Class Tuning

An immutable equal temperament: a reference pitch and a number of equal divisions of the octave, with the conversions of the tuning module bound to it. A thin convenience wrapper over a plain TuningTable.

Every conversion still takes a temperament of its own, defaulting to this one, so nothing the tuning functions offer is out of reach from the class — two temperaments can be read from a single object.

Example

import { Tuning } from '@libraz/libcantus';
Tuning.edo(19).divisions; // 19
Tuning.twelveTet().frequencyOf('A4'); // 440

Accessors

refStep

get refStep(): number
Step index whose frequency is Tuning.refFreq.

Returns number
- Defined in src/model/tuning.ts:210

refFreq

get refFreq(): number
Frequency in Hz of Tuning.refStep.

Returns number
- Defined in src/model/tuning.ts:215

divisions

get divisions(): number
Equal divisions of the octave; 12 is the standard temperament.

Returns number
- Defined in src/model/tuning.ts:220

data

get data(): TuningTable
A copy of the underlying plain tuning table.

Returns TuningTable
- Defined in src/model/tuning.ts:225

Methods

`Static`of

of(table: TuningTable): Tuning
Wrap a plain tuning table.

Every field is read off the table, so a deserialized or hand-written one cannot enter carrying a division count or a reference frequency no frequency follows from. None of the three has a default here, unlike Tuning.edo: a table that lost its reference frequency on the way through storage is refused rather than quietly retuned to A=440.
Parameters
- table: TuningTable
  The plain tuning table.
Returns Tuning
The wrapped tuning.
Throws
If a field is missing, the divisions are not a positive integer, the reference frequency is not a finite positive number, or the reference step is not finite.
Example
```
import { TWELVE_TET, Tuning } from '@libraz/libcantus';
Tuning.of(TWELVE_TET).divisions; // 12
```
- Defined in src/model/tuning.ts:65

`Static`edo

edo(divisions: number, refFreq?: number, refStep?: number): Tuning
Build an equal temperament with divisions divisions of the octave.
Parameters
- divisions: number
  Divisions of the octave (e.g. 19, 24, 31).
- OptionalrefFreq: number
  Reference frequency in Hz; 440 by default.
- OptionalrefStep: number
  Step index of the reference; 69 by default, the MIDI number of A4.
Returns Tuning
The tuning.
Throws
If the divisions are not a positive integer, the reference frequency is not a finite positive number, or the reference step is not finite. A negative or fractional reference step is accepted: it is what a tuner reading or a pitch-bend calibration lands on.
Example
```
import { Tuning } from '@libraz/libcantus';
Math.round(Tuning.edo(19).centsOfSteps(1)); // 63
```
- Defined in src/model/tuning.ts:96

`Static`twelveTet

twelveTet(): Tuning
Standard twelve-tone equal temperament, A4 (MIDI 69) = 440 Hz.

Returns Tuning
The tuning in which a step index is an ordinary MIDI number.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.twelveTet().stepOf(440); // 69
```
- Defined in src/model/tuning.ts:110

`Static`fromData

fromData(data: TuningTable): Tuning
Rebuild a tuning from the plain table Tuning.data hands out.
Parameters
- data: TuningTable
  The plain tuning table.
Returns Tuning
The wrapped tuning.

Throws
If the table describes no temperament; see Tuning.of.
- Defined in src/model/tuning.ts:121

`Static`fromJSON

fromJSON(data: TuningTable): Tuning
Rebuild a tuning from its Tuning.toJSON output.
Parameters
- data: TuningTable
  The serialized tuning table.
Returns Tuning
The wrapped tuning.

Throws
If the table describes no temperament; see Tuning.of.
- Defined in src/model/tuning.ts:132

`Static`ratioToCents

ratioToCents(numerator: number, denominator: number): number
Cents of a frequency ratio, e.g. 3:2 for the just perfect fifth.

A ratio is a relation between two frequencies rather than a place in a temperament, so this is the same figure under every tuning.
Parameters
- numerator: number
  Ratio numerator.
- denominator: number
  Ratio denominator.
Returns number
The interval in cents.
Throws
If either side is not a finite positive number.
Example
```
import { Tuning } from '@libraz/libcantus';
Math.round(Tuning.ratioToCents(3, 2)); // 702
```
- Defined in src/model/tuning.ts:152

`Static`centsToRatio

centsToRatio(cents: number): number
The frequency ratio an interval in cents spans, the inverse of Tuning.ratioToCents. Multiply a frequency by it to move the pitch by that many cents.
Parameters
- cents: number
  The interval in cents.
Returns number
The frequency ratio.
Throws
If cents is not finite, or the ratio it spans falls outside the range a number holds.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.centsToRatio(0); // 1
```
- Defined in src/model/tuning.ts:171

`Static`centsBetweenFreq

centsBetweenFreq(a: number, b: number): number
Interval in cents between two frequencies.
Parameters
- a: number
  Lower/first frequency in Hz.
- b: number
  Upper/second frequency in Hz.
Returns number
Cents from a to b, negative when b is lower.
Throws
If either frequency is not a finite positive number.
Example
```
import { Tuning } from '@libraz/libcantus';
Math.round(Tuning.centsBetweenFreq(440, 880)); // 1200
```
- Defined in src/model/tuning.ts:188

`Static`justDeviationCents

justDeviationCents(semitoneClass: number): number
Cents by which a five-limit just interval departs from its 12-TET tempering; positive means the just interval is the wider one.
Parameters
- semitoneClass: number
  Semitone class in [0, 12].
Returns number
The deviation in cents.
Throws
If semitoneClass is not an integer in [0, 12].
Example
```
import { Tuning } from '@libraz/libcantus';
Math.round(Tuning.justDeviationCents(7)); // 2
```
- Defined in src/model/tuning.ts:205

frequencyOf

frequencyOf(note: NoteLike, tuning?: TuningTable): number
Frequency in Hz of a note.

The note's MIDI number is read as a step index, which is how the tuning module numbers steps: under twelve divisions the two coincide, and under any other the step index keeps counting from the same reference.
Parameters
- note: NoteLike
  A note name, a MIDI number, plain note data, or a Note; it must carry an octave, since a bare pitch class has no frequency.
- tuning: TuningTable = ...
  A temperament to read the note under instead of this one.
Returns number
The frequency in Hz.
Throws
If the value is not a note, has no octave, or the frequency falls outside the range a number holds.
Example
```
import { Note } from '@libraz/libcantus';
import { Tuning } from '@libraz/libcantus';
const tuning = Tuning.twelveTet();
tuning.frequencyOf('A4'); // 440
tuning.frequencyOf(69); // 440
tuning.frequencyOf(Note.parse('A4')); // 440
```
- Defined in src/model/tuning.ts:252

frequencyOfStep

frequencyOfStep(step: number, tuning?: TuningTable): number
Frequency in Hz of a step index.

The step-numbered form of Tuning.frequencyOf, for the steps of a temperament that no twelve-tone note names.
Parameters
- step: number
  Step index; a MIDI number under twelve divisions.
- tuning: TuningTable = ...
  A temperament to read the step under instead of this one.
Returns number
The frequency in Hz.
Throws
If the step is not finite, or the frequency falls outside the range a number holds.
Example
```
import { Tuning } from '@libraz/libcantus';
const et19 = Tuning.edo(19);
et19.frequencyOfStep(69); // 440
et19.frequencyOfStep(70) > 440; // true
```
- Defined in src/model/tuning.ts:275

nearestStep

nearestStep(freq: number, tuning?: TuningTable): number
Nearest step index to a frequency, the rounded inverse of Tuning.frequencyOfStep.
Parameters
- freq: number
  Frequency in Hz.
- tuning: TuningTable = ...
  A temperament to read the frequency under instead of this one.
Returns number
The nearest step index.
Throws
If the frequency is not a finite positive number.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.twelveTet().nearestStep(442); // 69
```
- Defined in src/model/tuning.ts:293

stepOf

stepOf(freq: number, tuning?: TuningTable): number
Step index of a frequency, unrounded.

The exact inverse of Tuning.frequencyOfStep, keeping how far off the pitch sits — the figure a tuner display or a pitch-bend amount is built on, which Tuning.nearestStep rounds away.
Parameters
- freq: number
  Frequency in Hz.
- tuning: TuningTable = ...
  A temperament to read the frequency under instead of this one.
Returns number
The fractional step index.
Throws
If the frequency is not a finite positive number.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.twelveTet().stepOf(442) > 69; // true
```
- Defined in src/model/tuning.ts:314

centsFromNearestStep

centsFromNearestStep(freq: number, tuning?: TuningTable): number
How far a frequency sits from its nearest step, in cents; positive means sharp of the step, negative flat.
Parameters
- freq: number
  Frequency in Hz.
- tuning: TuningTable = ...
  A temperament to read the frequency under instead of this one.
Returns number
The signed deviation in cents.
Throws
If the frequency is not a finite positive number.
Example
```
import { Tuning } from '@libraz/libcantus';
Math.round(Tuning.twelveTet().centsFromNearestStep(442)); // 8
```
- Defined in src/model/tuning.ts:332

centsOfSteps

centsOfSteps(steps: number, tuning?: TuningTable): number
Cents spanned by a number of steps.
Parameters
- steps: number
  Number of steps.
- tuning: TuningTable = ...
  A temperament to measure the steps in instead of this one.
Returns number
The cents.
Throws
If the step count is not finite.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.twelveTet().centsOfSteps(1); // 100
```
- Defined in src/model/tuning.ts:349

stepsOfCents

stepsOfCents(cents: number, tuning?: TuningTable): number
Steps spanned by an interval in cents, unrounded — the inverse of Tuning.centsOfSteps.
Parameters
- cents: number
  The interval in cents.
- tuning: TuningTable = ...
  A temperament to measure the interval in instead of this one.
Returns number
The fractional step count.
Throws
If the cents are not finite.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.twelveTet().stepsOfCents(700); // 7
```
- Defined in src/model/tuning.ts:367

equals

equals(other: Tuning): boolean
Whether another tuning divides the octave the same way from the same reference pitch.
Parameters
- other: Tuning
  The tuning to compare with.
Returns boolean
True when reference step, reference frequency, and divisions all match.
- Defined in src/model/tuning.ts:379

toJSON

toJSON(): TuningTable
The plain tuning table, for JSON serialization.

Private class fields do not serialize, so an explicit toJSON keeps JSON.stringify(tuning) from collapsing to {}.

Returns TuningTable
A copy of the reference step, reference frequency, and divisions.
- Defined in src/model/tuning.ts:399

toString

toString(): string
The temperament as a readable label, so a template literal or a log line reads as the tuning.

Returns string
The divisions and the reference pitch, e.g. '12-EDO (step 69 = 440 Hz)'.
Example
```
import { Tuning } from '@libraz/libcantus';
Tuning.twelveTet().toString(); // '12-EDO (step 69 = 440 Hz)'
```
- Defined in src/model/tuning.ts:419

Class Tuning

Example

Index

Accessors

Methods

Accessors

refStep

Returns number

refFreq

Returns number

divisions

Returns number

data

Returns TuningTable

Methods

Staticof

Parameters

Returns Tuning

Throws

Example

Staticedo

Parameters

Returns Tuning

Throws

Example

StatictwelveTet

Returns Tuning

Example

StaticfromData

Parameters

Returns Tuning

Throws

StaticfromJSON

Parameters

Returns Tuning

Throws

StaticratioToCents

Parameters

Returns number

Throws

Example

StaticcentsToRatio

Parameters

Returns number

Throws

Example

StaticcentsBetweenFreq

Parameters

Returns number

Throws

Example

StaticjustDeviationCents

Parameters

Returns number

Throws

Example

frequencyOf

Parameters

Returns number

Throws

Example

frequencyOfStep

Parameters

Returns number

Throws

Example

nearestStep

Parameters

Returns number

Throws

Example

stepOf

Parameters

Returns number

Throws

Example

centsFromNearestStep

Parameters

Returns number

Throws

`Static`of

`Static`edo

`Static`twelveTet

`Static`fromData

`Static`fromJSON

`Static`ratioToCents

`Static`centsToRatio

`Static`centsBetweenFreq

`Static`justDeviationCents