34.01.03 · music-art / music-fundamentals

Musical form and analysis: sonata form, rondo, theme and variations; set theory in post-tonal music

stub3 tiersLean: nonepending prereqs

Anchor (Master): Schoenberg, A. — Fundamentals of Musical Composition (1967)

Intuition Beginner

Musical form is the architecture of a piece — how sections are organized in time. The smallest unit is a phrase, like a sentence in language. Two phrases often form a question-answer pair: the antecedent asks, the consequent answers. Group phrases together and larger shapes appear. Binary form has two sections, A then B. Ternary has three, A-B-A, where the opening returns after a contrast. These patterns let the listener orient: knowing where one is in a piece is half of listening.

Some forms stretch a single idea across a whole work. Theme and variations takes a melody and transforms it repeatedly — Mozart's variations can turn a simple tune into a dazzling display. Rondo alternates a recurring theme with contrasting episodes, A-B-A-C-A, the returns acting as landmarks. The most important large form in Western classical music is sonata form. Its three sections are exposition (two contrasting themes in different keys), development (themes fragmented and recombined dramatically), and recapitulation (themes restated, now all in the home key). Sonata form shaped symphonies, sonatas, quartets, and concertos for 150 years.

The twentieth century broke the frame. Arnold Schoenberg abandoned tonality, dissolving the hierarchy of keys that had made sonata form's argument possible. To analyze music no longer built on keys, Allen Forte developed pitch-class set theory, a way of grouping notes into families by the intervals between them. Form did not vanish, but it changed character — from tonal drama to texture, process, and series. This unit traces form from phrase to fugue to the set-theoretic analysis of atonal works.

Visual Beginner

Form	Sections	Typical use	Defining move
Binary	A – B	Baroque dances, early sonatas	Two related but contrasting halves
Ternary	A – B – A	Songs, minuets, nocturnes	Contrast, then return
Theme and variations	A – A′ – A″ – …	Classical slow movements, standalone works	One melody, repeated transformations
Rondo	A – B – A – C – A	Classical finales	Recurring refrain between episodes
Sonata form	Exposition – Development – Recapitulation	Symphonies, sonatas, quartets (first movements)	Tonal argument between two key areas
Fugue	Subject entries + episodes	Baroque keyboard and choral works	One theme in overlapping voices

Worked example Beginner

Take the first movement of Mozart's Symphony No. 40 in G minor as sonata form. The exposition opens in G minor with the famous first theme — tense, whispered, built from a rising leap and a falling half step. A transition drives toward the relative major, B-flat. The second theme arrives in B-flat major, gentler and more lyrical — the contrast of key and character is the exposition's argument. A closing theme rounds off the section, and the whole exposition repeats.

The development takes fragments of the first theme through distant keys, sequence upon sequence, the tension climbing. A retransition — a sustained dominant — pulls the ear back toward G minor. The recapitulation restates the first theme in G minor. Now the second theme also returns in G minor, not B-flat: the tonal conflict of the exposition is resolved. A brief coda closes. Three sections, one argument: depart, transform, return.

Check your understanding Beginner

Formal definition Intermediate+

Model the twelve pitch classes of equal temperament as $Z_{12}$ , with C = 0; octave equivalence folds every pitch onto one class 34.01.02 pending. A pitch-class (pc) set is a subset $A \subseteq Z_{12}$ . The normal form of $A$ is the ascending ordering of its elements, rotated so that the interval from first to last is minimized (ties broken toward the most compact left packing). The prime form is obtained by transposing the normal form to begin at $0$ and, if the set and its inversion would then differ, choosing the more left-packed of the two; prime forms are written in square brackets. Two pc sets with the same prime form lie in the same set class — the same orbit under transposition and inversion. Allen Forte catalogued $208$ distinct set classes of cardinalities $3$ through $9$ , each carrying a label such as 3-11 (the major/minor triad, prime form $[0, 3, 7]$ ) or 4-27 (the dominant seventh) ^{[source pending]}.

The interval vector $IV (A) = ⟨ n_{1}, \dots, n_{6} ⟩$ records, for each interval class $k \in {1, \dots, 6}$ , how many unordered pairs of elements of $A$ lie $k$ semitones apart:

n_{k} = # {{a, b} \subseteq A : min (∣ a - b ∣, 12 - ∣ a - b ∣) = k}, k = 1 \sum 6 n_{k} = (2 ∣ A ∣) .

Phrase structure and formal function (Caplin). A motif is the smallest identifiable musical unit. A phrase is a 2–4 measure span closed by a cadence. A period pairs an antecedent phrase (ending with a weak or half cadence — the question) with a consequent (ending with a stronger authentic cadence — the answer). A sentence is the other basic eight-measure theme-type: a presentation (a basic idea stated and repeated sequentially) followed by a continuation (fragmentation of the motif, accelerated harmonic rhythm, liquidation, cadence). William Caplin's formal-function theory labels what a passage does rather than what it contains: presentation, continuation, transition, subordinate-theme, development, recapitulation, post-cadential ^{[source pending]}. This complements the harmonic categories of 34.01.02: cadence types become functions, modulations become transitions.

Binary and ternary. Simple binary has two sections (A–B), each typically repeated. Rounded binary (A–B-A′) returns material from A at the close of B and is the ancestor of the Classical minuet and trio. Ternary (A–B-A) places a contrast between two statements of the same section; it is the song form common to nocturnes, marches, choruses, and popular music.

Variation forms. Theme and variations reiterates a theme under systematic change: melodic ornamentation, harmonic reharmonization, rhythmic or metric displacement, mode change, contrapuntal elaboration (canon, fugue), or character transformation (each variation a new mood). The passacaglia and chaconne fix a repeating bass line or harmonic progression (the ostinato) and vary the upper voices above it — Bach's D-minor Chaconne and the finale of Brahms's Fourth Symphony are canonical.

Rondo. The refrain A alternates with episodes: the five-part rondo A-B-A-C-A, the seven-part rondo A-B-A-C-A-B-A. The sonata-rondo hybrid fuses rondo with sonata-form development, the C behaving like a development and the final B′ like a recapitulation of the second theme — a Beethoven favourite [34.02.*].

Sonata form. The first-movement form of most Classical symphonies, sonatas, quartets, and concertos:

Section	Function	Key plan
Exposition	Present themes	First theme group in tonic (i); transition modulates; second theme group in dominant (V) or relative major (III); closing theme
Development	Fragment, sequence, modulate	Through related and distant keys; retransition returns to tonic
Recapitulation	Resolve the conflict	First theme in tonic; transition modified or non-modulating; second theme in tonic; closing theme in tonic
Coda (optional)	Confirm closure	Tonic

Hepokoski and Darcy read sonata form dialogically as a rotation through thematic zones with a recapitulation that must be won; Caplin reads it as a sequence of formal functions. Both treat the tonal argument between first and second theme groups as the form's engine ^{[, 34.01.02]}.

Concerto form. Baroque ritornello form (Vivaldi) alternates orchestral ritornello returns in related keys with solo episodes. The Classical double-exposition concerto has the orchestra present an exposition, then the soloist present a second exposition with wider thematic range; an unaccompanied cadenza precedes the recapitulation's coda [34.02.*].

Fugue. A contrapuntal form built on a single subject (S). The subject is stated alone, then answered in the dominant (answer, A — a real answer transposes S exactly, a tonal answer adjusts to preserve the key). A countersubject (CS) accompanies later entries; episodes are modulatory passages built from S and CS fragments. Stretto overlaps entries before the previous one finishes; inversion, augmentation, diminution, and retrograde transform the subject. Bach's Art of Fugue and Well-Tempered Clavier exhaust the form's resources 34.01.02 pending.

Serialism and post-serial analysis. Schoenberg's twelve-tone technique orders the twelve pitch classes into a tone row; admissible forms are prime (P), inversion (I), retrograde (R), and retrograde inversion (RI). The row and its transpositions generate a $12 \times 12$ matrix. Milton Babbitt's combinatoriality and integral serialism, and Messiaen's Mode de valeurs, serialize rhythm, dynamics, and articulation alongside pitch [42., 50., 34.02.03].

Key theorem with proof Intermediate+

The interval vector is the workhorse invariant of post-tonal analysis, and pinning down exactly what it does and does not determine is this section's key theorem: it is invariant under the full transposition-inversion group but fails to separate every set class ^{[source pending]}.

Theorem (interval-vector invariance and Z-relations). For any pitch-class set $A \subseteq Z_{12}$ and any transposition $T_{n} (x) = x + n$ or inversion $I_{n} (x) = n - x$ (mod $12$ ),

IV (T_{n} (A)) = IV (A) = IV (I_{n} (A)) .

Hence the interval vector is a $T / I$ -invariant. It is not complete: distinct set classes may share an interval vector. The pair 4-Z15 $= [0, 1, 4, 6]$ and 4-Z29 $= [0, 1, 3, 7]$ both have vector $⟨ 1, 1, 1, 1, 1, 1 ⟩$ yet are not $T / I$ -equivalent.

Proof. Transposition first. For any unordered pair ${a, b} \subseteq A$ ,

T_{n} (a) - T_{n} (b) = (a + n) - (b + n) = a - b (mod 12),

so $min (∣ T_{n} (a) - T_{n} (b) ∣, 12 - ∣ T_{n} (a) - T_{n} (b) ∣) = min (∣ a - b ∣, 12 - ∣ a - b ∣)$ : the pair maps to a pair of the same interval class. Since $T_{n}$ is a bijection on $Z_{12}$ , it induces a bijection on the unordered pairs of $A$ , so the count $n_{k}$ is unchanged for every $k$ . Thus $IV (T_{n} (A)) = IV (A)$ .

Inversion next. For any pair ${a, b}$ ,

∣ I_{n} (a) - I_{n} (b) ∣ = ∣ (n - a) - (n - b) ∣ = ∣ b - a ∣ = ∣ a - b ∣ (mod 12),

so again each pair is carried to a pair of identical interval class, and the induced map on pairs is bijective. Hence $IV (I_{n} (A)) = IV (A)$ .

To see the invariant is not complete, exhibit the all-interval tetrachords. For $A = {0, 1, 4, 6}$ the six unordered pairs yield interval classes

pair	class
(0,1)	1
(0,4)	4
(0,6)	6
(1,4)	3
(1,6)	5
(4,6)	2

giving $IV (A) = ⟨ 1, 1, 1, 1, 1, 1 ⟩$ . For $B = {0, 1, 3, 7}$ the pairs give classes $1, 3, 5, 2, 6, 4$ — the same multiset, hence $IV (B) = ⟨ 1, 1, 1, 1, 1, 1 ⟩$ .

The two sets are nonetheless in different $T / I$ -orbits. Their prime forms, $[0, 1, 4, 6]$ and $[0, 1, 3, 7]$ , are distinct, and prime form is by construction the canonical representative of the orbit: two sets with distinct prime forms lie in distinct orbits, so no $T_{n}$ or $I_{n}$ carries one onto the other. The interval vector therefore agrees on two inequivalent classes and cannot be a complete invariant. Forte flags such coincidences with the letter Z; the all-interval tetrachords 4-Z15 and 4-Z29 are the smallest and most cited example [34.01.02, 42.*].

Exercises Intermediate+

Exercise (hard, short answer).

A twelve-tone row generates 48 row forms via the operations P, I, R, RI and twelve transposition levels. Explain why the count is 48, and show that a palindromic row (one equal to its own retrograde) cuts the number to 24.

Answer

There are four operations (P, I, R, RI) and twelve transposition levels ( $0, \dots, 11$ ); for a generic row these $4 \times 12 = 48$ forms are all distinct. The Babbitt matrix arranges them: the twelve prime forms P $_{n}$ and twelve inversions I $_{n}$ fill a $12 \times 12$ square, and reading any row or column backward recovers the corresponding retrograde R $_{n}$ or retrograde inversion RI $_{n}$ .

If the row is palindromic, then R $_{0} =$ P $_{0}$ , and by transposing both sides R $_{n} =$ P $_{n}$ for every $n$ ; the R family collapses into the P family. Applying inversion to the palindrome gives RI $_{n} =$ I $_{n}$ , collapsing the RI family into the I family. The 48 distinct forms reduce to 24. Webern and Berg exploited such symmetries to bind a row together internally.

Advanced results Master

Three theories of sonata form. William Caplin's Classical Form (1998) builds a theory of formal functions: each passage is classified not by its thematic content but by what it does — present, continue, transition, develop, recapitulate, or close — with closure graded (perfect authentic, imperfect authentic, half, deceptive) to determine how a theme may end. James Hepokoski and Warren Darcy's Elements of Sonata Theory (2006) reads sonata form as a dialogic rotation through thematic zones (P, TR, S, C, ESC), with a recapitulation that is negotiated rather than automatic; sonatas come in types (Type 1, 2, 3) and may be deformed. Arnold Schoenberg's Fundamentals of Musical Composition (1967) treats form as organic growth from a motive by developing variation — the seed unfolds into the whole. Where Caplin asks what a section does, Hepokoski-Darcy ask how it argues with generic norms, and Schoenberg asks whence it grows. The disagreement is productive: the same Beethoven movement answers all three questions differently ^{[, 20.08., 20.04.]}.

Form and narrative. Leonard Meyer's Emotion and Meaning in Music (1956) grounds form in the listener's expectations: a refrain promises return, a dominant pedal promises tonic, and the composer's manipulation of those promises — fulfilment, delay, denial — is the felt shape of the work. Anthony Newcomb extended this to narrative, reading Schumann's symphonies and Schubert's instrumental works as stories with protagonists, setbacks, and resolutions, arguing that listeners impose plot structures on instrumental music. Lawrence Kramer's hermeneutic program asks the harder question of what music means, importing Clifford Geertz's thick description from cultural anthropology. Susan McClary's Feminine Endings (1991) gave the narrative reading a political edge: sonata form, she argued, stages a gendered drama in which a masculine first theme in the tonic penetrates, subdues, or assimilates a feminine second theme in the dominant — a reading that ignited debate about whether analytical categories encode social ones [31.02.*, 30.04.04].

Form and society. Sonata form flourished alongside the Enlightenment, and analysts have long read its dialectic of thematic and tonal conflict as the musical analogue of rational progress: thesis, antithesis, synthesis. The parallel is suggestive but should be handled with care. Theodor Adorno's Philosophy of New Music (1949) treated sonata form as the expression of bourgeois subjectivity — a subject who sets out, suffers alienation in the development, and is reconciled (or, in late Beethoven, pointedly not) in the recapitulation. For Adorno the dissolution of sonata form in Mahler and Schoenberg tracks the crisis of that subject under monopoly capitalism. Whether one accepts the sociology, the historical point stands: the form's prestige rose and fell with the institutions — the concert hall, the bourgeois public sphere, the cult of genius — that framed it [30.02.03, 32.17., 34.02.].

Post-tonal theory and mathematics. Allen Forte's pitch-class set theory (1973) gave analysts of atonal music a vocabulary of set classes, interval vectors, and set-complex relations; it remains the standard entry point though its cognitive neutrality has been contested. David Lewin's Generalized Musical Intervals and Transformations (1987) generalized the framework: a musical space is a set equipped with a group of intervals acting on it, and analysis becomes the study of transformations between objects rather than properties of objects in isolation. This transformational theory subsumes transposition, inversion, the neo-Riemannian $P$ , $L$ , $R$ , and rhythmic and motivic operations as instances of one pattern. Dmitri Tymoczko's A Geometry of Music (2011), building on Callender, Quinn, and Tymoczko, models $n$ -note chords as points in the orbifold $T^{n} / S_{n}$ ; voice leadings become geodesics, and the classical rules of parsimonious voice leading become statements about shortest paths in the quotient. Ian Quinn's General Equal-Tempered Harmony recasts harmony in terms of Fourier phases on the pitch-class circle. The mathematics is now a two-way street: music supplies problems for algebra and geometry [42., 20.09., 33.07., 50.].

Form in non-Western music. Western formal categories are not universal. Indian classical music organizes a performance as an unfolding of a raga (melodic framework) within a tala (rhythmic cycle); the slow opening alap explores the raga pulselessly before the jor and jhala introduce rhythm and accelerating tempo, with composition and variation negotiated between soloist and drummer rather than fixed in a score. The Arabic waslah is a suite of instrumental and vocal pieces in a single mode. Javanese gamelan music is structured by colotomic patterns — the cyclic striking of gongs and kettle-gongs (kenong, kempul) that mark the form — rather than by thematic return. Japanese gagaku inherits the jo-ha-kyu principle of introduction, scatter, and rush. Each system answers the same question — how to organize sound in time — with different architecture, and the comparison tests whether sonata form's dramatic logic is a local convention or a deeper tendency [31.05., 31.02., 34.02.03].

Form in popular music. Popular music runs on a smaller repertoire of forms, and their simplicity is a strength. The verse-chorus structure alternates narrative verses with a recurring, hook-laden chorus; a bridge provides contrast, and intro and outro frame the song. The 32-bar AABA form, standardized by Tin Pan Alley (Gershwin, Porter, Berlin), chains two A sections, a release (B, the bridge), and a final A — the harmonic cousin of sonata form's tonal arc. The 12-bar blues is a three-line scheme over a I–IV–I–V–I progression that underlies everything from Robert Johnson to bebop. Strophic form (the same music for each stanza) serves folk song and hymns; through-composed form, in which new material continually replaces old, marks progressive rock and art song. Memorability tracks formal economy: the earworm thrives on the return a listener can predict and then sing [30.02.03, 29.05., 36.].

Form and computing. Computational approaches now engage form directly. David Cope's Experiments in Musical Intelligence (EMI) analyzed the syntactic fingerprints of Bach, Mozart, and Chopin and generated convincingly style-faithful inventions, sonata movements, and chorales — provoking sharp debate about whether style simulation is composition. The music21 toolkit (Michael Cuthbert) provides a Python library for symbolic music analysis, including automated formal segmentation and harmonic parsing. Music Information Retrieval (MIR) trains models on audio for automatic chord recognition, beat tracking, and structure analysis (verse/chorus/bridge detection), the last often by self-similarity matrices over spectral features. Generative systems from Brian Eno's ambient procedures to contemporary diffusion and transformer models raise the question Meyer posed of expectation: a model that reproduces a style's statistics need not manipulate expectation with intent, and the gap between the two is where the aesthetic and copyright arguments now turn [33.07., 50., 36.*].

Form and cognition. Cognitive science reframes form as a memory structure. To follow a sonata, a listener must remember the first theme across the development and recognize its return — a demand on working and long-term musical memory that explains why teaching and repeated listening deepen appreciation. David Huron's Sweet Anticipation (2006) recasts Meyer's expectation theory in the predictive-processing framework: the brain is a prediction machine, musical form is the choreography of its errors, and tonal cadences are reward signals. Isabelle Peretz and Robert Zatorre's neuroscientific work maps tonal and formal processing to temporal-lobe and frontal networks and shows it dissociable from language [29.04., 29.05., 29.02.*].

Form and emotion. The emotional force of large-scale form is the meeting point of analysis and psychology. Patrik Juslin and John Sloboda's Handbook of Music and Emotion catalogues mechanisms — brainstem reflex, episodic memory, musical expectancy, emotional contagion — by which form moves us. Stefan Koelsch's work on music and neurochemistry implicates the dopaminergic reward system in peak responses to cadential closure and thematic return. John Sloboda's surveys of musical chills locate the strongest peaks at structural returns — the reprise of a theme after a wrenching development — connecting the analytic event (the recapitulation) to the physiological one. The Kantian sublime, in this light, is not far away: the listener survives the development's disorder and is returned, transformed, to the tonic [29.11.02, 29.02.03, 20.04.*].

Connections Master

Musical form is built on the harmonic and contrapuntal substrate of 34.01.02: cadences punctuate periods, modulations drive developments, voice-leading routines shape the themes that sonata form and fugue manipulate. Every analytic claim in the Western art music strand (34.02.*) — Bach's fugues, the Classical symphony, Romantic character pieces, the 20th-century dissolution of tonality (34.02.03) — presupposes the formal types catalogued here, and the historical survey to come (34.02.02) is where those types are traced across repertoires.

Form is heard as well as built. The cognitive and emotional ground lies in psychoacoustics (29.03.03), cognition (29.05.), and emotion theories (29.11.02), which together explain why a recapitulation's return registers as resolution and a deceptive cadence as surprise. Memory systems (29.04.) are the substrate without which large-scale form cannot be tracked at all: a sonata is, among other things, a controlled exercise in what a listener can be asked to remember.

The mathematics connects upstream to set theory, group theory, and algebra (42.): $Z_{12}$ , the $T / I$ dihedral group of 34.01.02, Forte's set classes, and the orbifolds of voice-leading space are pure-algebra objects, and the question of whether they are discovered or invented belongs to mathematical ontology (20.09.) and aesthetics (20.04.). The philosophy of whether form prescribes or describes reaches into philosophy of science (20.08.) and philosophy of art (20.04.*).

Computational and cultural threads run forward: AI and algorithmic composition (33.07., 50.) formalize form generation and analysis; media literacy (36.) examines how platform recommendation and the popular-music economy reshape the forms of the present; ethnomusicology and cultural anthropology (31.02., 31.05.*) carry the comparative question to non-Western architectures; and the gender and society strands (30.04.04, 30.02.03) inherit McClary's and Adorno's politically charged readings of the sonata.

Historical and philosophical context Master

The theory of musical form was codified a generation after the forms themselves. Heinrich Christoph Koch's Versuch einer Anleitung zur Composition (1782–93) described phrase structure, periods, and the sonata-allegro plan in empirical detail, treating form as the grammar a competent composer already obeyed. Anton Reicha's Traité de haute composition musicale (1826) catalogued fugue, variation, and sonata form as teachable schemata. In the 19th century Adolf Bernhard Marx coined the term Sonatenform and fixed the exposition–development–recapitulation triad in the German pedagogical imagination — a schematization later projected back onto Haydn and Mozart, who had composed by more flexible lights.

Analytic theory in the 20th century split between descriptive and prescriptive impulses. Donald Tovey's essays treated each work as an individual, resisting the tyranny of the textbook schema; Schoenberg's Fundamentals of Musical Composition (1967) taught form as organic yet also proposed ideal templates. Caplin and Hepokoski-Darcy, in different keys, restore the descriptive ambition while sharpening the categories — Caplin by function, Hepokoski-Darcy by dialogic type. The philosophical question — whether form is a property of the work, a construct of the listener, or a convention of a style — is never far below the surface [20.08., 20.04.].

When Schoenberg dissolved tonality, the formal functions hitched to tonal drama lost their engine. Allen Forte's The Structure of Atonal Music (1973) responded by building a taxonomy of pitch-class collections that could organize atonal works the way keys and themes organized tonal ones. The tool was controversial — George Perle and others argued set theory obscured the row-based logic of serial music, and cognitive scientists questioned whether listeners actually hear set classes — but it gave post-tonal analysis its first shared vocabulary. Lewin's transformational reframing and Tymoczko's geometric one deepened the mathematics without resolving the aesthetic question of whether post-tonal form persuades by the same mechanisms as tonal form [42.*, 34.02.03].

Behind the history lies the ancient question of whether musical form is discovered or invented. The Pythagorean and Rameauian line hears form as the unfolding of natural order; the conventionalist and cultural-relativist line hears it as a learned grammar that East and West elaborate differently. The curriculum carries both: sonata form as the Enlightenment's supreme tonal argument, and the world's other architectures — raga, maqam, colotomic cycle, AABA, 12-bar blues — as equally valid answers to the problem of organizing sound in time [33.01.02, 31.05., 20.09.].

Bibliography Master

Koch, Heinrich Christoph. Introductory Essay on Composition: The Mechanical Rules of Melody. Trans. N. K. Baker. New Haven: Yale University Press, 1983. Originally published 1782–93.
Reicha, Anton. Traité de haute composition musicale. Paris, 1826.
Marx, Adolf Bernhard. Die Lehre von der musikalischen Komposition. Leipzig, 1837–47.
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Tovey, Donald Francis. Essays in Musical Analysis. London: Oxford University Press, 1935–39.
Meyer, Leonard B. Emotion and Meaning in Music. Chicago: University of Chicago Press, 1956.
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Lewin, David. Generalized Musical Intervals and Transformations. New Haven: Yale University Press, 1987.
Newcomb, Anthony. "Schumann and Late Eighteenth-Century Narrative Strategies." 19th-Century Music 11 (1987): 164–174.
Caplin, William E. Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. New York: Oxford University Press, 1998.
McClary, Susan. Feminine Endings: Music, Gender, and Sexuality. Minneapolis: University of Minnesota Press, 1991.
Adorno, Theodor W. Philosophy of New Music. Trans. R. Hullot-Kentor. Minneapolis: University of Minnesota Press, 2006. Originally published 1949.
Cope, David. Experiments in Musical Intelligence. Madison, WI: A-R Editions, 1996.
Hepokoski, James, and Warren Darcy. Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata. New York: Oxford University Press, 2006.
Huron, David. Sweet Anticipation: Music and the Psychology of Expectation. Cambridge, MA: MIT Press, 2006.
Tymoczko, Dmitri. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press, 2011.
Juslin, Patrik N., and John A. Sloboda, eds. Handbook of Music and Emotion. Oxford: Oxford University Press, 2010.