music theory

Neo-Riemannian Transformations/Fanfare

Neo-Riemannian theory in music in short describes pitch relationships between major and minor triads. It examines the effect of efficient voice leading, or in other words, what happens when one pitch of a triad changes by a tone or semi-tone. These single pitch changes are categorized into three basic triadic transformations: P=parallel, R=relative and L=leading-tone exchange transformations. The parallel and relative transformations transform a triad into its respective parallel and relative major or minor triad. The leading tone exchange transformation transforms a major triad to the minor triad with roots related by a major third.

In the example below, a P transformation transforms a C major triad into a C minor triad, an R transformation transforms a C major triad into an A minor triad, and an L transformation changes a C major triad into an E minor triad. All of these transformations are reversible, so that a P transformation applied to a C minor triad transforms it into a C major triad, and so on. Since two of the pitches stay the same across a transformation, we can say that a transformation also preserves a particular interval across a transformationthe P transformation preserves a perfect fifth, and the R and L transformations preserve major and minor thirds, respectively.

P, R, L Triadic Transformations

Transformations can be applied successively or simultaneously and in any number or order. They are also used to explain how to connect chords that are not harmonically closely related. The example below shows how look a series of L and P transformations leads to a succession of chords.

Successive L & P Transformations

The next example shows L & P transformations applied simultaneously. Here, all of the intermediary minor chords are subsumed in the simultaneous transformations, and the result is a succession of major triads. For additional information on Neo-Riemannian transformations, check out the links below.

Simultaneous L & P Transformations

Today’s piece applies successions of major chords using simultaneous LP and PL transformations to create a majestic fanfare, which also turns out to be a great major triad study for guitar!

(Please consider supporting this site! Sheet music and tablature for Fanfare and other guitar studies available here: Innovative Studies for Guitar – Volume 1)

Fanfare

Additional resources:

https://en.wikipedia.org/wiki/Neo-Riemannian_theory

https://tonnetz.liamrosenfeld.com/explain-music

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