audio_file.onchange = function() {
  var file = this.files[0];
  var reader = new FileReader();
  var context = new(window.AudioContext || window.webkitAudioContext)();
  reader.onload = function() {
    context.decodeAudioData(reader.result, function(buffer) {
      prepare(buffer);
    });
  };
  reader.readAsArrayBuffer(file);
};

function prepare(buffer) {
  var offlineContext = new OfflineAudioContext(1, buffer.length, buffer.sampleRate);
  var source = offlineContext.createBufferSource();
  source.buffer = buffer;
  var filter = offlineContext.createBiquadFilter();
  filter.type = "lowpass";
  source.connect(filter);
  filter.connect(offlineContext.destination);
  source.start(0);
  offlineContext.startRendering();
  offlineContext.oncomplete = function(e) {
    process(e);
  };
}

function process(e) {
  var filteredBuffer = e.renderedBuffer;
  //If you want to analyze both channels, use the other channel later
  var data = filteredBuffer.getChannelData(0);
  var max = arrayMax(data);
  var min = arrayMin(data);
  var threshold = min + (max - min) * 0.98;
  var peaks = getPeaksAtThreshold(data, threshold);
  var intervalCounts = countIntervalsBetweenNearbyPeaks(peaks);
  var tempoCounts = groupNeighborsByTempo(intervalCounts);
  tempoCounts.sort(function(a, b) {
    return b.count - a.count;
  });
  if (tempoCounts.length) {
    output.innerHTML = tempoCounts[0].tempo;
  }
}

// http://tech.beatport.com/2014/web-audio/beat-detection-using-web-audio/
function getPeaksAtThreshold(data, threshold) {
  var peaksArray = [];
  var length = data.length;
  for (var i = 0; i < length;) {
    if (data[i] > threshold) {
      peaksArray.push(i);
      // Skip forward ~ 1/4s to get past this peak.
      i += 10000;
    }
    i++;
  }
  return peaksArray;
}

function countIntervalsBetweenNearbyPeaks(peaks) {
  var intervalCounts = [];
  peaks.forEach(function(peak, index) {
    for (var i = 0; i < 10; i++) {
      var interval = peaks[index + i] - peak;
      var foundInterval = intervalCounts.some(function(intervalCount) {
        if (intervalCount.interval === interval) return intervalCount.count++;
      });
      //Additional checks to avoid infinite loops in later processing
      if (!isNaN(interval) && interval !== 0 && !foundInterval) {
        intervalCounts.push({
          interval: interval,
          count: 1
        });
      }
    }
  });
  return intervalCounts;
}

function groupNeighborsByTempo(intervalCounts) {
  var tempoCounts = [];
  intervalCounts.forEach(function(intervalCount) {
    //Convert an interval to tempo
    var theoreticalTempo = 60 / (intervalCount.interval / 44100);
    theoreticalTempo = Math.round(theoreticalTempo);
    if (theoreticalTempo === 0) {
      return;
    }
    // Adjust the tempo to fit within the 90-180 BPM range
    while (theoreticalTempo < 90) theoreticalTempo *= 2;
    while (theoreticalTempo > 180) theoreticalTempo /= 2;

    var foundTempo = tempoCounts.some(function(tempoCount) {
      if (tempoCount.tempo === theoreticalTempo) return tempoCount.count += intervalCount.count;
    });
    if (!foundTempo) {
      tempoCounts.push({
        tempo: theoreticalTempo,
        count: intervalCount.count
      });
    }
  });
  return tempoCounts;
}

// http://stackoverflow.com/questions/1669190/javascript-min-max-array-values
function arrayMin(arr) {
  var len = arr.length,
    min = Infinity;
  while (len--) {
    if (arr[len] < min) {
      min = arr[len];
    }
  }
  return min;
}

function arrayMax(arr) {
  var len = arr.length,
    max = -Infinity;
  while (len--) {
    if (arr[len] > max) {
      max = arr[len];
    }
  }
  return max;
}

<input id="audio_file" type="file" accept="audio/*"></input>
<audio id="audio_player"></audio>
<p>
  Most likely tempo: <span id="output"></span>
</p>