Safe Haskell	Safe-Inferred

Util.Affine

Contents

base types
pitch

Description

Affine and instances. module Util.Affine (Affine(..), (.-^)) where

Synopsis

class Num (Diff p) => Affine p where
- type Diff p
- (.-.) :: p -> p -> Diff p
- (.+^) :: p -> Diff p -> p
(.-^) :: Affine p => p -> Diff p -> p
newtype Chromatic = Chromatic Int
newtype ChromaticSteps = ChromaticSteps Int
newtype Diatonic = Diatonic Int
newtype DiatonicSteps = DiatonicSteps Int
newtype FChromatic = FChromatic Double
newtype FChromaticSteps = FChromaticSteps Double
newtype FDiatonic = FDiatonic Double
newtype FDiatonicSteps = FDiatonicSteps Double

Documentation

class Num (Diff p) => Affine p where Source #

Simplified version of AffineSpace from the vector-space package.

Num gives access to negate and (+) and (*). It's probably technically too much because it also has fromInteger, but I don't think I need the whole AdditiveGroup etc. alternative numeric hierarchy.

Associated Types

type Diff p Source #

Methods

(.-.) :: p -> p -> Diff p infixl 6 Source #

(.+^) :: p -> Diff p -> p infixl 6 Source #

Instances

Instances details

Affine Chromatic Source #
Instance details Defined in Util.Affine Associated Types type Diff Chromatic Source # Methods (.-.) :: Chromatic -> Chromatic -> Diff Chromatic Source # (.+^) :: Chromatic -> Diff Chromatic -> Chromatic Source #
Affine Diatonic Source #
Instance details Defined in Util.Affine Associated Types type Diff Diatonic Source # Methods (.-.) :: Diatonic -> Diatonic -> Diff Diatonic Source # (.+^) :: Diatonic -> Diff Diatonic -> Diatonic Source #
Affine FChromatic Source #
Instance details Defined in Util.Affine Associated Types type Diff FChromatic Source # Methods (.-.) :: FChromatic -> FChromatic -> Diff FChromatic Source # (.+^) :: FChromatic -> Diff FChromatic -> FChromatic Source #
Affine FDiatonic Source #
Instance details Defined in Util.Affine Associated Types type Diff FDiatonic Source # Methods (.-.) :: FDiatonic -> FDiatonic -> Diff FDiatonic Source # (.+^) :: FDiatonic -> Diff FDiatonic -> FDiatonic Source #
Affine UTCTime Source #
Instance details Defined in Util.Affine Associated Types type Diff UTCTime Source # Methods (.-.) :: UTCTime -> UTCTime -> Diff UTCTime Source # (.+^) :: UTCTime -> Diff UTCTime -> UTCTime Source #

(.-^) :: Affine p => p -> Diff p -> p infixl 6 Source #

base types

pitch

newtype Chromatic Source #

Absolute chromatic steps.

Constructors

Chromatic Int

Instances

Instances details

Show Chromatic Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> Chromatic -> ShowS # show :: Chromatic -> String # showList :: [Chromatic] -> ShowS #
Eq Chromatic Source #
Instance details Defined in Util.Affine Methods (==) :: Chromatic -> Chromatic -> Bool # (/=) :: Chromatic -> Chromatic -> Bool #
Ord Chromatic Source #
Instance details Defined in Util.Affine Methods compare :: Chromatic -> Chromatic -> Ordering # (<) :: Chromatic -> Chromatic -> Bool # (<=) :: Chromatic -> Chromatic -> Bool # (>) :: Chromatic -> Chromatic -> Bool # (>=) :: Chromatic -> Chromatic -> Bool # max :: Chromatic -> Chromatic -> Chromatic # min :: Chromatic -> Chromatic -> Chromatic #
Affine Chromatic Source #
Instance details Defined in Util.Affine Associated Types type Diff Chromatic Source # Methods (.-.) :: Chromatic -> Chromatic -> Diff Chromatic Source # (.+^) :: Chromatic -> Diff Chromatic -> Chromatic Source #
type Diff Chromatic Source #
Instance details Defined in Util.Affine type Diff Chromatic = ChromaticSteps

newtype ChromaticSteps Source #

Relative chromatic steps, modulo pc_per_octave.

Constructors

ChromaticSteps Int

Instances

Instances details

Enum ChromaticSteps Source #
Instance details Defined in Util.Affine Methods succ :: ChromaticSteps -> ChromaticSteps # pred :: ChromaticSteps -> ChromaticSteps # toEnum :: Int -> ChromaticSteps # fromEnum :: ChromaticSteps -> Int # enumFrom :: ChromaticSteps -> [ChromaticSteps] # enumFromThen :: ChromaticSteps -> ChromaticSteps -> [ChromaticSteps] # enumFromTo :: ChromaticSteps -> ChromaticSteps -> [ChromaticSteps] # enumFromThenTo :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps -> [ChromaticSteps] #
Num ChromaticSteps Source #
Instance details Defined in Util.Affine Methods (+) :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # (-) :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # (*) :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # negate :: ChromaticSteps -> ChromaticSteps # abs :: ChromaticSteps -> ChromaticSteps # signum :: ChromaticSteps -> ChromaticSteps # fromInteger :: Integer -> ChromaticSteps #
Integral ChromaticSteps Source #
Instance details Defined in Util.Affine Methods quot :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # rem :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # div :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # mod :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # quotRem :: ChromaticSteps -> ChromaticSteps -> (ChromaticSteps, ChromaticSteps) # divMod :: ChromaticSteps -> ChromaticSteps -> (ChromaticSteps, ChromaticSteps) # toInteger :: ChromaticSteps -> Integer #
Real ChromaticSteps Source #
Instance details Defined in Util.Affine Methods toRational :: ChromaticSteps -> Rational #
Show ChromaticSteps Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> ChromaticSteps -> ShowS # show :: ChromaticSteps -> String # showList :: [ChromaticSteps] -> ShowS #
Eq ChromaticSteps Source #
Instance details Defined in Util.Affine Methods (==) :: ChromaticSteps -> ChromaticSteps -> Bool # (/=) :: ChromaticSteps -> ChromaticSteps -> Bool #
Ord ChromaticSteps Source #
Instance details Defined in Util.Affine Methods compare :: ChromaticSteps -> ChromaticSteps -> Ordering # (<) :: ChromaticSteps -> ChromaticSteps -> Bool # (<=) :: ChromaticSteps -> ChromaticSteps -> Bool # (>) :: ChromaticSteps -> ChromaticSteps -> Bool # (>=) :: ChromaticSteps -> ChromaticSteps -> Bool # max :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps # min :: ChromaticSteps -> ChromaticSteps -> ChromaticSteps #

newtype Diatonic Source #

Constructors

Diatonic Int

Instances

Instances details

Show Diatonic Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> Diatonic -> ShowS # show :: Diatonic -> String # showList :: [Diatonic] -> ShowS #
Eq Diatonic Source #
Instance details Defined in Util.Affine Methods (==) :: Diatonic -> Diatonic -> Bool # (/=) :: Diatonic -> Diatonic -> Bool #
Ord Diatonic Source #
Instance details Defined in Util.Affine Methods compare :: Diatonic -> Diatonic -> Ordering # (<) :: Diatonic -> Diatonic -> Bool # (<=) :: Diatonic -> Diatonic -> Bool # (>) :: Diatonic -> Diatonic -> Bool # (>=) :: Diatonic -> Diatonic -> Bool # max :: Diatonic -> Diatonic -> Diatonic # min :: Diatonic -> Diatonic -> Diatonic #
Affine Diatonic Source #
Instance details Defined in Util.Affine Associated Types type Diff Diatonic Source # Methods (.-.) :: Diatonic -> Diatonic -> Diff Diatonic Source # (.+^) :: Diatonic -> Diff Diatonic -> Diatonic Source #
type Diff Diatonic Source #
Instance details Defined in Util.Affine type Diff Diatonic = DiatonicSteps

newtype DiatonicSteps Source #

Constructors

DiatonicSteps Int

Instances

Instances details

Enum DiatonicSteps Source #
Instance details Defined in Util.Affine Methods succ :: DiatonicSteps -> DiatonicSteps # pred :: DiatonicSteps -> DiatonicSteps # toEnum :: Int -> DiatonicSteps # fromEnum :: DiatonicSteps -> Int # enumFrom :: DiatonicSteps -> [DiatonicSteps] # enumFromThen :: DiatonicSteps -> DiatonicSteps -> [DiatonicSteps] # enumFromTo :: DiatonicSteps -> DiatonicSteps -> [DiatonicSteps] # enumFromThenTo :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps -> [DiatonicSteps] #
Num DiatonicSteps Source #
Instance details Defined in Util.Affine Methods (+) :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # (-) :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # (*) :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # negate :: DiatonicSteps -> DiatonicSteps # abs :: DiatonicSteps -> DiatonicSteps # signum :: DiatonicSteps -> DiatonicSteps # fromInteger :: Integer -> DiatonicSteps #
Integral DiatonicSteps Source #
Instance details Defined in Util.Affine Methods quot :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # rem :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # div :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # mod :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # quotRem :: DiatonicSteps -> DiatonicSteps -> (DiatonicSteps, DiatonicSteps) # divMod :: DiatonicSteps -> DiatonicSteps -> (DiatonicSteps, DiatonicSteps) # toInteger :: DiatonicSteps -> Integer #
Real DiatonicSteps Source #
Instance details Defined in Util.Affine Methods toRational :: DiatonicSteps -> Rational #
Show DiatonicSteps Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> DiatonicSteps -> ShowS # show :: DiatonicSteps -> String # showList :: [DiatonicSteps] -> ShowS #
Eq DiatonicSteps Source #
Instance details Defined in Util.Affine Methods (==) :: DiatonicSteps -> DiatonicSteps -> Bool # (/=) :: DiatonicSteps -> DiatonicSteps -> Bool #
Ord DiatonicSteps Source #
Instance details Defined in Util.Affine Methods compare :: DiatonicSteps -> DiatonicSteps -> Ordering # (<) :: DiatonicSteps -> DiatonicSteps -> Bool # (<=) :: DiatonicSteps -> DiatonicSteps -> Bool # (>) :: DiatonicSteps -> DiatonicSteps -> Bool # (>=) :: DiatonicSteps -> DiatonicSteps -> Bool # max :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps # min :: DiatonicSteps -> DiatonicSteps -> DiatonicSteps #

newtype FChromatic Source #

Constructors

FChromatic Double

Instances

Instances details

Show FChromatic Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> FChromatic -> ShowS # show :: FChromatic -> String # showList :: [FChromatic] -> ShowS #
Eq FChromatic Source #
Instance details Defined in Util.Affine Methods (==) :: FChromatic -> FChromatic -> Bool # (/=) :: FChromatic -> FChromatic -> Bool #
Ord FChromatic Source #
Instance details Defined in Util.Affine Methods compare :: FChromatic -> FChromatic -> Ordering # (<) :: FChromatic -> FChromatic -> Bool # (<=) :: FChromatic -> FChromatic -> Bool # (>) :: FChromatic -> FChromatic -> Bool # (>=) :: FChromatic -> FChromatic -> Bool # max :: FChromatic -> FChromatic -> FChromatic # min :: FChromatic -> FChromatic -> FChromatic #
Affine FChromatic Source #
Instance details Defined in Util.Affine Associated Types type Diff FChromatic Source # Methods (.-.) :: FChromatic -> FChromatic -> Diff FChromatic Source # (.+^) :: FChromatic -> Diff FChromatic -> FChromatic Source #
type Diff FChromatic Source #
Instance details Defined in Util.Affine type Diff FChromatic = FChromaticSteps

newtype FChromaticSteps Source #

Constructors

FChromaticSteps Double

Instances

Instances details

Num FChromaticSteps Source #
Instance details Defined in Util.Affine Methods (+) :: FChromaticSteps -> FChromaticSteps -> FChromaticSteps # (-) :: FChromaticSteps -> FChromaticSteps -> FChromaticSteps # (*) :: FChromaticSteps -> FChromaticSteps -> FChromaticSteps # negate :: FChromaticSteps -> FChromaticSteps # abs :: FChromaticSteps -> FChromaticSteps # signum :: FChromaticSteps -> FChromaticSteps # fromInteger :: Integer -> FChromaticSteps #
Show FChromaticSteps Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> FChromaticSteps -> ShowS # show :: FChromaticSteps -> String # showList :: [FChromaticSteps] -> ShowS #
Eq FChromaticSteps Source #
Instance details Defined in Util.Affine Methods (==) :: FChromaticSteps -> FChromaticSteps -> Bool # (/=) :: FChromaticSteps -> FChromaticSteps -> Bool #
Ord FChromaticSteps Source #
Instance details Defined in Util.Affine Methods compare :: FChromaticSteps -> FChromaticSteps -> Ordering # (<) :: FChromaticSteps -> FChromaticSteps -> Bool # (<=) :: FChromaticSteps -> FChromaticSteps -> Bool # (>) :: FChromaticSteps -> FChromaticSteps -> Bool # (>=) :: FChromaticSteps -> FChromaticSteps -> Bool # max :: FChromaticSteps -> FChromaticSteps -> FChromaticSteps # min :: FChromaticSteps -> FChromaticSteps -> FChromaticSteps #

newtype FDiatonic Source #

Constructors

FDiatonic Double

Instances

Instances details

Show FDiatonic Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> FDiatonic -> ShowS # show :: FDiatonic -> String # showList :: [FDiatonic] -> ShowS #
Eq FDiatonic Source #
Instance details Defined in Util.Affine Methods (==) :: FDiatonic -> FDiatonic -> Bool # (/=) :: FDiatonic -> FDiatonic -> Bool #
Ord FDiatonic Source #
Instance details Defined in Util.Affine Methods compare :: FDiatonic -> FDiatonic -> Ordering # (<) :: FDiatonic -> FDiatonic -> Bool # (<=) :: FDiatonic -> FDiatonic -> Bool # (>) :: FDiatonic -> FDiatonic -> Bool # (>=) :: FDiatonic -> FDiatonic -> Bool # max :: FDiatonic -> FDiatonic -> FDiatonic # min :: FDiatonic -> FDiatonic -> FDiatonic #
Affine FDiatonic Source #
Instance details Defined in Util.Affine Associated Types type Diff FDiatonic Source # Methods (.-.) :: FDiatonic -> FDiatonic -> Diff FDiatonic Source # (.+^) :: FDiatonic -> Diff FDiatonic -> FDiatonic Source #
type Diff FDiatonic Source #
Instance details Defined in Util.Affine type Diff FDiatonic = FDiatonicSteps

newtype FDiatonicSteps Source #

Constructors

FDiatonicSteps Double

Instances

Instances details

Num FDiatonicSteps Source #
Instance details Defined in Util.Affine Methods (+) :: FDiatonicSteps -> FDiatonicSteps -> FDiatonicSteps # (-) :: FDiatonicSteps -> FDiatonicSteps -> FDiatonicSteps # (*) :: FDiatonicSteps -> FDiatonicSteps -> FDiatonicSteps # negate :: FDiatonicSteps -> FDiatonicSteps # abs :: FDiatonicSteps -> FDiatonicSteps # signum :: FDiatonicSteps -> FDiatonicSteps # fromInteger :: Integer -> FDiatonicSteps #
Show FDiatonicSteps Source #
Instance details Defined in Util.Affine Methods showsPrec :: Int -> FDiatonicSteps -> ShowS # show :: FDiatonicSteps -> String # showList :: [FDiatonicSteps] -> ShowS #
Eq FDiatonicSteps Source #
Instance details Defined in Util.Affine Methods (==) :: FDiatonicSteps -> FDiatonicSteps -> Bool # (/=) :: FDiatonicSteps -> FDiatonicSteps -> Bool #
Ord FDiatonicSteps Source #
Instance details Defined in Util.Affine Methods compare :: FDiatonicSteps -> FDiatonicSteps -> Ordering # (<) :: FDiatonicSteps -> FDiatonicSteps -> Bool # (<=) :: FDiatonicSteps -> FDiatonicSteps -> Bool # (>) :: FDiatonicSteps -> FDiatonicSteps -> Bool # (>=) :: FDiatonicSteps -> FDiatonicSteps -> Bool # max :: FDiatonicSteps -> FDiatonicSteps -> FDiatonicSteps # min :: FDiatonicSteps -> FDiatonicSteps -> FDiatonicSteps #