Part III: Harmony—The Rainbow of Transcendence

The seven chapters on harmony reveal something extraordinary: a complete reimagining of how pitch relationships can generate both structure and color, grounded not in historical convention but in acoustic resonance, mathematical symmetry, and spiritual vision. Where rhythm gave us the "charm of impossibilities" through temporal symmetry, and melody showed us how contour and birdsong transcend conventional phrase structure, harmony completes the theological rainbow—modes that exist simultaneously in multiple tonal atmospheres while committing to none, chords that emerge from natural resonance rather than theoretical construction, and progressions that move through kaleidoscopic transformations while maintaining crystalline clarity.

Beyond Functional Harmony: The Liberation of Dissonance

Messiaen begins with a radical proposition: what if dissonances didn't need to resolve? The concept of added notes (Chapter XIII) transforms our entire relationship with harmonic tension. Those pitches that traditional harmony treats as temporary—passing tones, appoggiatura, suspensions—become permanent residents within the chord. They don't resolve; they simply are. The added sixth and augmented fourth aren't ornaments awaiting resolution—they're structural members possessing "full citizenship in the chord."

Consider what this means for your music: every chord can be a destination, not just a waypoint. That suspended fourth you've been dutifully resolving? Let it ring. That added ninth creating delicious friction? It's not friction—it's the chord's natural resonance. Messiaen shows us that harmonic richness doesn't require constant motion; it can achieve stasis without stagnation, creating what he calls "stained-glass window effects" where multiple inversions and colorings of the same harmonic essence shimmer with internal life.

The parallel he draws between added notes and added values isn't mere theoretical elegance—it's compositional methodology. Both techniques share "the same charm, somewhat perverse": they make music "limp deliciously," introducing asymmetry and supplementation that transforms without destroying. If your rhythms use added values to create temporal complexity, why shouldn't your harmonies use added notes to create vertical richness? The principle of enrichment through "foreign" elements operates across all parameters.

Three Chords That Change Everything

Chapter XIV presents three harmonic building blocks that open radical compositional possibilities. First, the chord on the dominant saturates diatonic space—all seven notes of the major scale sounding simultaneously. But rather than creating chaos, this maximal density hovers between tension and stasis, especially when treated with Messiaen's "multicolor work," arranging inversions over a common bass to create harmonic halos.

Second, the chord of resonance grounds harmony in acoustic reality. Built from the overtone series, this sonority claims legitimacy from nature itself—it's not constructed; it's discovered. When Messiaen writes of "natural harmony" as "pre-existent, having always been enclosed in the melody, awaiting manifestation," he's describing harmonic choices as acts of revelation rather than invention. Your task isn't to create harmony from nothing but to filter and refine what acoustic resonance already offers.

Third, the chord in fourths abandons tertian stacking entirely. Perfect and augmented fourths create ambiguous, hovering sonorities neither major nor minor, suggesting harmonic space beyond traditional categories. Jazz composers rediscovered these voicings decades later; Messiaen systematizes them through connection to his fifth mode of limited transpositions.

But the chapter's most profound moment comes not in these specific chords but in Messiaen's aesthetic manifesto on "natural harmony." His description of "swords of fire, those sudden stars, those flows of blue-orange lavas, those planets of turquoise" isn't hyperbole—it's a composer articulating the synaesthetic experience of harmonic color. He's giving you permission to hear harmonies as colors, textures, even temperatures. The 71 examples of chord connections that follow aren't prescriptive formulas but demonstrations of possibility—here's how these materials behave in practice, now discover what they might do in your music.

The Enlargement Principle: Making Small Things Large

Chapter XV transforms our understanding of harmonic gesture through a simple but powerful idea: what if ornamental details became structural gestures? The pedal group, passing group, and embellishment group take single-note phenomena and inflate them into complete musical structures possessing their own internal organization.

This isn't just theoretical elegance—it's compositionally liberating. That pedal point anchoring your bass? Make it a complete repeating pattern, a miniature ostinato with its own rhythm, melody, and harmony. Those passing tones connecting chord tones? Turn them into entire sequences of harmonic progressions moving through pitch space. That ornamental flourish? Expand it into a cadenza-like scroll that takes its time, reveling in surface detail while ultimately serving ornamental function.

The upbeat-accent-termination complex represents Messiaen's most practical contribution to phrase structure. Every musical gesture contains anacrusis (preparation), accent (arrival), and termination (dissolution). But Messiaen liberates these from their traditional durations—upbeats and terminations become "immense," separated by rests, or even appearing independently. Example 310 shows how cutting gesture into fragments creates "impression of effort, of exhaustion"—the discontinuity itself becomes expressive content.

Think about your own music: how are your phrases articulated? Do they follow predictable anacrusis-downbeat-continuation patterns, or might some benefit from extended preparation building to sudden, devastating accents? Could terminations linger, dissolving slowly in quasi-atonal chromatic descents? The examples demonstrate "anguish," "desire," "horror," "effort"—these structural articulations serve emotional ends.

The Modes: Seven Windows Into Infinite Possibility

Chapter XVI is the theoretical keystone, presenting the modes of limited transpositions—symmetrical pitch collections that can only be transposed a certain number of times before reproducing their original content. But grasping this technically isn't enough; you need to hear what they offer compositionally.

These modes exist "in the atmosphere of several tonalities at once, without polytonality." This isn't vague mysticism—it's precise description of perceptual reality. An octatonic collection (Mode 2) suggests C, E♭, F♯, and A major/minor simultaneously. You can emphasize one (through bass notes, dominant sevenths, thematic design) or leave the tonal impression unsettled. Either way, you're working with harmonic ambiguity as an aesthetic resource, not a problem to solve.

The connection to nonretrogradable rhythms reveals deep unity: both embody symmetry, both create the "charm of impossibilities," both operate without polytonality/polyrhythm despite containing multiple implications. The modes aren't just pitch collections—they're manifestations of the same organizational principle governing temporal structure. If you're working with symmetrical rhythms, why wouldn't you use symmetrical pitch collections?

Messiaen's treatment of individual modes is revealing. Mode 1 (whole-tone) he avoids as "exhausted" by Debussy—useful lesson in compositional economy. Some materials, however elegant, become cliché through overuse. Mode 2 (octatonic) receives extensive treatment because its three transpositions offer both constraint and variety. Mode 3 approaches chromatic saturation (nine of twelve pitches) while maintaining modal identity through its gaps and symmetries.

Modes 4–7, each transposable six times, offer "less interest" precisely because greater transposability means less constraint, less recognizable identity. Yet Messiaen uses them where their particular colors fit—Mode 5 connects to the chord in fourths and its associated melodic formula; Mode 6 appears in rhythmic contexts requiring its specific sonority. The lesson: not all materials need equal emphasis. Some modes might dominate your vocabulary; others serve specialized roles.

Flexibility in Practice: Modulation and Mixture

Chapters XVII-XVIII demonstrate that modal purity isn't dogma. You can mix modes with major tonality (Chapter XVII), emphasizing particular pitches or using dominant sevenths to create tonal orientation. You can modulate a mode to itself by changing transposition levels—Mode 2 at transposition 1 to Mode 2 at transposition 3, maintaining character while creating harmonic motion. You can modulate between different modes—Mode 3 to Mode 2, Mode 2 to Mode 6—accessing diverse harmonic palettes while remaining within symmetrical structures.

Chapter XVIII clarifies what modes aren't: they're not traditional modal scales (those transpose twelve times), they're not systematic atonality (modes can suggest tonal centers), and they're not polytonality (the "modal force always absorbs" potential polytonal implications). This last distinction matters profoundly: polytonality creates clash through juxtaposition of incompatible centers; polymodality (Chapter XIX) creates unified fields containing multiple implications.

Think practically: you might start a piece in Mode 2, mix it with G major passages using dominant sevenths to establish tonal orientation, modulate to Mode 3 at a contrasting section, return to Mode 2 at a different transposition level, and conclude in pure G major. The modes aren't exclusive systems; they're colors on your palette, resources to deploy according to expressive need.

Polymodality: The Summit of Harmonic Complexity

Chapter XIX presents polymodality—simultaneous superposition of different modes in different textural layers—as the culmination of harmonic practice. This isn't about complexity for its own sake; it's about creating stratified textures where each layer maintains internal consistency while combining to produce emergent harmonic properties.

The principle is simple: upper staff uses Mode 3, lower staff uses Mode 2, each operating melodically and harmonically within its assigned mode. But the resultant vertical combinations create sonorities neither mode produces alone. Example 371 shows two pedal groups of unequal length (five chords vs. four chords) repeating until they meet again at departure—minimalist phasing applied to polymodal harmony.

Polymodal modulation operates at even higher structural levels. You can change transpositions of superposed modes (Example 376), invert which mode appears in which layer (Example 380), or substitute entirely different modes (Examples 381-382). Example 381's detailed performance instructions—pedal sounds octave higher, true bass in sixteenth-notes, specific organ registration—reveal how timbral differentiation supports polymodal clarity. Different modes receive different timbres, helping listeners perceive stratification.

The observation that Fragment B uses all chromatic pitches except E, with E's arrival augmenting the effect of subsequent modulation, demonstrates sophisticated pitch-class planning. You're not just layering modes; you're managing aggregate completion, strategic omission, and dramatic arrival as compositional parameters.

Composing with These Materials: Practical Pathways

How might you actually use this harmonic system? Several approaches suggest themselves:

Modal Purity: Write entirely within single modes, changing transposition levels for formal contrast. Explore how long you can sustain Mode 2 or Mode 3 before needing change. Investigate the characteristic melodic and harmonic gestures each mode generates naturally.

Strategic Mixture: Combine modal passages with tonal sections. Use modes for mystical, suspended, or ambiguous passages; use traditional tonality for grounded, directional music. The contrast itself becomes compositional material.

Polymodal Stratification: Create textures with independent modal layers. Pedal group in Mode 3 beneath passagework in Mode 2. Melody in Mode 6 over accompaniment in Mode 7. Experiment with which combinations create richest emergent sonorities.

Parametric Integration: Coordinate modal choices with rhythmic procedures. If you're using nonretrogradable rhythms, use modes of limited transpositions. If you're using added values, use added notes. Let the same organizational principles govern all parameters.

Coloristic Focus: Treat specific chords as color fields—linger on the chord of resonance, the chord in fourths, saturated dominant structures. Use resonance effects (chord clusters above or below structural harmonies) to create harmonic halos. Think vertically about timbre and texture as much as progression.

Gestural Articulation: Shape phrases using upbeat-accent-termination complexes. Experiment with "immense" preparations and dissolutions. Try separating elements with rests, or presenting terminations without preceding accents. Use structural gesture as expressive content.

Practice: Exercises for Harmonic Exploration

These exercises move from simple to complex. Don't rush—each level builds skills for the next.

Level 1: Added Notes

Exercise 1.1: The Added Sixth Take a simple four-bar progression in C major (C–F–G–C). Now add the sixth to every chord (A to C major, D to F major, E to G major). Play both versions. Notice how the added sixths create warmth without changing harmonic function.

Exercise 1.2: The Added Augmented Fourth Return to your C–F–G–C progression. Add F♯ to the C major chord (the augmented fourth). Let it ring—don't resolve it. This is the characteristic Messiaen sonority. Try adding the augmented fourth to other chords in the progression.

Exercise 1.3: Combining Added Notes Build a C major chord with both added sixth (A) and added augmented fourth (F♯): C–E–F♯–G–A. This is the Mode 2 chord. Transpose it through the three Mode 2 transposition levels and listen to how the color remains consistent while pitch content changes.

Level 2: Single Mode Composition

Exercise 2.1: Mode 2 Melody Write an 8-bar melody using only the pitches of Mode 2, first transposition: C–C♯–D♯–E–F♯–G–A–B♭. Notice which intervals occur naturally (minor seconds, minor thirds, tritones). Let the mode's internal structure guide your contour choices.

Exercise 2.2: Mode 2 Harmonization Harmonize your melody using only chords built from Mode 2 pitches. Every note in every chord must belong to the mode. Discover which triads, seventh chords, and added-note structures are available.

Exercise 2.3: Mode 3 Exploration Repeat exercises 2.1 and 2.2 using Mode 3, first transposition: C–D–E♭–E–F♯–G–A♭–B♭–B. With nine pitches available, you have more harmonic options but the mode still excludes three chromatic pitches (D♭, F, A). Notice how these "gaps" create the mode's distinctive character.

Level 3: Modal Modulation

Exercise 3.1: Transposition Change Write a passage in Mode 2, first transposition. At the midpoint, shift to Mode 2, second transposition (C♯–D–E–F–G–A♭–B♭–B). Find smooth voice-leading between the two transpositions—which pitches are common to both?

Exercise 3.2: Mode-to-Mode Modulation Write a passage that begins in Mode 2 and modulates to Mode 3. Plan the transition: which pitches do these modes share in your chosen transpositions? Can you find a chord that belongs to both modes as a pivot?

Exercise 3.3: Modal-Tonal Mixture Write a passage in Mode 2 that clearly establishes F♯ major as tonal center. Use the dominant seventh of F♯ (C♯7) and frequent returns to F♯ in the bass. Notice how tonal orientation and modal color coexist.

Level 4: Special Chords and Resonance

Exercise 4.1: Chord of Resonance Build the chord of resonance from a low C: add the pitches suggested by the overtone series (E, G, B♭, D, F♯, and higher partials as desired). Voice it in different registrations—spread across the keyboard, clustered in middle register, with wide bass and close upper voices.

Exercise 4.2: Stained-Glass Window Take one chord (try the chord of resonance or the added-sixth-plus-augmented-fourth chord). Create a passage where this single harmony appears in multiple inversions over a pedal bass, with different voicings and registrations. The harmony doesn't change; only its coloring shifts.

Exercise 4.3: Superior and Inferior Resonance Write a simple chord progression. Add "superior resonance" (small chord clusters above each main chord) and "inferior resonance" (clusters below). Experiment with how close or distant these resonance clusters are from the principal harmony.

Level 5: Enlargement and Gesture

Exercise 5.1: Pedal Group Create a four-chord pattern (not a single pedal note, but a complete repeating progression). Loop this as an ostinato in one hand while the other hand plays freely above or below it. The looping pattern functions as a single "enlarged pedal."

Exercise 5.2: Upbeat-Accent-Termination Write a phrase with exaggerated gesture: an "immense" upbeat (four or more bars of preparation building in register and dynamics), a sudden accent (fortissimo arrival), and an extended termination (gradual dissolution over several bars). Then try separating these elements with rests.

Exercise 5.3: Embellishment Group Write a held chord. Before resolving it, insert an "immense scroll"—an elaborate flourish that ornaments the chord's top note before finally moving to the next harmony. The flourish should feel like a single ornament despite lasting several beats.

Level 6: Polymodality

Exercise 6.1: Two-Mode Superposition Right hand: write a passage using Mode 3, first transposition. Left hand: write an accompaniment using Mode 2, second transposition. Each hand must stay strictly within its assigned mode. Listen to the vertical combinations that result—neither mode alone produces these sonorities.

Exercise 6.2: Unequal Pedal Groups Create two polymodal pedal groups of different lengths (e.g., 5 chords in Mode 3 above, 4 chords in Mode 2 below). Loop both simultaneously. They'll realign after 20 iterations—but notice the shifting vertical relationships along the way.

Exercise 6.3: Polymodal Modulation Write a passage that begins with Mode 3 over Mode 2, then modulates to Mode 2 over Mode 3 (exchange which mode is in which layer). Finally, modulate to a completely different combination (Mode 6 over Mode 4, for instance). Plan voice-leading for smooth transitions.

Level 7: Integration

Exercise 7.1: Complete Miniature Write a 16-bar piece that uses:

• Added notes (at least added sixth and augmented fourth)
• One mode of limited transpositions as primary harmonic material
• At least one modal modulation (transposition change or mode change)
• One instance of upbeat-accent-termination articulation

Exercise 7.2: Parametric Coordination Write a passage combining:

• Nonretrogradable rhythm in one voice
• Mode of limited transpositions in harmony
• Added values in melodic rhythm
• Added notes in chord voicings

The symmetry principles should operate in parallel across parameters.

Exercise 7.3: Your Harmonic Signature After working through these exercises, identify:

• Which mode(s) appeal most to your ear?
• Which added-note combinations feel most characteristic?
• What voicing preferences have emerged?
• How do you tend to handle modal modulation?

Document these discoveries in Part IV (the composer's workbook). This is the beginning of understanding your own harmonic language through Messiaen's method of systematic self-observation.

The Transcendental Rainbow

Messiaen concludes his modes chapter by asking whether we need reminding of their deeper purpose: creating "that sort of theological rainbow which the musical language, of which we seek edification and theory, attempts to be." This isn't decorative rhetoric—it's statement of purpose.

The modes exist "in the atmosphere of several tonalities" because they embody transcendence, hovering between earthly key areas without settling into any. They possess "impossibility of transposition" because this creates "strange charm," the fascination with structural impossibility that pervades the entire treatise. They connect to nonretrogradable rhythms because symmetry—whether temporal or transpositional—manifests divine order, eternal structures existing outside human temporality.

You don't need to share Messiaen's theology to recognize what he's offering: harmonic materials that escape traditional functional progressions while avoiding arbitrary chromaticism, colors that shimmer with internal complexity while maintaining perceptual clarity, structures that feel inevitable through their symmetrical logic yet utterly distinctive from conventional harmony. Whether you hear them as manifestations of divine order or simply as powerful compositional resources, the modes work.

Your Harmonic Journey

The seven harmony chapters present not a rigid system but an invitation. Start where connection feels strongest—perhaps the added-note principle resonates with how you already enrich chords, or the upbeat-accent-termination complex clarifies phrase structures you've been using intuitively, or a specific mode's color captivates your ear.

Messiaen provides 200+ musical examples not as prescriptions but as demonstrations: here's what these materials might do, now discover what they do in your hands. The extensive catalog of chord connections in Chapter XIV isn't exhaustive formula-book but creative springboard. The polymodal combinations in Chapter XIX aren't the only possibilities but examples of what superposition offers.

Most importantly: these techniques exist to serve expression, not to display technique. Every harmonic choice Messiaen describes connects to affective goals—"anguish," "tenderness," "divine love," "infinite gorgeousness." The question isn't "how do I use Mode 2?" but "what does Mode 2 help me express?" The theological rainbow isn't about complexity for its own sake; it's about discovering harmonic materials adequate to spiritual and emotional experience that traditional harmony can't quite capture.

Your task now isn't to master every mode, memorize every cadence formula, or systematically work through every polymodal combination. It's to find which materials speak to your musical imagination, experiment with them in your own contexts, discover what they enable that your previous harmonic vocabulary didn't. Some composers might use these modes as primary language; others might deploy them sparingly for special moments. Both approaches are valid.

The harmony section culminates not in prescriptive rules but in generous offering: here are resources for creating harmonic language both systematic and sensuous, both structurally rigorous and coloristically luxuriant. The modes await your filtering, refining, transforming presence. The theological rainbow isn't something Messiaen created—it's something he discovered and now invites you to explore for yourself.

What colors will you find there?