Rhythmic Pedal

Definition: A rhythmic pattern repeating ostinato-fashion, indefatigably, independent of other rhythmic activity surrounding it, functioning as a temporal anchor analogous to harmonic pedal points.

Messiaen's Treatment: Messiaen introduces the rhythmic pedal as a rhythm that repeats itself indefatigably without concern for the rhythms surrounding it. This can accompany music of entirely different rhythm or mingle with other pedals.

Example 60 presents a complex texture: clarinet sings principal melody (transposing down an octave from notation), violin's light formulas create secondary counterpoint, cello harmonics two octaves above notation form a first rhythmic pedal whose "airy sonority envelops and unifies all the rest in its mysterious halo." Example 61 provides this pedal's rhythm.

The pedal divides into two nonretrogradable rhythms (A and B), the second composed of two groups where one retrogrades the other, with a central common value at the cross (actually a half-note coined in four eighth-notes, unchanged in retrograde). The rhythm repeats several times consecutively, constituting a rhythmic pedal. The quoted fragment contains three expressions: X, Y, Z (first two expressions plus beginning of third). The rhythmic pedal of fifteen values occurs simultaneously with a melodic pedal of five notes; there is disproportion between rhythm and melody.

Example 62 presents the piano's second rhythmic pedal. Example 60 describes complex multi-layered structure: melodic pedal (five notes) concurrent with rhythmic pedal (fifteen values) concurrent with harmonic pedal (twenty-nine chords forming unexpected rhythmic variants). Messiaen notes: "Rhythmicize your harmonies!" quoting Paul Dukas's pedagogical advice.

The harmonic analysis reveals sophisticated modal construction: chords employ "dominant with appoggiaturas" (stained-glass window effect from Chapter XIV), use Mode 3 (measures 1-4) and Mode 2 (measures 5-6), and the melodic pedal uses whole-tone scale, which can be tolerated when mixed with harmonic combinations foreign to it.

Modern Context: The rhythmic pedal concept extends traditional harmonic pedal points (sustained bass notes) into the temporal domain. This creates:

• Temporal stratification: Multiple independent temporal layers operating simultaneously
• Ostinato textures: Repeating patterns providing structural continuity
• Polyrhythmic complexity: Independent periodicities creating rich temporal interaction

The technique relates to:

• Isorhythm: Medieval repeating rhythmic patterns (taleae) cycling through melodic patterns (colores) of different lengths
• Minimalist loops: Repeating patterns of different lengths cycling against each other (Reich, Glass), though minimalism typically employs simpler patterns
• Stravinsky's ostinatos: Repeating rhythmic/melodic cells providing structural foundations
• Polymetric layers: Multiple simultaneous metric streams (Ives, Carter)

Messiaen's description of disproportion between rhythmic pedal (fifteen values), melodic pedal (five notes), and harmonic pedal (twenty-nine chords) creates a three-dimensional polyrhythmic structure where pitch-repetition rate, durational-pattern repetition rate, and harmonic-succession rate all differ. This represents maximum parametric independence—each musical dimension operates with its own periodicity.

The connection to Chapter XIX's polymodality (previewed through the reference to treating pedal-groups) demonstrates Messiaen's systematic parametric thinking: operations applicable to rhythm (pedals, superposition, independence) find analogous application to harmony (polymodal superposition, modal pedals, modal independence).

The Dukas quotation—"Rhythmicize your harmonies!"—encapsulates Messiaen's integrated approach: rhythm and harmony should not operate independently but should interact, with harmonic successions possessing their own rhythmic profiles. This challenges traditional harmonic thinking where chord progressions follow voice-leading logic separate from rhythmic considerations.

Examples: Examples 60–62 demonstrate complex multi-layered rhythmic pedal textures with melodic and harmonic dimensions integrated.