Enum LPR 

pub enum LPR {
    Leading = 0,
    Parallel = 1,
    Relative = 2,
}

The LPR implementation enumerates the primary transformations considered within the Neo-Riemannian theory. Each transformation is its own inverse (meaning consecutive applications of the same transformation will return the original triad) and may be chained together in both disctrete and continuous space to explore relationships between triads. These transformation act on the given triad based on the quality of the interval between the first and second notes (i.e., the root and third chord factors) meaning the effect of the transformation is dictated by whether the triad starts with a major or minor third.

With The transformations are:

• Leading (L):
  • [Major] decrement the root by a semitone; move to the fifth
  • [Minor] increment the fifth by a semitone; move to the root
• Parallel (P):
  • [Major] decrement the third by a semitone
  • [Minor] increment the third by a semitone
• Relative (R):
  • [Major] add a whole tone to the fifth; move to the root
  • [Minor] subtract a whole tone from the root; move to the fifth

Using category theory we could define these transformations to be contravariant functors mapping between categories of triads.

Variants

Leading = 0

Leading (L) transformation

Parallel = 1

Parallel (P) transformation

Relative = 2

Relative (R) transformation

Implementations

impl LPR

pub const fn is_leading(&self) -> bool

Returns true if the enum is LPR::Leading otherwise false

pub const fn is_parallel(&self) -> bool

Returns true if the enum is LPR::Parallel otherwise false

pub const fn is_relative(&self) -> bool

Returns true if the enum is LPR::Relative otherwise false

impl LPR

pub const fn leading() -> Self

a functional constructor returning a Leading transformation

pub const fn parallel() -> Self

a functional constructor returning a Parallel transformation

pub const fn relative() -> Self

a functional constructor returning a Relative transformation

pub fn iter() -> LPRIter

pub fn apply<X, Y>(self, triad: X) -> Y

where Self: Dirac<X, Output = Y>,

a convenience method for applying a transformation onto a triad, panicking on failure.

Trait Implementations

impl AsRef<str> for LPR

fn as_ref(&self) -> &str

Converts this type into a shared reference of the (usually inferred) input type.

impl Clone for LPR

fn clone(&self) -> LPR

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for LPR

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

Formats the value using the given formatter.

impl Default for LPR

fn default() -> LPR

Returns the “default value” for a type.

impl<S, T, K> Dirac<&TriadBase<S, K, T>> for &LPR

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn apply(self, rhs: &TriadBase<S, K, T>) -> Self::Output

impl<S, T, K> Dirac<&TriadBase<S, K, T>> for LPR

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn apply(self, rhs: &TriadBase<S, K, T>) -> Self::Output

impl<S, T, K> Dirac<&mut TriadBase<S, K, T>> for LPR

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn apply(self, rhs: &mut TriadBase<S, K, T>) -> Self::Output

impl<S, T, K> Dirac<TriadBase<S, K, T>> for &LPR

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn apply(self, rhs: TriadBase<S, K, T>) -> Self::Output

impl<S, T, K> Dirac<TriadBase<S, K, T>> for &mut LPR

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn apply(self, rhs: TriadBase<S, K, T>) -> Self::Output

impl<S, T, K> Dirac<TriadBase<S, K, T>> for LPR

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn apply(self, rhs: TriadBase<S, K, T>) -> Self::Output

impl Display for LPR

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

Formats the value using the given formatter.

impl EnumCount for LPR

const COUNT: usize = 3usize

impl From<LPR> for i128

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for i16

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for i32

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for i64

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for i8

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for isize

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for u128

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for u16

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for u32

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for u64

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for u8

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<LPR> for usize

fn from(value: LPR) -> Self

Converts to this type from the input type.

impl From<i128> for LPR

fn from(value: i128) -> Self

Converts to this type from the input type.

impl From<i16> for LPR

fn from(value: i16) -> Self

Converts to this type from the input type.

impl From<i32> for LPR

fn from(value: i32) -> Self

Converts to this type from the input type.

impl From<i64> for LPR

fn from(value: i64) -> Self

Converts to this type from the input type.

impl From<i8> for LPR

fn from(value: i8) -> Self

Converts to this type from the input type.

impl From<isize> for LPR

fn from(value: isize) -> Self

Converts to this type from the input type.

impl From<u128> for LPR

fn from(value: u128) -> Self

Converts to this type from the input type.

impl From<u16> for LPR

fn from(value: u16) -> Self

Converts to this type from the input type.

impl From<u32> for LPR

fn from(value: u32) -> Self

Converts to this type from the input type.

impl From<u64> for LPR

fn from(value: u64) -> Self

Converts to this type from the input type.

impl From<u8> for LPR

fn from(value: u8) -> Self

Converts to this type from the input type.

impl From<usize> for LPR

fn from(value: usize) -> Self

Converts to this type from the input type.

impl FromStr for LPR

type Err = ParseError

The associated error which can be returned from parsing.

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

Parses a string s to return a value of this type.

impl Hash for LPR

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl IntoEnumIterator for LPR

type Iterator = LPRIter

fn iter() -> LPRIter

impl Ord for LPR

fn cmp(&self, other: &LPR) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for LPR

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

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for LPR

fn partial_cmp(&self, other: &LPR) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<S, T, K> Transform<LPR> for TriadBase<S, K, T>

where K: TriadType, K::Rel: TriadType, S: TriadRepr<Elem = T>, T: Copy + FromPrimitive + One + PitchMod<Output = T> + Add<Output = T> + Sub<Output = T>,

type Output = TriadBase<S, <K as Relative>::Rel, T>

fn transform(self, transformation: LPR) -> Self::Output

impl TryFrom<&str> for LPR

type Error = ParseError

The type returned in the event of a conversion error.

fn try_from(s: &str) -> Result<LPR, <Self as TryFrom<&str>>::Error>

Performs the conversion.

impl TryFrom<char> for LPR

type Error = TriadError

The type returned in the event of a conversion error.

fn try_from(value: char) -> Result<Self, Self::Error>

Performs the conversion.

impl VariantArray for LPR

const VARIANTS: &'static [Self]

impl VariantNames for LPR

const VARIANTS: &'static [&'static str]

Names of the variants of this enum

impl Copy for LPR

impl Eq for LPR

impl StructuralPartialEq for LPR