Class ExtendedMonzo

constructor

• new ExtendedMonzo(vector, residual?, cents?): ExtendedMonzo

• Construct a fractional monzo with multiplicative residue and arbitrary cents offset.

  Parameters

  • vector: FractionalMonzo

    Fractional monzo part.
  • Optional residual: Fraction

    Multiplicative residue that is too complex to fit in the vector part.
  • cents: number = 0

    Cents offset.

  Returns ExtendedMonzo

cents

residual

vector

numberOfComponents

• get numberOfComponents(): number

• Number of components in the monzo vector part.

  Returns number

abs

• abs(): ExtendedMonzo

• Pitch-space absolute value of the extended monzo.

  Returns ExtendedMonzo

  The extended monzo unchanged or negated if negative originally.

add

• add(other): ExtendedMonzo

• Combine the extended monzo with another in pitch-space.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns ExtendedMonzo

  The product of the extended monzos in frequency-space.

approximateHarmonic

• approximateHarmonic(denominator): ExtendedMonzo

• Find the closest approximation of the extended monzo in a harmonic series.

  Parameters

  • denominator: number

    Denominator of the harmonic series.

  Returns ExtendedMonzo

  The closest approximant in the series.

approximateSimple

• approximateSimple(eps?): ExtendedMonzo

• Simplify the extended monzo under the given threshold

  Parameters

  • Optional eps: number

    Error threshold, default = 0.001

  Returns ExtendedMonzo

  Simple approximant of the extended monzo.

approximateSubharmonic

• approximateSubharmonic(numerator): ExtendedMonzo

• Find the closest approximation of the extended monzo in a subharmonic series.

  Parameters

  • numerator: number

    Numerator of the subharmonic series.

  Returns ExtendedMonzo

  The closest approximant in the series.

clone

• clone(): ExtendedMonzo

• Create a deep copy of this extended monzo.

  Returns ExtendedMonzo

  A clone with independent vector part.

compare

• compare(other): number

• Compare this extended monzo with another.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns number

  Result < 0 if other is larger than this. Result > 0 if other is smaller than this. Result == 0 if other is equal to this in size.

div

• div(scalar): ExtendedMonzo

• Inverse rescale the extended monzo in pitch-space.

  Parameters

  • scalar: number | Fraction

    Inverse scaling factor.

  Returns ExtendedMonzo

  The rescaled extended monzo.

equals

• equals(other): boolean

• Check if this extended monzo has the same size as another.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns boolean

  true if the extended monzos are of equal size.

getConvergent

• getConvergent(depth): ExtendedMonzo

• Obtain a convergent of this extended monzo.

  Parameters

  • depth: number

    How many continued fraction coefficients to use after the whole part.

  Returns ExtendedMonzo

  Approximant of the extended monzo.

isCents

• isCents(): boolean

• Check if the extended monzo is pure cents.

  Returns boolean

  true if the extended monzo has no vector or residual.

isComposite

• isComposite(): boolean

• Check if the extended monzo is combination of fractional, equal temperament or cents parts.

  Returns boolean

  true if the extended monzo is not simply fractional, equal temperament or pure cents.

isEqualTemperament

• isEqualTemperament(): boolean

• Check if the extended monzo represents a generic EDJI interval.

  Returns boolean

  true if the extended monzo can be interpreted as pitch-space fraction of a frequency-space fraction.

isFractional

• isFractional(): boolean

• Check if the extended monzo represents a musical fraction.

  Returns boolean

  true if the extended monzo can be interpreted as a ratio in frequency-space.

isPowerOfTwo

• isPowerOfTwo(): boolean | 0

• Check if the extended monzo is a power of two in frequency space.

  Returns boolean | 0

  true if the extended monzo is a power of two.

mmod

• mmod(other): ExtendedMonzo

• Calculate modulus with respect to another extended monzo.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns ExtendedMonzo

  This modulo the other.

mod

• mod(other): ExtendedMonzo

• Calculate truncated modulus with respect to another extended monzo.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns ExtendedMonzo

  This modulo the other truncated towards zero cents.

mul

• mul(scalar): ExtendedMonzo

• Rescale the extended monzo in pitch-space.

  Parameters

  • scalar: number | Fraction

    Scaling factor.

  Returns ExtendedMonzo

  The rescaled extended monzo.

neg

• neg(): ExtendedMonzo

• Return a pitch-space negative of the extended monzo.

  Returns ExtendedMonzo

  The frequency-space inverse of the extended monzo.

stretch

• stretch(scalar): ExtendedMonzo

• Rescale the extended monzo in pitch-space and store the offset as cents.

  Parameters

  • scalar: number

    Scaling factor.

  Returns ExtendedMonzo

  The rescaled extended monzo where only the cents offset differs from the original.

strictEquals

• strictEquals(other): boolean

• Check for strict equality between this and another extended monzo.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns boolean

  true if the extended monzos share the same vector, residual and cents offset.

sub

• sub(other): ExtendedMonzo

• Subtract another extended monzo from this one in pitch-space.

  Parameters

  • other: ExtendedMonzo

    Another extended monzo.

  Returns ExtendedMonzo

  This monzo divided by the other monzo in frequency-space.

toCents

• toCents(): number

• Convert the extended monzo to cents.

  Returns number

  Size of the extended monzo in cents.

toContinued

• toContinued(): number[]

• Gets an array of the extended monzo representing a continued fraction. The first element always contains the whole part.

  Returns number[]

  Array of continued fraction coefficients.

toEqualTemperament

• toEqualTemperament(): [Fraction, Fraction]

• Convert the extended monzo to pitch-space fraction of a frequency-space fraction.

  Returns [Fraction, Fraction]

  Pair of the pitch-space fraction and the equave as a frequency-space fraction.

  Throws

  An error if the extended monzo cannot be represented as an EDJI interval.

toFraction

• toFraction(): Fraction

• Convert the extended monzo to a fraction in frequency-space.

  Returns Fraction

  Musical ratio as a fraction in frequency-space.

  Throws

  An error if the extended monzo cannot be represented as a ratio.

toIntegerMonzo

• toIntegerMonzo(): number[]

• Convert the extended monzo to a simple monzo with integer coefficients.

  Returns number[]

  Array of prime exponents.

  Throws

  An error if the extended monzo cannot be represented as sufficiently simple ratio in frequency-space.

totalCents

• totalCents(): number

• Convert the extended monzo to cents.

  Returns number

  Size of the extended monzo in cents.

valueOf

• valueOf(): number

• Convert the extended monzo to frequency-space ratio.

  Returns number

  The frequency-space multiplier corresponding to this extended monzo.

Static fromCents

• fromCents(cents, numberOfComponents): ExtendedMonzo

• Construct an extended monzo from an interval measured in cents.

  Parameters

  • cents: number

    The amount of cents to convert. An octave (2/1) divided into 12 semitones 100 cents each.
  • numberOfComponents: number

    Number of components in the monzo vector part.

  Returns ExtendedMonzo

  Extended monzo with a zero vector part and the specified cents offset.

Static fromEqualTemperament

• fromEqualTemperament(fractionOfEquave, equave?, numberOfComponents?): ExtendedMonzo

• Construct an extended monzo from a pitch-space fraction of a frequency-space fraction.

  Parameters

  • fractionOfEquave: FractionValue

    Fraction of the equave measured in pitch-space.
  • Optional equave: FractionValue

    Equave measured in frequency-space. Defaults to the octave (2/1).
  • Optional numberOfComponents: number

    Number of components in the monzo vector part.

  Returns ExtendedMonzo

  Extended monzo representing N-of-EDO (default) or a generic EDJI interval.

Static fromFraction

• fromFraction(fraction, numberOfComponents): ExtendedMonzo

• Construct an extended monzo from a rational number.

  Parameters

  • fraction: FractionValue

    Rational number to convert.
  • numberOfComponents: number

    Number of components in the monzo vector part.

  Returns ExtendedMonzo

  Extended monzo representing the just intonation interval.

Static fromValue

• fromValue(value, numberOfComponents): ExtendedMonzo

• Constuct an extended monzo from a value measured in frequency-space.

  Parameters

  • value: number

    Musical ratio in frequency-space.
  • numberOfComponents: number

    Number of components in the monzo vector part.

  Returns ExtendedMonzo

  Extended monzo with a zero vector part and the specified value converted to a cents offset.