@sebastbake/music-tempo/src/TempoInduction.ts

Finding out tempo of the music

/**
 * Find clusters
 * @param {Array} events - the onsets from which the tempo is induced
 * @param {Object} [params={}] - parameters
 * @param {Number} [params.widthTreshold=0.025] - the maximum difference in IOIs which are in the same cluster
 * @param {Number} [params.maxIOI=2.5] - the maximum IOI for inclusion in a cluster
 * @param {Number} [params.minIOI=0.07] - the minimum IOI for inclusion in a cluster
 * @return {{clIntervals: Array, clSizes: Array}} - object with clusters
 */

interface Clusters {
  clIntervals: number[];
  clSizes: number[];
}

type processRhythmicEventsOptions = {
  widthTreshold?: number;
  maxIOI?: number;
  minIOI?: number;
};

const defaultprocessRhythmicEventsOptions = {
  widthTreshold: 0.025,
  maxIOI: 2.5,
  minIOI: 0.07,
}

export function processRhythmicEvents(
  events: number[],
  {
    widthTreshold = 0.025,
    maxIOI = 2.5,
    minIOI = 0.07,
  }: processRhythmicEventsOptions = defaultprocessRhythmicEventsOptions
): Clusters {
  const length = events.length;

  let clIntervals: number[] = [],
    clSizes: number[] = [],
    clCount = 0;

  for (let i = 0; i < length - 1; i++) {
    for (let j = i + 1; j < length; j++) {
      let ioi = events[j] - events[i];
      if (ioi < minIOI) {
        continue;
      }
      if (ioi > maxIOI) {
        break;
      }
      let k = 0;
      for (; k < clCount; k++) {
        if (Math.abs(clIntervals[k] - ioi) < widthTreshold) {
          if (
            Math.abs(clIntervals[k + 1] - ioi) <
            Math.abs(clIntervals[k] - ioi) &&
            k < clCount - 1
          ) {
            k++;
          }
          clIntervals[k] =
            (clIntervals[k] * clSizes[k] + ioi) / (clSizes[k] + 1);
          clSizes[k]++;
          break;
        }
      }
      if (k != clCount) continue;
      clCount++;
      for (; k > 0 && clIntervals[k - 1] > ioi; k--) {
        clIntervals[k] = clIntervals[k - 1];
        clSizes[k] = clSizes[k - 1];
      }
      clIntervals[k] = ioi;
      clSizes[k] = 1;
    }
  }
  if (clCount == 0) {
    throw "Fail to find IOIs";
  }
  clIntervals.length = clCount;
  clSizes.length = clCount;
  return { clIntervals, clSizes };
}
/**
 * Merge similar intervals
 * @param {Object} clusters - object with clusters
 * @param {Array} clusters.clIntervals - clusters IOIs array
 * @param {Array} clusters.clSizes - clusters sizes array
 * @param {Object} [params={}] - parameters
 * @param {Number} [params.widthTreshold=0.025] - the maximum difference in IOIs which are in the same cluster
 * @return {{clIntervals: Array, clSizes: Array}} - object with clusters
 */

type mergeClustersOptions = {
  widthTreshold?: number;
};

const defaultMergeClustersOptions = { widthTreshold: 0.025 };

export function mergeClusters(
  clusters: Clusters,
  { widthTreshold = 0.025 }: mergeClustersOptions = defaultMergeClustersOptions
): Clusters {
  let clIntervals = clusters.clIntervals,
    clSizes = clusters.clSizes;
  let clCount = clIntervals.length;

  for (let i = 0; i < clCount; i++)
    for (let j = i + 1; j < clCount; j++)
      if (Math.abs(clIntervals[i] - clIntervals[j]) < widthTreshold) {
        clIntervals[i] =
          (clIntervals[i] * clSizes[i] + clIntervals[j] * clSizes[j]) /
          (clSizes[i] + clSizes[j]);
        clSizes[i] = clSizes[i] + clSizes[j];
        --clCount;
        for (let k = j + 1; k <= clCount; k++) {
          clIntervals[k - 1] = clIntervals[k];
          clSizes[k - 1] = clSizes[k];
        }
      }
  clIntervals.length = clCount;
  clSizes.length = clCount;
  return { clIntervals, clSizes };
}
/**
 * Score intervals
 * @param {Object} clusters - object with clusters
 * @param {Array} clusters.clIntervals - clusters IOIs array
 * @param {Array} clusters.clSizes - clusters sizes array
 * @param {Object} [params={}] - parameters
 * @param {Number} [params.widthTreshold=0.025] - the maximum difference in IOIs which are in the same cluster
 * @param {Number} [params.maxTempos=10] - initial amount of tempo hypotheses
 * @return {{clScores: Array, clScoresIdxs: Array}} - object with intervals scores
 */

type ClusterScore = {
  clScores: number[];
  clScoresIdxs: number[];
};

type calculateScoreOptions = {
  widthTreshold?: number;
  maxTempos?: number;
};

const defaultCalculateScoreOptions = { widthTreshold: 0.025, maxTempos: 10 };

export function calculateScore(
  clusters: Clusters,
  { widthTreshold = 0.025, maxTempos = 10 }: calculateScoreOptions = defaultCalculateScoreOptions
): ClusterScore {
  let clIntervals = clusters.clIntervals,
    clSizes = clusters.clSizes,
    clScores: number[] = [],
    clScoresIdxsMeta: Array<{ score: number; idx: number }> = [];
  let clCount = clIntervals.length;

  for (let i = 0; i < clCount; i++) {
    clScores[i] = 10 * clSizes[i];
    clScoresIdxsMeta[i] = { score: clScores[i], idx: i };
  }

  clScoresIdxsMeta.sort((a, b) => b.score - a.score);
  if (clScoresIdxsMeta.length > maxTempos) {
    for (let i = maxTempos - 1; i < clScoresIdxsMeta.length - 1; i++) {
      if (clScoresIdxsMeta[i].score == clScoresIdxsMeta[i + 1].score) {
        maxTempos++;
      } else {
        break;
      }
    }
    clScoresIdxsMeta.length = maxTempos;
  }

  const clScoresIdxs = clScoresIdxsMeta.map((a) => a.idx);

  for (let i = 0; i < clCount; i++) {
    for (let j = i + 1; j < clCount; j++) {
      let ratio = clIntervals[i] / clIntervals[j];
      let isFraction = ratio < 1;
      let d, err;
      d = isFraction ? Math.round(1 / ratio) : Math.round(ratio);
      if (d < 2 || d > 8) continue;

      if (isFraction) err = Math.abs(clIntervals[i] * d - clIntervals[j]);
      else err = Math.abs(clIntervals[i] - clIntervals[j] * d);
      let errTreshold = isFraction ? widthTreshold : widthTreshold * d;
      if (err >= errTreshold) continue;

      d = d >= 5 ? 1 : 6 - d;
      clScores[i] += d * clSizes[j];
      clScores[j] += d * clSizes[i];
    }
  }
  return { clScores, clScoresIdxs };
}
/**
 * Get array of tempo hypotheses
 * @param {Object} clusters - object with clusters
 * @param {Array} clusters.clIntervals - clusters IOIs array
 * @param {Array} clusters.clSizes - clusters sizes array
 * @param {Array} clusters.clScores - clusters scores array
 * @param {Array} clusters.clScoresIdxs - clusters scores indexes array
 * @param {Object} [params={}] - parameters
 * @param {Number} [params.widthTreshold=0.025] - the maximum difference in IOIs which are in the same cluster
 * @param {Number} [params.minBeatInterval=0.3] - the minimum inter-beat interval (IBI) (0.30 seconds == 200 BPM)
 * @param {Number} [params.maxBeatInterval=1] - the maximum inter-beat interval (IBI) (1.00 seconds ==  60 BPM)
 * @return {Array} tempoList - tempo hypotheses array
 */

type createTempoListOptions = {
  widthTreshold?: number;
  minBeatInterval?: number;
  maxBeatInterval?: number;
};

const defaultTempoListOptions = {
  widthTreshold: 0.025,
  minBeatInterval: 0.3,
  maxBeatInterval: 1,
};

export function createTempoList(
  { clIntervals, clScores, clScoresIdxs }: Clusters & ClusterScore,
  {
    widthTreshold = 0.025,
    minBeatInterval = 0.3,
    maxBeatInterval = 1,
  }: createTempoListOptions = defaultTempoListOptions
): number[] {
  const tempoList: number[] = [];
  let clCount = clIntervals.length;

  for (let i = 0; i < clScoresIdxs.length; i++) {
    let idx = clScoresIdxs[i];
    let newSum = clIntervals[idx] * clScores[idx];
    let newWeight = clScores[idx];
    let err, errTreshold;
    for (let j = 0; j < clCount; j++) {
      if (j == idx) continue;
      let ratio = clIntervals[idx] / clIntervals[j];
      let isFraction = ratio < 1;
      let d = isFraction ? Math.round(1 / ratio) : Math.round(ratio);
      if (d < 2 || d > 8) continue;

      if (isFraction) {
        err = Math.abs(clIntervals[idx] * d - clIntervals[j]);
        errTreshold = widthTreshold;
      } else {
        err = Math.abs(clIntervals[idx] - d * clIntervals[j]);
        errTreshold = widthTreshold * d;
      }
      if (err >= errTreshold) continue;

      if (isFraction) {
        newSum += (clIntervals[j] / d) * clScores[j];
      } else {
        newSum += clIntervals[j] * d * clScores[j];
      }
      newWeight += clScores[j];
    }
    let beat = newSum / newWeight;

    while (beat < minBeatInterval) beat *= 2;
    while (beat > maxBeatInterval) beat /= 2;

    tempoList.push(beat);
  }
  return tempoList;
}