Determine the key of a song by its chords

Question

How can I programmatically find the key of a song just by knowing the chord sequence of the song?
I asked some people how they would determine the key of a song and they all said they do it 'by ear' or by 'trial and error' and by telling if a chord resolves a song or not... For the average musician that is probably fine, but as a programmer that really isn't the answer that I was looking for.

So I started looking for music related libraries to see if anyone else has written an algorithm for that yet. But although I found a really big library called 'tonal' on GitHub: https://danigb.github.io/tonal/api/index.html I couldn't find a method that would accept an array of chords and return the key.

My language of choice will be JavaScript (NodeJs), but I'm not necessarily looking for a JavaScript answer. Pseudo code or an explanation that can be translated into code without too much trouble would be totally fine.

As some of you mentioned correctly, the key in a song can change. I'm not sure if a change in key could be detected reliably enough. So, for now let's just say, I'm looking for an algorithm that makes a good approximation on the key of a given chord sequence.

... After looking into the circle of fifths, I think I found a pattern to find all chords that belong to each key. I wrote a function getChordsFromKey(key) for that. And by checking the chords of a chord sequence against every key, I can create an array containing probabilities of how likely it is that the key matches the given chord sequence: calculateKeyProbabilities(chordSequence). And then I added another function estimateKey(chordSequence), which takes the keys with the highest probability-score and then checks if the last chord of the chord sequence is one of them. If that is the case, it returns an array containing only that chord, otherwise it returns an array of all chords with the highest probability-score. This does an OK job, but it still doesn't find the correct key for a lot of songs or returns multiple keys with equal probabililty. The main problem being chords like A5, Asus2, A+, A°, A7sus4, Am7b5, Aadd9, Adim, C/G etc. that are not in the circle of fifths. And the fact that for instance the key C contains the exact same chords as the key Am, and G the same as Em and so on...
Here is my code:

'use strict'
const normalizeMap = {
    "Cb":"B",  "Db":"C#",  "Eb":"D#", "Fb":"E",  "Gb":"F#", "Ab":"G#", "Bb":"A#",  "E#":"F",  "B#":"C",
    "Cbm":"Bm","Dbm":"C#m","Eb":"D#m","Fbm":"Em","Gb":"F#m","Ab":"G#m","Bbm":"A#m","E#m":"Fm","B#m":"Cm"
}
const circleOfFifths = {
    majors: ['C', 'G', 'D', 'A',  'E',  'B',  'F#', 'C#', 'G#','D#','A#','F'],
    minors: ['Am','Em','Bm','F#m','C#m','G#m','D#m','A#m','Fm','Cm','Gm','Dm']
}

function estimateKey(chordSequence) {
    let keyProbabilities = calculateKeyProbabilities(chordSequence)
    let maxProbability = Math.max(...Object.keys(keyProbabilities).map(k=>keyProbabilities[k]))
    let mostLikelyKeys = Object.keys(keyProbabilities).filter(k=>keyProbabilities[k]===maxProbability)

    let lastChord = chordSequence[chordSequence.length-1]

    if (mostLikelyKeys.includes(lastChord))
         mostLikelyKeys = [lastChord]
    return mostLikelyKeys
}

function calculateKeyProbabilities(chordSequence) {
    const usedChords = [ ...new Set(chordSequence) ] // filter out duplicates
    let keyProbabilities = []
    const keyList = circleOfFifths.majors.concat(circleOfFifths.minors)
    keyList.forEach(key=>{
        const chords = getChordsFromKey(key)
        let matchCount = 0
        //usedChords.forEach(usedChord=>{
        //    if (chords.includes(usedChord))
        //        matchCount++
        //})
        chords.forEach(chord=>{
            if (usedChords.includes(chord))
                matchCount++
        })
        keyProbabilities[key] = matchCount / usedChords.length
    })
    return keyProbabilities
}

function getChordsFromKey(key) {
    key = normalizeMap[key] || key
    const keyPos = circleOfFifths.majors.includes(key) ? circleOfFifths.majors.indexOf(key) : circleOfFifths.minors.indexOf(key)
    let chordPositions = [keyPos, keyPos-1, keyPos+1]
    // since it's the CIRCLE of fifths we have to remap the positions if they are outside of the array
    chordPositions = chordPositions.map(pos=>{
        if (pos > 11)
            return pos-12
        else if (pos < 0)
            return pos+12
        else
            return pos
    })
    let chords = []
    chordPositions.forEach(pos=>{
        chords.push(circleOfFifths.majors[pos])
        chords.push(circleOfFifths.minors[pos])
    })
    return chords
}

// TEST

//console.log(getChordsFromKey('C'))
const chordSequence = ['Em','G','D','C','Em','G','D','Am','Em','G','D','C','Am','Bm','C','Am','Bm','C','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em','Em','C','D','Am','Am','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em','Em','C','D','Em']

const key = estimateKey(chordSequence)
console.log('Example chord sequence:',JSON.stringify(chordSequence))
console.log('Estimated key:',JSON.stringify(key)) // Output: [ 'Em' ]

Answer 1

The chords in a song of a particular key are predominantly members of the key's scale. I imagine you could get a good approximation statistically (if there is enough data) by comparing the predominant accidentals in the chords listed to the key signatures of the keys.

See https://en.wikipedia.org/wiki/Circle_of_fifths

Of course, a song in any key can/will have accidentals not in the keys scale, so it would likely be a statistical approximation. But over several bars, if you add up the accidentals and filter out all but the ones that occur most often, you may be able to match to a key signature.

Addendum: as Jonas w correctly points out, you may be able to get the signature, but you won't likely be able to determine if it is a major or minor key.

Answer 2

Here's what I came up with. Still new with modern JS so apologies for messiness and bad use of map().

I looked around the internals of the tonal library, it has a function scales.detect(), but it was no good since it required every note present. Instead I used it as inspiration and flattened the progression into a simple note list and checked this in all transpositions as a subset of all the possible scales.

const _ = require('lodash');
const chord = require('tonal-chord');
const note = require('tonal-note');
const pcset = require('tonal-pcset');
const dictionary = require('tonal-dictionary');
const SCALES = require('tonal-scale/scales.json');
const dict = dictionary.dictionary(SCALES, function (str) { return str.split(' '); });

//dict is a dictionary of scales defined as intervals
//notes is a string of tonal notes eg 'c d eb'
//onlyMajorMinor if true restricts to the most common scales as the tonal dict has many rare ones
function keyDetect(dict, notes, onlyMajorMinor) {
    //create an array of pairs of chromas (see tonal docs) and scale names
    var chromaArray = dict.keys(false).map(function(e) { return [pcset.chroma(dict.get(e)), e]; });
    //filter only Major/Minor if requested
    if (onlyMajorMinor) { chromaArray = chromaArray.filter(function (e) { return e[1] === 'major' || e[1] === 'harmonic minor'; }); }
 //sets is an array of pitch classes transposed into every possibility with equivalent intervals
 var sets = pcset.modes(notes, false);

 //this block, for each scale, checks if any of 'sets' is a subset of any scale
 return chromaArray.reduce(function(acc, keyChroma) {
    sets.map(function(set, i) {
        if (pcset.isSubset(keyChroma[0], set)) {
            //the midi bit is a bit of a hack, i couldnt find how to turn an int from 0-11 into the repective note name. so i used the midi number where 60 is middle c
            //since the index corresponds to the transposition from 0-11 where c=0, it gives the tonic note of the key
            acc.push(note.pc(note.fromMidi(60+i)) + ' ' + keyChroma[1]);
            }
        });
        return acc;
    }, []);

    }

const p1 = [ chord.get('m','Bb'), chord.get('m', 'C'), chord.get('M', 'Eb') ];
const p2 = [ chord.get('M','F#'), chord.get('dim', 'B#'), chord.get('M', 'G#') ];
const p3 = [ chord.get('M','C'), chord.get('M','F') ];
const progressions = [ p1, p2, p3 ];

//turn the progression into a flat string of notes seperated by spaces
const notes = progressions.map(function(e) { return _.chain(e).flatten().uniq().value(); });
const possibleKeys = notes.map(function(e) { return keyDetect(dict, e, true); });

console.log(possibleKeys);
//[ [ 'Ab major' ], [ 'Db major' ], [ 'C major', 'F major' ] ]

Some drawbacks:
- doesn't give the enharmonic note you want necessarily. In p2, the more correct response is C# major, but this could be fixed by checking somehow with the original progression.
-‎ won't deal with 'decorations' to chords that are out of the key, which might occur in pop songs, eg. CMaj7 FMaj7 GMaj7 instead of C F G. Not sure how common this is, not too much I think.

Answer 3

Given an array of tones like this:

var tones = ["G","Fis","D"];

We can firstly generate a unique Set of tones:

tones = [...new Set(tones)];

Then we could check for the appearence of # and bs :

var sharps = ["C","G","D","A","E","H","Fis"][["Fis","Cis","Gis","Dis","Ais","Eis"].filter(tone=>tones.includes(tone)).length];

Then do the same with bs and get the result with:

var key = sharps === "C" ? bs:sharps;

However, you still dont know if its major or minor, and many componists do not care of the upper rules (and changed the key inbetween )...

Answer 4

You might be able too keep an structure with keys for every "supported" scale, with as value an array with chords matching that scale.

Given a chord progression you can then start by making a shortlist of keys based on your structure.

With multiple matches you can try to make an educated guess. For example, add other "weight" to any scale that matches the root note.

Answer 5

You can use the spiral array, a 3D model for tonality created by Elaine Chew, which has a key detection algorithm.

Chuan, Ching-Hua, and Elaine Chew. "Polyphonic audio key finding using the spiral array CEG algorithm." Multimedia and Expo, 2005. ICME 2005. IEEE International Conference on. IEEE, 2005.

My recent tension model, which is available in a .jar file here, also outputs the key (in addition to the tension measures) based on the spiral array. It can either take a musicXML file or text file as input that just takes a list of pitch names for each 'time window' in your piece.

Herremans D., Chew E.. 2016. Tension ribbons: Quantifying and visualising tonal tension. Second International Conference on Technologies for Music Notation and Representation (TENOR). 2:8-18.

Answer 6

One approach would be to find all the notes being played, and compare to the signature of different scales and see which is the best match.

Normally a scale signature is pretty unique. A natural minor scale will have the same notes as a major scale (that is true for all the modes), but generally when we say minor scale we mean the harmonic minor scale, which has a specific signature.

So comparing what notes are in the chords with your different scales should give you a good estimate. And you could refine by adding some weight to different notes (for example the ones that come up the most, or the first and last chords, the tonic of each chord, etc.)

This seems to handle most basic cases with some accuracy:

'use strict'
const allnotes = [
  "C", "C#", "D", "Eb", "E", "F", "F#", "G", "Ab", "A", "Bb", "B"
]

// you define the scales you want to validate for, with name and intervals
const scales = [{
  name: 'major',
  int: [2, 4, 5, 7, 9, 11]
}, {
  name: 'minor',
  int: [2, 3, 5, 7, 8, 11]
}];

// you define which chord you accept. This is easily extensible,
// only limitation is you need to have a unique regexp, so
// there's not confusion.

const chordsDef = {
  major: {
    intervals: [4, 7],
    reg: /^[A-G]$|[A-G](?=[#b])/
  },
  minor: {
    intervals: [3, 7],
    reg: /^[A-G][#b]?[m]/
  },
  dom7: {
    intervals: [4, 7, 10],
    reg: /^[A-G][#b]?[7]/
  }
}

var notesArray = [];

// just a helper function to handle looping all notes array
function convertIndex(index) {
  return index < 12 ? index : index - 12;
}


// here you find the type of chord from your 
// chord string, based on each regexp signature
function getNotesFromChords(chordString) {

  var curChord, noteIndex;
  for (let chord in chordsDef) {
    if (chordsDef[chord].reg.test(chordString)) {
      var chordType = chordsDef[chord];
      break;
    }
  }

  noteIndex = allnotes.indexOf(chordString.match(/^[A-G][#b]?/)[0]);
  addNotesFromChord(notesArray, noteIndex, chordType)

}

// then you add the notes from the chord to your array
// this is based on the interval signature of each chord.
// By adding definitions to chordsDef, you can handle as
// many chords as you want, as long as they have a unique regexp signature
function addNotesFromChord(arr, noteIndex, chordType) {

  if (notesArray.indexOf(allnotes[convertIndex(noteIndex)]) == -1) {
    notesArray.push(allnotes[convertIndex(noteIndex)])
  }
  chordType.intervals.forEach(function(int) {

    if (notesArray.indexOf(allnotes[noteIndex + int]) == -1) {
      notesArray.push(allnotes[convertIndex(noteIndex + int)])
    }

  });

}

// once your array is populated you check each scale
// and match the notes in your array to each,
// giving scores depending on the number of matches.
// This one doesn't penalize for notes in the array that are
// not in the scale, this could maybe improve a bit.
// Also there's no weight, no a note appearing only once
// will have the same weight as a note that is recurrent. 
// This could easily be tweaked to get more accuracy.
function compareScalesAndNotes(notesArray) {
  var bestGuess = [{
    score: 0
  }];
  allnotes.forEach(function(note, i) {
    scales.forEach(function(scale) {
      var score = 0;
      score += notesArray.indexOf(note) != -1 ? 1 : 0;
      scale.int.forEach(function(noteInt) {
        // console.log(allnotes[convertIndex(noteInt + i)], scale)

        score += notesArray.indexOf(allnotes[convertIndex(noteInt + i)]) != -1 ? 1 : 0;

      });

      // you always keep the highest score (or scores)
      if (bestGuess[0].score < score) {

        bestGuess = [{
          score: score,
          key: note,
          type: scale.name
        }];
      } else if (bestGuess[0].score == score) {
        bestGuess.push({
          score: score,
          key: note,
          type: scale.name
        })
      }



    })
  })
  return bestGuess;

}


document.getElementById('showguess').addEventListener('click', function(e) {
  notesArray = [];
  var chords = document.getElementById('chodseq').value.replace(/ /g,'').replace(/["']/g,'').split(',');
  chords.forEach(function(chord) {
    getNotesFromChords(chord)
  });
  var guesses = compareScalesAndNotes(notesArray);
  var alertText = "Probable key is:";
  guesses.forEach(function(guess, i) {
    alertText += (i > 0 ? " or " : " ") + guess.key + ' ' + guess.type;
  });
  
  alert(alertText)
  
})

<input type="text" id="chodseq" />

<button id="showguess">
Click to guess the key
</button>

For your example, it gives G major, that's because with a harmonic minor scale, there are no D major or Bm chords.

You can try easy ones: C, F, G or Eb, Fm, Gm

Or some with accidents: C, D7, G7 (this one will give you 2 guesses, because there's a real ambiguity, without giving more information, it could be both)

One with accidents but accurate: C, Dm, G, A

Answer 7

If you're not opposed to switching languages, music21 (my library, disclaimer) in Python would do this:

from music21 import stream, harmony

chordSymbols = ['Cm', 'Dsus2', 'E-/C', 'G7', 'Fm', 'Cm']
s = stream.Stream()
for cs in chordSymbols:
    s.append(harmony.ChordSymbol(cs))
s.analyze('key')

Returns: <music21.key.Key of c minor>

The system will know the difference between, say C# major and Db major. It has a full vocabulary of chord names so things like "Dsus2" won't confuse it. The only thing that might bite a newcomer is that flats are written with minus signs so "E-/C" instead of "Eb/C"

Answer 8

There is an online free tool (MazMazika Songs Chord Analyzer), which analyzes and detects the chords of any song very fast. You can process the song through file upload (MP3/WAV) or by pasting YouTube / SoundCloud links. After processing the file, you can play the song while seeing all the chords playing along in-real time, as well as a table containing all the chords, each chord is assigned to a time-position & a number ID, which you can click to go directly to the corresponding chord and it`s time-position.

https://www.mazmazika.com/chordanalyzer