Neo-Riemannian Theory, the P (3,0) Chord, and Rock Music

Neo-Riemannian theory is an extremely versatile way of analyzing and composing harmony and focuses on moving chord tones by half step to lead into new chords, known as voice leading transformations.  There are three types of transformations: parallel (P) – when a major triad becomes minor, (or vice versa), relative (R) – where the relative major or minor of a triad is created), and Leading Tone (l) – where the root of a major triad moves down by a half step and becomes the fifth of a minor chord (reversed for minor chords).  In addition to transformations, Neo-Riemannian theory extends into the realm of 7th chords and pitch classes focusing on the same principle of voices moving by half step from one chord into the next.  Two articles that boast great knowledge on this topic are Samuel Reenan and Richard Bass’ “Types and Applications of P3-0 Seventh Chord Transformations in Late Nineteenth-Century Music” and David Forrest’s “PL Voice Leading and the Uncanny in Pop Music”.  Both articles provide bountiful references to repertoire where they demonstrate the versatility and uniqueness of Neo-Riemannian voice leading transformations in multiple harmonic contexts.

The Reenan and Bass article focuses on the different types of P3,0 transformations, how to notate them, as well as their application in nineteenth-century repertoire.  To begin, they discuss the basis of what P (3,0) is.  In simple terms, it takes a traditional seventh chord (MA7, dom7, mi7, ø7, o7, +7) and manipulates three of the chord tones by half step, while one remains the same.  An example would be CMA7 to C#7, where the 7th of CMA7 remains the same, and the other three chord tones (C, E, and G) move up by half step (to C#, E#, and G#) to create C#7.  To notate this, Reenan and Bass use the following format: P (3,0) p↑(7).  In this case the lower-case ‘p’ stands for parallel motion, meaning all three of the CMA7’s triad tones move in the same direction, the ‘↑’ indicates they move in an upwards direction by half step (inversely, ‘↓’ would mean they move in a downwards direction by half step), and the seven in parenthesis ‘(7)’ indicates that the 7th of the chord is shared by both CMA7 and the new chord C#7.  In some cases, two of the chord tones can move in one direction (indicated by the up or down arrow) while one of the chord tones moves in the opposite direction.  This is called contrary motion, and the lower-case ‘p’ should be replaced with ‘c’ (for contrary motion), and the chord degree moving in contrary motion would be placed in brackets ‘[x]’ (for example: c↑[7](5) would change CMA7 into Gø7: C–Db, E–F, G–G, B–Bb).  Reenan and Bass then exhibit these ideas in an authentic situation, recalling Strauss’ “Ruhe, meine Seele!”: “The opening four measures of “Ruhe, meine Seele!” act as a microcosm of the motivic and voice-leading procedures developed later in the work. This progression, shown in Figure 9a, is remarkable at the outset for the contrary P (3,0) transformation connecting C7 and F#m7. The same P 3,0 type recurs two more times at points of structural articulation: measures 22–23 (F7 to Bm7) and 39–40 (returning to C7 and F#m7).”  In this case, the P (3,0) c↓[1](3) transformation describes how two distantly related chords can somewhat flow into one another through voice leading, as the root of C7 moves up in contrary motion to the 5th and 7th (which move down) and the 3rd remains the same.  Coupled with a descending baseline, this allows Strauss to uniquely provide tonal closure for the work.

In the Forrest article, he explains how uncanny responses are often triggered by certain psychological and sociological phenomenon, which are often the subject matter of pop-music containing PL/LP progressions.  To explain this connection, Forrest begins by referencing various psychological and sociological phenomenon which cause such uncanny responses in the first place; such as: wax figures, ventriloquism, dead bodies, and epileptic seizures.  Upon studying pop songs which utilize the PL/LP progression, he discovers many of these songs contain lyrics which reference these topics:  “Surveying pop music from the past sixty years reveals that uncanny topics associated with PL and LP motion tend to fall into at least one of six generic categories: (1) directly questioning reality; (2) visions, such as dreams, memories, and hallucinations; (3) psychological conditions, such as depression, disorientation, and drug addiction; (4) supernatural phenomena; (5) the process of transcending mental barriers; and (6) descriptions of dystopia.”  Forrest continues by explaining all these phenomenon take something familiar (like the human body) and make it unfamiliar, and this is what results in uncanny responses.  He then defines the PL/LP harmonic progression, labeling it a multitude of fashions.  Most simply as the relation of a I chord and bVI chord (EX: D Major triad and Bb Major triad), I to III, or bIII to V.  However, since there are so many harmonic functions where a major triad’s root could move up or down by major third, it is best to name the PL/LP progression using a Neo-Riemannien terminology.  In this sense, the PL transformation occurs when the root motion moves down by a major third (D Major to Bb Major) and begins with a Parallel transformation (D Major to D minor), followed by a Leading Tone transformation (D minor to Bb Major).  The LP transformation is the inverse, occurring when the root motion moves up by a major third (Bb Major to D Major), and begins with the Leading Tone Transformation (Bb Major to D minor) is followed by the Parallel Transformation (D minor to D Major).  The result of distantly related chords flowing into each other through voice leading is a unique, somewhat unsettling sound, which pairs fantastically with uncanny lyrics.

I fully support Reenan and Bass’s studies of the versatility of P (3,0) in seventh chords as they support their claims with bountiful repertoire examples and thorough theoretical explanations that highlight the uniqueness of P (3,0).  In addition to Strauss’ “Ruhe, meine Seele!”, they refer to multiple other pieces of nineteenth-century repertoire to include the Prelude of Wagner’s Tristan and Isolde and the different ways P (3,0) can be used.  Most importantly, they discuss many ways in which P (3,0) can be coupled with other 7th chord transformations as well as octatonic pitch classes to create even more unique harmonic progressions:  “For example, a P 3,0 that connects a dominant seventh to a minor seventh with a tritone-related root, or P (3,0) c↓[r](3), may be coupled with a P(1,0)  moving the third of the minor seventh up by half step to yield a larger-scale connection between two dominant sevenths separated by a tritone , or P(3,0) +P(1,0)→P(2,0).”  Thus, this technique allows for composers to modulate to distantly related chords of the same chord-quality.  By shifting the music to a new place while keeping the same timbral sonority, melodic or pitch-class thematic material can be sequenced into a new key or tonal center in an especially unique fashion.

I fully agree with Forrest’s claims of how the PL/LP progression complements lyrics in a unique way to obtain an especially uncanny feeling.  It is difficult to argue his claims as he lists dozens of pop songs from the mid 1900s to 2016 where lyrics pertaining to drugs, homicide, and strange dreams set up a song for an uncanny feeling and are further (appropriately) supported by the PL/LP progression.  He justifies how the PL/LP progression enhances this uncanny effect in many ways, with a particularly clear example from Audioslave’s “I Am the Highway”: “Each metaphor is set to a diatonic ascending-fifths sequence in A minor, ||: C–G–d–a :||. The final metaphor, “I am not your autumn moon, I am the night,” replaces the expected A-minor tonic chord with an E-major dominant chord, producing an LP phrase frame between C and E, and signifying his transcendence beyond his lover’s restrictive definitions of him.”  By replacing an expected A-minor tonic chord with an E-major dominant chord, the music now takes something the listener is familiar with (the expected chord progression), and turns it into something unfamiliar by introducing a new chord which contains tones from outside the diatonic key.  Many listeners can agree that when the sounds of a song’s harmony match the ideas portrayed in the lyrics, it enhances the clarity of the song’s message and tone.  From my own experiences, I have found the most satisfaction in song writing when composing music and lyrics which tell the same story.  It offers a way to simultaneously share raw emotions through the music and refined emotions through the lyrics.  While I have used techniques such as complicating harmony as the song’s storyline grows more complex, I have yet to implement the PL/LP progression and look pairing its unique sound should I find myself writing about any of the phenomenons described in Forrest’s studies.

In conclusion, both articles illustrate the versatility and uniqueness of Neo-Riemannian transformations, using harmonic environments from various repertoire to prove their claims.  Reenan and Bass expertly showcase the many ways in which P (3,0) has been used in nineteenth century repertoire to devise unique sounding modulations between distantly related seventh chords.  Comparably, Forrest describes how the unique sound of PL/LP transformations can enhance uncanny lyricism as a result of the transformation being fundamentally uncanny in itself.  Hence, both articles consequently advocate for the versatility of Neo-Riemannien analysis and implore writers to include this theoretical view in their arsenal of compositional techniques.  

Bibliography

Bass, Richard, and Samuel Reenan. “Types and Applications of P3-0 Seventh Chord Transformations in Late Nineteenth-Century Music” Society for Music Theory (August 2015): 1–12.

Forrest, David. “PL Voice Leading and the Uncanny in Pop Music.” Society for Music Theory (December 2017): 1–25.