Module neoriemannian 

Neo-Riemannian transformations of triads: music21’s analysis.neoRiemannian.

Each of L, P and R moves one pitch of a major or minor triad and keeps the other two, turning major into minor and back:

          C E G (C major)
  L: C -> B      B E G   (E minor)
  P: E -> E-     C E- G  (C minor)
  R: G -> A      C E A   (A minor)

Chains of them name the other relations: slide is LPR, the Nebenverwandt RLP, the chromatic and disjunct mediants two or three steps each, and PLPLPL walks a hexatonic cycle back to where it began.

Enums

ChainOrder

The order a chain of transformations is read in.

HexatonicSystem

Richard Cohn’s four hexatonic systems, each the six triads one cycle of PL passes through, named by the pitch classes of their roots.

Mediant

A chromatic mediant: root motion by a third, mode kept, one common tone.

MediantSide

Which of the two disjunct mediants: root motion by a chromatic third, mode changed, no common tone.

Respell

Whether a result keeps the spelling the transformations gave it.

Transform

One of the three neo-Riemannian transformations.

Functions

chromatic_mediant

chord’s chromatic mediant, respelled: music21’s chromaticMediants.

complete_hexatonic

The six triads of chord’s hexatonic cycle, PLPLPL, ending on chord again or its enharmonic: music21’s completeHexatonic. With Respell::Simplify each step is respelled before the next is taken.

disjunct_mediant

chord’s disjunct mediant on side, respelled: music21’s disjunctMediants.

hexatonic_system

The hexatonic system of chord’s root: music21’s hexatonicSystem. Only the root’s pitch class counts, so sevenths and diminished triads are classed too.

is_chromatic_mediant

The chromatic mediant taking from to to’s normal order: music21’s isChromaticMediant.

is_neo_r

The first of transforms taking from to to’s normal order: music21’s isNeoR.

lrp_chain

Every chord a chain of transformations passes through, in order: music21’s LRP_combinations with eachOne=True. With Respell::Simplify each is respelled on its own; the chain itself runs on the spellings the transformations give.

lrp_combination

Where a chain of transformations ends: music21’s LRP_combinations. No transformations at all leave chord as it was.

nebenverwandt

Nebenverwandt, RLP: a minor triad to its major dominant, a major one to its minor subdominant. music21’s N.

simpler_enharmonics

chord respelled with the best enharmonics, duration kept: music21’s _simplerEnharmonics. B# F- G comes back as C E G.

slide

Slide, LPR: the third held, major root a semitone below the minor. music21’s S.