Teoria.js

Teoria.js is a lightweight and fast JavaScript library for music theory, both Jazz and Classical. It aims at providing an intuitive programming interface for music software (such as Sheet Readers, Sheet Writers, MIDI Players etc.).

This fork replaces the pitch and interval representation of Teoria. The [fifths, octaves] representation used in Teoria is elegant, but it does not [easily] extend to pitch-classes outside the Western tonal system of twelve semitones per octave.

This fork uses instead a vector of [steps, semitones], where steps is the "diatonic distance" of an interval, and semitones the number of semitones. Thus, a major third is represented as [2, 4]. It is easy to identify the relationship with e.g. the minor third [2, 3], which belongs to the same pitch-class but has different accidentals and sound differently. The diminished fourth [3, 4] sounds the same as the major third, but belongs to a different pitch-class.

This model can easily represent intervals with higher resoultion than semitones, by using fractional numbers as semitones. For example, a third between major and minor can be written [2, 3.5].

Features

• A pitch object (teoria.Pitch), which understands alterations, octaves, key number, frequency and etc. and Helmholtz notation

• A chord object (teoria.Chord), which understands everything from simple major/minor chords to advanced Jazz chords (Ab#5b9, F(#11) and such)

• A scale object (teoria.Scale), The scale object is a powerful presentation of a scale, which supports quite a few handy methods. A scale can either be constructed from the predefined scales, which by default contains the 7 modes (Ionian, Dorian, Phrygian etc.) a major and minor pentatonic and the harmonic chromatic scale or from an arbitrary array of intervals. The scale object also supports solfège, which makes it perfect for tutorials on sight-reading.

• An interval object (teoria.Interval), which makes it easy to find the interval between two pitches, or find a pitch that is a given interval from a pitch. There's also support for counting the interval span in semitones and inverting the interval.

Usage

$ npm install teoria

Can be used with both Node and Browserify/webpack/etc.

... or less preferable

Include the bundled build file, teoria.js from this repository, directly:

<script src="path/to/teoria.js"></script>

Syntax

This is just a short introduction to what teoria-code looks like, for a technical library reference, look further down this document.

// Create pitches:
var a4 = teoria.pitch('a4');       // Scientific notation
var g5 = teoria.pitch("g''");      // Helmholtz notation
var c3 = teoria.pitch.fromKey(28); // From a piano key number

// Find and create pitches based on intervals
teoria.interval(a4, g5);    // Returns a Interval object representing a minor seventh
teoria.interval(a4, 'M6');  // Returns a Pitch representing F#5
a4.interval('m3');          // Returns a Pitch representing C#4
a4.interval(g5);            // Returns a Interval object representing a minor seventh
a4.interval(teoria.pitch('bb5')).invert(); // Returns a Interval representing a major seventh

// Create scales, based on pitches.
a4.scale('mixolydian').simple();  // Returns: ["a", "b", "c#", "d", "e", "f#", "g"]
a4.scale('aeolian').simple();     // Returns: ["a", "b", "c", "d", "e", "f", "g"]
g5.scale('ionian').simple();      // Returns: ["g", "a", "b", "c", "d", "e", "f#"]
g5.scale('dorian');               // Returns a Scale object

// Create chords with the powerful chord parser
a4.chord('sus2').name;    // Returns the name of the chord: 'Asus2'
c3.chord('m').name;       // Returns 'Cm'
teoria.chord('Ab#5b9');   // Returns a Chord object, representing a Ab#5b9 chord
g5.chord('dim');          // Returns a Chord object, representing a Gdim chord

// Calculate pitch frequencies or find the pitch corresponding to a frequency
teoria.pitch.fromFrequency(467); // Returns: {'pitch':{...},'cents':3.102831} -> A4# a little out of tune.
a4.fq(); // Outputs 440
g5.fq(); // Outputs 783.9908719634985

// teoria allows for crazy chaining:
teoria.pitch('a')    // Create a pitch, A3
  .scale('lydian')  // Create a lydian scale with that pitch as root (A lydian)
  .interval('M2')   // Transpose the whole scale a major second up (B lydian)
  .get('third')     // Get the third pitch of the scale (D#4)
  .chord('maj9')    // Create a maj9 chord with that pitch as root (D#maj9)
  .toString();      // Make a string representation: 'D#maj9'

Documentation

teoria.pitch (name | coord)

name - The name argument is the pitch name as a string. The pitch can both be expressed in scientific and Helmholtz notation. Some examples of valid pitch names: Eb4, C#,,, C4, d#'', Ab2

coord - If the first argument isn't a string, but a coord array, it will instantiate a Pitch instance.

teoria.pitch.fromKey(key)

A static method that returns an instance of Pitch set to the pitch at the given piano key, where A0 is key number 1. See Wikipedia's piano key article for more information.

teoria.pitch.fromFrequency(fq)

A static method returns an object containing two elements:

pitch - A Pitch which corresponds to the closest pitch with the given frequency

cents - A number value of how many cents the pitch is out of tune

teoria.pitch.fromMIDI(pitch)

• Returns an instance of Pitch set to the corresponding MIDI pitch value.

pitch - A number ranging from 0-127 representing a MIDI pitch value

teoria.pitch.fromString(pitch)

• Returns an instance of Pitch representing the pitch name

pitch - The name argument is the pitch name as a string. The pitch can both be expressed in scientific and Helmholtz notation. Some examples of valid pitch names: Eb4, C#,,, C4, d#'', Ab2

Pitch.name()

• The name of the pitch, in lowercase letter (only the name, not the accidental signs)

Pitch.octave()

• The numeric value of the octave of the pitch

Pitch.accidental()

• Returns the string symbolic of the accidental sign (x, #, b or bb)

Pitch.accidentalValue()

• Returns the numeric value (mostly used internally) of the sign: x = 2, # = 1, b = -1, bb = -2

Pitch#key([whitekeys])

• Returns the piano key number. E.g. A4 would return 49

whitekeys - If this parameter is set to true only the white keys will be counted when finding the key number. This is mostly for internal use.

Pitch#midi()

• Returns a number ranging from 0-127 representing a MIDI pitch value

Pitch#fq([concertPitch])

• Calculates and returns the frequency of the pitch.

concertPitch - If supplied this number will be used instead of the normal concert pitch which is 440hz. This is useful for some classical music.

Pitch#chroma()

• Returns the pitch class (index) of the pitch.

This allows for easy enharmonic checking:

teoria.pitch('e').chroma() === teoria.pitch('fb').chroma();

The chroma number is ranging from pitch class C which is 0 to 11 which is B

Pitch#scale(scaleName)

• Returns an instance of Scale, with the tonic/root set to this pitch.

scaleName - The name of the scale to be returned. 'minor', 'chromatic', 'ionian' and others are valid scale names.

Pitch#interval(interval)

• A sugar function for calling teoria.interval(pitch, interval);

Look at the documentation for teoria.interval

Pitch#transpose(interval)

• Like the #interval method, but changes this pitch, instead of returning a new

Pitch#chord([name])

• Returns an instance of Chord, with root pitch set to this pitch

name - The name attribute is the last part of the chord symbol. Examples: 'm7', '#5b9', 'major'. If the name parameter isn't set, a standard major chord will be returned.

Pitch#helmholtz()

• Returns the pitch name formatted in Helmholtz notation.

Example: teoria.pitch('A5').helmholtz() -> "a''"

Pitch#scientific()

• Returns the pitch name formatted in scientific notation.

Example: teoria.pitch("ab'").scientific() -> "Ab4"

Pitch#enharmonics(oneAccidental)

• Returns all pitches that are enharmonic with the pitch

oneAccidental - Boolean, if set to true, only enharmonic pitches with one accidental is returned. E.g. results such as 'eb' and 'c#' but not 'ebb' and 'cx'

teoria.pitch('c').enharmonics().toString();
// -> 'dbb, b#'

teoria.pitch('c').enharmonics(true).toString();
// -> 'b#'

Pitch#solfege(scale, showOctaves)

• Returns the solfege step in the given scale context

scale - An instance of Scale, which is the context of the solfege step measuring

showOctaves - A boolean. If set to true, a "Helmholtz-like" notation will be used if there's bigger intervals than an octave

Pitch#scaleDegree(scale)

• Returns this pitch's degree in a given scale (Scale). For example a D in a C major scale will return 2 as it is the second degree of that scale. If however the pitch isn't a part of the scale, the degree returned will be 0, meaning that the degree doesn't exist. This allows this method to be both a scale degree index finder and an "isPitchInScale" method.

scale - An instance of Scale which is the context of the degree measuring

Pitch#toString([dontShow])

• Usability function for returning the pitch as a string

dontShow - If set to true the octave will not be included in the returned string.

Chord(root, chord)

• A chord class with a lot of functionality to alter and analyze the chord.

root - A Pitch instance which is to be the root of the chord

chord - A string containing the chord symbol. This can be anything from simple chords, to super-advanced jazz chords thanks to the detailed and robust chord parser engine. Example values: 'm', 'm7', '#5b9', '9sus4 and '#11b5#9'

teoria.chord(name || pitch[, octave || symbol])

• A simple function for getting the pitches, no matter the octave, in a chord

name - A string containing the full chord symbol, with pitch name. Examples: 'Ab7', 'F#(#11b5)'

pitch - Instead of supplying a string containing the full chord symbol, one can pass a Pitch object instead. The pitch will be considered root in the new chord object

octave - If the first argument of the function is a chord name (typeof "string"), then the second argument is an optional octave number (typeof "number") of the root.

symbol - A string containing the chord symbol (excluding the pitch name)

Chord.name

• Holds the full chord symbol, inclusive the root name.

Chord.root

• Holds the Pitch that is the root of the chord.

Chord#pitches()

• Returns an array of Pitchs that the chord consists of.

Chord#simple()

• Returns an Array of only the pitches' names, not the full Pitch objects.

Chord#bass()

• Returns the bass pitch of the chord (The pitch voiced the lowest)

Chord#voicing([voicing])

• Works both as a setter and getter. If no parameter is supplied the current voicing is returned as an array of Intervals

voicing - An optional array of intervals in simple-format that represents the current voicing of the chord.

Here's an example:

var bbmaj = teoria.chord('Bbmaj7');
// Default voicing:
bbmaj.voicing();  // #-> ['P1', 'M3', 'P5', 'M7'];
bbmaj.pitches();    // #-> ['bb', 'd', 'f', 'a'];

// New voicing
bbmaj.voicing(['P1', 'P5', 'M7', 'M10']);
bbmaj.pitches();    // #-> ['bb', 'f', 'a', 'd'];

NB: Note that above returned results are pseudo-results, as they will be returned wrapped in Interval and Pitch objects.

Chord#quality()

• Returns a string which holds the quality of the chord, 'major', 'minor', 'augmented', 'diminished', 'half-diminished', 'dominant' or undefined

Chord#get(interval)

• Returns the pitch at a given interval in the chord, if it exists.

interval - A string name of an interval, for example 'third', 'fifth', 'ninth'.

Chord#dominant([additional])

• Returns the naïvely chosen dominant which is a perfect fifth away.

additional - Additional chord extension, for example: 'b9' or '#5'

Chord#subdominant([additional])

• Returns the naïvely chosen subdominant which is a perfect fourth away.

additional - Like the dominant's.

Chord#parallel([additional])

• Returns the parallel chord for major and minor triads

additional - Like the dominant's

Chord#chordType()

• Returns the type of the chord: 'dyad', 'triad', 'trichord', 'tetrad' or 'unknown'.

Chord#interval(interval)

• Returns the same chord, a interval away

Chord#transpose(interval)

• Like the #interval method, except it's this chord that gets changed instead of returning a new chord.

Chord#toString()

• Simple usability function which is an alias for Chord.name

Scale(tonic, scale)

• The teoria representation of a scale, with a given tonic.

tonic - A Pitch which is to be the tonic of the scale

scale - Can either be a name of a scale (string), or an array of absolute intervals that defines the scale. The scales supported by default are:

• major
• minor
• ionian (Alias for major)
• dorian
• phrygian
• lydian
• mixolydian
• aeolian (Alias for minor)
• locrian
• majorpentatonic
• minorpentatonic
• chromatic
• harmonicchromatic (Alias for chromatic)
• blues
• doubleharmonic
• flamenco
• harmonicminor
• melodicminor

teoria.scale(tonic, scale)

• Sugar function for constructing a new Scale object

Scale.pitches()

• Returns an array of Pitchs which is the scale's pitches

Scale.name

• The name of the scale (if available). Type string or undefined

Scale.tonic

• The Pitch which is the scale's tonic

Scale#simple()

• Returns an Array of only the pitches' names, not the full Pitch objects.

Scale#type()

• Returns the type of the scale, depending on the number of pitches. A scale of length x gives y:
• 2 gives 'ditonic'
• 3 gives 'tritonic'
• 4 gives 'tetratonic'
• 5 gives 'pentatonic'
• 6 gives 'hexatonic',
• 7 gives 'heptatonic',
• 8 gives 'octatonic'

Scale#get(index)

• Returns the pitch at the given scale index

index - Can be a number referring to the scale step, or the name (string) of the scale step. E.g. 'first', 'second', 'fourth', 'seventh'.

Scale#solfege(index, showOctaves)

• Returns the solfege name of the given scale step

index Same as Scale#get

showOctaves - A boolean meaning the same as showOctaves in Pitch#solfege

teoria.interval(from, to)

• A sugar function for the #from and #between methods of the same namespace and for creating Interval objects.

teoria.interval(string: from)

• A sugar method for the Interval.fromString function

teoria.interval(Pitch: from, string: to)

• A sugar method for the Interval.from function

teoria.interval(Pitch: from, Interval: to)

• Like above, but with a Interval instead of a string representation of the interval

teoria.interval(Pitch: from, Pitch: to)

• A sugar method for the Interval.between function

teoria.interval.from -> Interval.from

teoria.interval.between -> Interval.between

teoria.interval.invert -> Interval.invert

teoria.Interval.fromString -> Interval.fromString

Interval(coord)

• A representation of a music interval

Interval.fromString(simpleInterval)

• Returns a Interval representing the interval expressed in string form.

Interval.from(from, to)

• Returns a pitch which is a given interval away from a root pitch.

from - The Pitch which is the root of the measuring

to - A Interval

Interval.between(from, to)

• Returns an interval object which represents the interval between two pitches.

from and to are two Pitchs which are the pitches that the interval is measured from. For example if 'a' and 'c' are given, the resulting interval object would represent a minor third.

Interval.between(teoria.pitch("a"), teoria.pitch("c'")) -> teoria.interval('m3')

Interval.invert(simpleInterval)

• Returns the inversion of the interval provided

simpleInterval - An interval represented in simple string form. Examples:

• 'm3' = minor third
• 'P4' = perfect fourth
• 'A4' = augmented fifth
• 'd7' = diminished seventh
• 'M6' = major sixth.

'm' = minor, 'M' = major, 'A' = augmented and 'd' = diminished

The number may be prefixed with a - to signify that its direction is down. E.g.:

m-3 means a descending minor third, and P-5 means a descending perfect fifth.

Interval.coord

• The interval representation of the interval

Interval.number()

• The interval number (A ninth = 9, A seventh = 7, fifteenth = 15)

Interval.value()

• The value of the interval - That is a ninth = 9, but a downwards ninth is = -9

Interval.toString()

• Returns the simpleInterval representation of the interval. E.g. 'P5', 'M3', 'A9', etc.

Interval.base()

• Returns the name of the simple interval (not compound)

Interval.type()

• Returns the type of array, either 'perfect' (1, 4, 5, 8) or 'minor' (2, 3, 6, 7)

Interval.quality([verbose])

• The quality of the interval ('dd', 'd' 'm', 'P', 'M', 'A' or 'AA')

verbose is set to a truish value, then long quality names are returned: 'doubly diminished', 'diminished', 'minor', etc.

Interval.direction([dir])

• The direction of the interval

dir - If supplied, then the interval's direction is to the newDirection which is either 'up' or 'down'

Interval#semitones()

• Returns the number of semitones the interval span.

Interval#simple([ignoreDirection])

• Returns the simple part of the interval as a Interval. Example:

ignoreDirection - An optional boolean that, if set to true, returns the "direction-agnostic" interval. That is the interval with a positive number.

teoria.interval('M17').simple();    // #-> 'M3'
teoria.interval('m23').simple();    // #-> 'm2'
teoria.interval('P5').simple();     // #-> 'P5'
teoria.interval('P-4').simple();    // #-> 'P-4'

// With ignoreDirection = true
teoria.interval('M3').simple(true);     // #->'M3'
teoria.interval('m-10').simple(true);   // #-> 'm3'

NB: Note that above returned results are pseudo-results, as they will be returned wrapped in Interval objects.

Interval#octaves()

• Returns the number of compound intervals

Interval#isCompound()

• Returns a boolean value, showing if the interval is a compound interval

Interval#add(interval)

• Adds the interval to this interval, and returns a Interval representing the result of the addition

Interval#equal(interval)

• Returns true if the supplied interval is equal to this interval

Interval#greater(interval)

• Returns true if the supplied interval is greater than this interval

Interval#smaller(interval)

• Returns true if the supplied interval is smaller than this interval

Interval#invert()

• Returns the inverted interval as a Interval

Interval#qualityValue() - internal

• Returns the relative to default, value of the quality. E.g. a teoria.interval('M6'), will have a relative quality value of 1, as all the intervals defaults to minor and perfect respectively.