This section maps the interconnections across Messiaen's system—the parametric analogies, technique clusters, and conceptual threads that unify rhythm, melody, and harmony.
Rhythm (Horizontal) Harmony (Vertical) Shared Principle
Nonretrogradable rhythms (Ch. V) Modes of limited transposition (Ch. XVI) Symmetry creates "impossibility" Added values (Ch. III) Added notes (Ch. XIII) Enrichment through supplementation Polyrhythm (Ch. VI) Polymodality (Ch. XIX) Independence of simultaneous layers Rhythmic pedal (Ch. VI) Pedal group (Ch. XV) Repetition as structural anchor
The "Charm of Impossibilities" (Ch. I) unifies all:
Nonretrogradable rhythms → "unity of movement" (beginning and end identical)
Limited transposition modes → "tonal ubiquity" (multiple tonalities at once)
Both → "theological rainbow" pointing toward transcendence
Technique Domain Chapter Effect
Added value Rhythm III Metric displacement, "delicious limping" Added note Harmony XIII Harmonic enrichment, color Dot addition Rhythm IV 1.5× augmentation Added sixth Harmony XIII Characteristic Debussy sonority Added aug. fourth Harmony XIII Mode 2 chord color
Shared aesthetic : "Somewhat perverse charm" of foreign elements that enrich without destroying identity.
Technique Domain Chapter Symmetry Type
Nonretrogradable rhythm Rhythm V Temporal palindrome Mode of limited transposition Harmony XVI Pitch-class invariance Central common value Rhythm V Axis of reflection Ternary sentence Form XI Formal arch (ABCBA)
Shared property : Structure reads same in multiple directions or positions.
Original Enlarged Form Chapter
Pedal tone Pedal group XV Passing tone Passing group XV Embellishment Embellishment group XV Appoggiatura Upbeat-accent-termination XV
Shared principle : Single-note phenomena become complete musical structures.
Hindu rhythm analysis
├── Added values (Ch. III)
├── Inexact augmentation (Ch. IV)
└── Nonretrogradable rhythms (Ch. V)
Impressionist harmony
├── Added notes
├── Added sixth chord
├── Whole-tone scale (Mode 1)
└── Stained-glass window effect
Liturgical chant
├── Anthem forms
├── Alleluia/vocalise
├── Kyrie structure (3×3)
├── Sequence form
└── Psalmody
Avian vocalization
├── Rhythmic freedom
├── Melodic unpredictability
├── Ornamental density
└── Registral extremes
Form Structure Key Technique
Terminal development Build to climax over pedals Elimination, amplification Three-theme development Themes → final theme emerges Teleological form Theme 1 variations + Theme 2 developments Alternating structure Developmental contrast
Form Structure Liturgical Origin
Anthem Refrain alternating with verses Antiphonal psalmody Alleluia Intonation + jubilus + verse Mass Proper Psalmody Reciting tone + cadence Office psalmody Kyrie 3×3 invocations Mass Ordinary Sequence Paired strophes, same final Medieval sequence
Type Pattern Periods
Song-sentence ABA' 3 (theme, middle, final) Binary ABAB' 4 (theme, commentary alternation) Ternary ABCBA 5 (arch form)
Chord Type Source Mode Chapter
Added sixth + aug. fourth Mode 2 XIII, XIV, XVI Chord of resonance Mode 3 XIV, XVI Chord in fourths Mode 5 XIV, XVI Dominant with all scale tones Diatonic (not a mode) XIV
Operation Factor Chapter
Classical augmentation 2× IV Classical diminution 0.5× IV Triple augmentation 3× IV Quadruple augmentation 4× IV
Operation Effect Chapter
Added note +1 small value III Added rest +1 small rest III Added dot +0.5 original III, IV Dot withdrawal −0.33 original IV
Operation Components Chapter
Inexact augmentation Different rates per layer IV Augmentation + added value Proportional + non-proportional IV
Operation Effect Historical Model Chapter
Elimination Progressive reduction Beethoven 5th Symphony X Interversion Pitch reordering Dupré improvisation X Registral change Octave displacement Berg Lyric Suite X Contrary motion Melodic inversion Traditional counterpoint VIII Retrograde Temporal reversal Traditional counterpoint V, VIII
Type Layers Result
Unequal lengths Different periods Phasing until realignment Different augmentations Same rhythm, different rates Tempo stratification Rhythm + retrograde Forward + backward Mirror counterpoint Rhythmic canon Staggered entries Imitative texture Canon by dot addition Following voice dotted 1.5× stretching Canon of nonretrogradables Palindromic entries Symmetrical canon Rhythmic pedal Ostinato layer Temporal anchor
Technique Spiritual Meaning
Nonretrogradable rhythm Eternity (no beginning/end distinction) Modes of limited transposition Divine presence in multiple "tonalities" Symmetry Divine order, perfection Bird song "Servants of immaterial joy" Alleluia/vocalise Sacred jubilation Kyrie (3×3) Trinity Stained-glass window effect Cathedral light, sacred space Natural harmony Pre-existent in divine creation
Ch. I: Aesthetic Foundation
↓
Ch. II–VII: RHYTHM Ch. VIII–XII: MELODY
II: Hindu source VIII: Intervals, contours
III: Added values ←──────────────→ XIII: Added notes
IV: Augmentation/diminution IX: Bird song
V: Nonretrogradable ←────────────→ XVI: Limited transposition
VI: Polyrhythm ←─────────────────→ XIX: Polymodality
VII: Notation
X: Development
XI: Sentences
XII: Forms
↓
Ch. XIII–XIX: HARMONY
XIII: Added notes
XIV: Special chords
XV: Enlargement
XVI: Modes (KEYSTONE)
XVII: Modal modulation
XVIII: Relations to other systems
XIX: Polymodality (CULMINATION)
Topic Primary Chapter Related Chapters
Rhythm basics II, III IV, V, VI, VII Polyrhythm VI III, IV, V Melodic intervals VIII X Bird song IX VIII Development techniques X VIII, XI Phrase/sentence structure XI XII Large forms XII XI Debussy's influence XIII VIII, XIV Chords XIV XIII, XVI Dissonance/foreign notes XV XIII, XIV Modes XVI XVII, XVIII, XIX Mixing modes with tonality XVII XVI, XVIII Modes vs. other systems XVIII XVI, XVII Polymodality XIX VI, XVI, XVII