Struct EqualDivision 

pub struct EqualDivision { /* private fields */ }

An equal division of an arbitrary interval.

12edo is twelve equal divisions of the octave, 13edt thirteen of the tritave. Nothing here assumes the period is an octave, so a degree past the period simply carries on into the next one — which for Bohlen-Pierce means the pitches never line up with an octave at all.

Implementations

impl EqualDivision

pub fn new( divisions: UnsignedIntegerType, period_cents: FloatType, ) -> Result<Self>

Divides a period given in cents.

Errors on a period that is not a positive real number, or on no divisions at all.

pub fn of_ratio( divisions: UnsignedIntegerType, numerator: IntegerType, denominator: IntegerType, ) -> Result<Self>

Divides the interval numerator/denominator.

The ratio is remembered, so the division names itself after it.

pub fn octave(divisions: UnsignedIntegerType) -> Result<Self>

Divides the octave — an EDO, and what everyone means by default.

pub fn tritave(divisions: UnsignedIntegerType) -> Result<Self>

Divides the tritave, 3/1 — an EDT, which is Bohlen-Pierce’s period.

pub fn divisions(&self) -> UnsignedIntegerType

How many steps the period is divided into.

pub fn period_cents(&self) -> FloatType

The period, in cents.

pub fn period_ratio(&self) -> Option<(IntegerType, IntegerType)>

The ratio the period was given as, where it was given as one.

pub fn repeats_at_the_octave(&self) -> bool

Whether the period is an octave, which is what makes this an ordinary EDO.

pub fn step_cents(&self) -> FloatType

One step, in cents.

pub fn cents_at(&self, degree: IntegerType) -> FloatType

How far above the tonic degree steps sit, in cents.

A degree past the period carries on into the next one, and a negative degree goes below the tonic.

pub fn ratio_at(&self, degree: IntegerType) -> FloatType

The frequency ratio of degree steps above the tonic.

pub fn degrees(&self) -> Vec<FloatType>

Every degree of one period, in cents, from nought up to but not including the period.

pub fn nearest_degree(&self, cents: FloatType) -> IntegerType

The degree nearest cents above the tonic.

pub fn error_at_cents(&self, cents: FloatType) -> FloatType

How far the nearest degree sits from cents; positive is sharp.

pub fn approximation_of(&self, interval: &Monzo) -> (IntegerType, FloatType)

The degree nearest interval, and how far off it sounds in cents.

This is how well the division does a just interval, which for an EDO is the whole question of whether it is worth using.

pub fn patent_val(&self, limit: IntegerType) -> Result<Val>

The patent val of this division, read up to limit.

Each prime is mapped to the nearest whole number of steps, which for an octave division is the familiar patent val. For a period that is not an octave this is the generalized reading, and the octave itself then gets a mapping like any other prime rather than being the period. Errors for a limit that is not a prime the module carries.

pub fn mos( &self, steps: UnsignedIntegerType, notes: UnsignedIntegerType, ) -> Result<MosScale>

The scale of notes notes made by stacking steps of this division.

This is the wiki’s 3\22 — three steps of twenty-two — handed to the moment-of-symmetry machinery.

Trait Implementations

impl Clone for EqualDivision

fn clone(&self) -> EqualDivision

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for EqualDivision

impl Debug for EqualDivision

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for EqualDivision

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 EqualDivision

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

Names the division the way the literature does: 12edo, 13edt, 9ed3/2.

impl FromStr for EqualDivision

fn from_str(text: &str) -> Result<Self>

Reads 12edo, 13edt, 13ed3 and 9ed3/2.

type Err = Error

The associated error which can be returned from parsing.

impl PartialEq for EqualDivision

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

Equality operator ==.

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

Inequality operator !=.

impl Serialize for EqualDivision

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 EqualDivision