\[ cents = \left \lfloor 1200 \frac{ \log_{10}(f/refF) }{\log_{10}2} \right \rfloor \]

Where \(f\) is the fundamental frequency and \(refF\) is the frequency from the closes note. Since \(\log_{10}2\) is a constant that we can precalculate, we just use it directly in our code.

var findCentsOffPitch = function(freq, refFreq) {
		// We need to find how far freq is from baseFreq in cents
		var log2 = 0.6931471805599453; // Math.log(2)
		var multiplicativeFactor = freq / refFreq;

		// We use Math.floor to get the integer part and ignore decimals
		var cents = Math.floor(1200 * (Math.log(multiplicativeFactor) / log2));
		return cents;
};