Enum TuningSystem 

pub enum TuningSystem {
    Equal(EqualDivision),
    CarlosHarmonic,
    CarlosHarmonic24,
    PythagoreanTuning,
    FiveLimit,
    ElevenLimit,
    FortyThreeTone,
    Javanese,
    Thai,
    PtolemyIntenseDiatonic,
    IndianAlt,
    Indian22,
    QuarterCommaMeantone,
    WerckmeisterIII,
    Rameau,
    KirnbergerIII,
    Vallotti,
    YoungII,
    ThirdCommaMeantone,
    SixthCommaMeantone,
    WerckmeisterIV,
    WerckmeisterV,
    KirnbergerI,
    NeidhardtI,
    Silbermann,
    LehmanBach,
}

Supported tuning systems and ratio tables.

Every system repeats at a period, and a degree past the end of one is the same degree a period up. The ratio tables repeat at the octave; an equal division repeats wherever its period is, so Bohlen-Pierce climbs by tritaves.

Variants

Equal(EqualDivision)

Equal steps of one period. 12edo is ordinary equal temperament, 6edo the whole-tone scale and 24edo quarter tones, and the period need not be an octave: 13edt is Bohlen-Pierce.

CarlosHarmonic

Twelve-tone harmonic-series scale (Wendy Carlos’s Harmonic).

Not just intonation, despite its former name: the degrees are the harmonic series 16:17:18:19:20:21:22:24:26:27:28:30, which reaches the 19-limit. TuningSystem::FiveLimit is the classical 12-tone JI scale.

CarlosHarmonic24

Twenty-four-tone harmonic-series scale.

PythagoreanTuning

Twelve-tone Pythagorean tuning table.

FiveLimit

Twelve-tone five-limit table.

ElevenLimit

Twenty-nine-tone eleven-limit table.

FortyThreeTone

Forty-three-tone ratio table.

Javanese

Five-tone Javanese equal-temperament approximation.

Thai

Seven-tone Thai equal-temperament approximation.

PtolemyIntenseDiatonic

Ptolemy’s intense diatonic, also Zarlino’s just major scale.

Greek and Renaissance European, despite once being filed here as an Indian scale — the archive names it ptolemy.scl.

IndianAlt

Alternate seven-tone PtolemyIntenseDiatonic scale table.

Indian22

Twenty-two-tone PtolemyIntenseDiatonic scale table.

QuarterCommaMeantone

Twelve-tone quarter-comma meantone temperament (Aaron, 1523).

WerckmeisterIII

Twelve-tone Werckmeister III well temperament (1681).

Rameau

Twelve-tone Rameau modified meantone temperament (1725).

KirnbergerIII

Twelve-tone Kirnberger III well temperament (1744).

Vallotti

Twelve-tone Vallotti well temperament (c. 1754).

YoungII

Twelve-tone Thomas Young well temperament no. 2 (1799).

ThirdCommaMeantone

A twelve-tone third-comma meantone temperament (Salinas, 1577).

SixthCommaMeantone

A twelve-tone sixth-comma meantone temperament (Salinas, 1577).

WerckmeisterIV

A twelve-tone Werckmeister IV well temperament (1681).

WerckmeisterV

A twelve-tone Werckmeister V well temperament (1681).

KirnbergerI

A twelve-tone Kirnberger I well temperament (1766).

NeidhardtI

A twelve-tone Neidhardt I well temperament (1724).

Silbermann

A twelve-tone Gottfried Silbermann temperament no. 1 (c. 1730).

LehmanBach

A twelve-tone Lehman-Bach temperament (2005).

Implementations

impl TuningSystem

pub const EQUAL_TEMPERAMENT: Self

Twelve-tone equal temperament, 12edo.

pub const WHOLE_TONE: Self

The whole-tone scale, six equal steps to the octave.

pub const QUARTER_TONE: Self

Quarter tones, twenty-four equal steps to the octave.

pub fn id(self) -> String

Returns the canonical identifier used by FromStr.

pub fn display_name(self) -> String

Returns a compact display name for this tuning system.

pub fn description(self) -> String

Returns a short description of this tuning system.

pub fn ratio(self, index: usize) -> FloatType

The frequency ratio of a degree above the system’s starting pitch.

pub fn ratio_at(self, index: FloatType) -> FloatType

The same for a fractional degree. A whole degree is the system’s own step exactly; between two, the pitch is interpolated as the equal division of the period with as many steps would place it.

pub fn exact_ratio(self, index: usize) -> Option<Ratio>

The degree as an exact ratio, where it is one.

Every ratio table has one for each degree, and so does an equal division of a whole-number period, as a root of it: a step of 13edt is the thirteenth root of three. A division of an irrational period, Carlos Alpha’s 78 cents, has none.

pub fn label(self, index: UnsignedIntegerType) -> String

A name for a degree, counted from C-1.

A system of twelve degrees to the octave names each degree for its key, C♯/D♭4, however it is tuned, and so does any other system on a degree that lands on a key. Every other degree is the pitch it sounds, as TuningSystem::pitch_at spells it, with its microtone: G0(+2c) is the thirteenth step of Bohlen-Pierce. Ptolemy’s intense diatonic and the Sa-grama are named in sargam, Re0.

pub fn period_of(self, index: UnsignedIntegerType) -> UnsignedIntegerType

Which period a degree falls in, counting from nought.

pub fn frequency(self, index: UnsignedIntegerType) -> FloatType

The frequency in hertz of a degree above C-1.

pub fn frequency_at(self, index: FloatType) -> FloatType

The frequency in hertz of a fractional degree above C-1.

pub fn nearest_degree(self, hertz: FloatType) -> Result<IntegerType>

The degree sounding nearest hertz, counted from C-1 as TuningSystem::frequency counts, and measured in cents. Errors on a frequency that is not a finite number above nought.

use music21_rs::tuningsystem::TuningSystem;

let nineteen = TuningSystem::edo(19);
// A4 at 440 Hz is nearest degree 5 of the fifth period above C-1.
assert_eq!(nineteen.nearest_degree(440.0)?, 5 * 19 + 14);

pub fn pitch_at(self, index: IntegerType) -> Result<Pitch>

The pitch a degree sounds, counted from C-1: spelled as the nearest pitch-space value is spelled, with any remainder as a microtone.

use music21_rs::tuningsystem::TuningSystem;

// Degree 4 of the five-limit table is a just major third above C-1.
let e = TuningSystem::FiveLimit.pitch_at(64)?;
assert_eq!(e.name_with_octave(), "E4");
assert!((e.microtone().unwrap().cents() + 13.686).abs() < 1e-3);

pub fn cents(self, index: UnsignedIntegerType) -> FloatType

How far a degree lies from the same degree of the equal division of the same period into as many steps, in cents. Nought all the way up for an equal division, which is its own reference.

pub fn cents_at(self, index: FloatType) -> FloatType

The same for a fractional degree.

pub fn degrees_per_period(self) -> UnsignedIntegerType

How many degrees the system has before it repeats: twelve for most of the tables, and the number of divisions for an equal one.

pub fn period_cents(self) -> FloatType

The interval the system repeats at, in cents: an octave for every table, and whatever an equal division divides.

pub fn repeats_at_the_octave(self) -> bool

Whether the system repeats at the octave.

pub fn is_keyboard(self) -> bool

Whether the system has twelve degrees to the octave, one for each key of a keyboard.

pub const fn edo(divisions: UnsignedIntegerType) -> Self

An equal division of the octave into a number of steps fixed where it is written, for naming one in a constant. It is a compile error in a constant, and a panic otherwise, to ask for no steps at all; a count read at runtime goes through EqualDivision::octave, which is an error instead.

Trait Implementations

impl Clone for TuningSystem

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for TuningSystem

impl Debug for TuningSystem

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for TuningSystem

Available on crate feature serde only.

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for TuningSystem

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl From<TuningSystem> for AnyTuningSystem

fn from(tuning_system: TuningSystem) -> Self

Converts to this type from the input type.

impl FromStr for TuningSystem

fn from_str(s: &str) -> Result<Self, Self::Err>

Reads a system’s id: a table’s name, or an equal division as it writes itself (19edo, 13edt, 9ed3/2). EqualTemperament, WholeTone and QuarterTone read as 12edo, 6edo and 24edo.

type Err = Error

The associated error which can be returned from parsing.

impl PartialEq for TuningSystem

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl Serialize for TuningSystem

Available on crate feature serde only.

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for TuningSystem