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Fraction API ​

RMT Compose uses Fraction.js for arbitrary-precision rational arithmetic. This ensures exact calculations without floating-point rounding errors.

Creating Fractions ​

Integer ​

javascript
new Fraction(440)    // 440/1
new Fraction(0)      // 0/1
new Fraction(-5)     // -5/1

Rational ​

javascript
new Fraction(3, 2)   // 3/2 (perfect fifth)
new Fraction(5, 4)   // 5/4 (major third)
new Fraction(-1, 4)  // -1/4

Large Numbers ​

Arbitrary precision is supported:

javascript
new Fraction(123456789, 987654321)
new Fraction("355", "113")  // Approximation of pi

Arithmetic Methods ​

add(other) ​

Adds two fractions:

javascript
new Fraction(1, 2).add(new Fraction(1, 3))  // 5/6
new Fraction(440).add(new Fraction(20))      // 460

sub(other) ​

Subtracts fractions:

javascript
new Fraction(3, 4).sub(new Fraction(1, 4))  // 2/4 = 1/2
new Fraction(5).sub(new Fraction(2))         // 3

mul(other) ​

Multiplies fractions:

javascript
new Fraction(3, 2).mul(new Fraction(5, 4))  // 15/8
new Fraction(440).mul(new Fraction(2))       // 880 (octave)

div(other) ​

Divides fractions:

javascript
new Fraction(3, 2).div(new Fraction(2))     // 3/4
new Fraction(60).div(new Fraction(120))     // 1/2 (beat duration)

neg() ​

Returns the negation:

javascript
new Fraction(5).neg()      // -5
new Fraction(-3, 2).neg()  // 3/2

pow(exponent) ​

Raises to a power:

javascript
new Fraction(2).pow(new Fraction(3))      // 8 (2^3)
new Fraction(2).pow(new Fraction(-1))     // 1/2 (2^-1)
new Fraction(2).pow(new Fraction(1, 12))  // 12-TET semitone (irrational)

Irrational Results

Non-integer exponents produce irrational numbers that cannot be represented as exact fractions. RMT Compose uses SymbolicPower to preserve these algebraically where possible.

abs() ​

Returns absolute value:

javascript
new Fraction(-5, 3).abs()  // 5/3

inverse() ​

Returns the reciprocal:

javascript
new Fraction(3, 2).inverse()  // 2/3
new Fraction(4).inverse()     // 1/4

mod(other) ​

Modulo operation:

javascript
new Fraction(7).mod(new Fraction(3))  // 1

Comparison Methods ​

equals(other) ​

javascript
new Fraction(1, 2).equals(new Fraction(2, 4))  // true
new Fraction(3, 2).equals(new Fraction(3, 2))  // true

compare(other) ​

Returns -1, 0, or 1:

javascript
new Fraction(1, 2).compare(new Fraction(2, 3))  // -1 (less than)
new Fraction(3, 2).compare(new Fraction(3, 2))  // 0 (equal)
new Fraction(5, 4).compare(new Fraction(1))     // 1 (greater than)

Conversion Methods ​

valueOf() ​

Returns JavaScript number (may lose precision):

javascript
new Fraction(3, 2).valueOf()  // 1.5
new Fraction(1, 3).valueOf()  // 0.3333333333333333

toString() ​

Returns string representation:

javascript
new Fraction(3, 2).toString()  // "3/2"
new Fraction(4).toString()     // "4"

toFraction() ​

Returns simplified string:

javascript
new Fraction(6, 4).toFraction()  // "3/2"

Properties ​

n (numerator) ​

javascript
new Fraction(3, 2).n  // 3

d (denominator) ​

javascript
new Fraction(3, 2).d  // 2

s (sign) ​

javascript
new Fraction(3, 2).s   // 1
new Fraction(-3, 2).s  // -1

Common Patterns in RMT Compose ​

Frequency Ratios ​

javascript
// Perfect fifth above base
module.baseNote.getVariable('frequency').mul(new Fraction(3, 2))

// Octave above
module.baseNote.getVariable('frequency').mul(new Fraction(2))

// Perfect fourth below
module.baseNote.getVariable('frequency').div(new Fraction(4, 3))

Beat Calculations ​

javascript
// Duration of one beat at current tempo
new Fraction(60).div(module.findTempo(module.baseNote))

// Two beats
new Fraction(60).div(module.findTempo(module.baseNote)).mul(new Fraction(2))

// Half beat (eighth note)
new Fraction(60).div(module.findTempo(module.baseNote)).mul(new Fraction(1, 2))

Sequential Timing ​

javascript
// Start after previous note ends
module.getNoteById(prev).getVariable('startTime')
  .add(module.getNoteById(prev).getVariable('duration'))

See Also ​

Released under the RMT Personal Non-Commercial License

Copyright 2026-present Cyril Monkewitz