Music Theory

Notation

The Staff

• Neumes — symbols used in medieval manuscripts to notate plainchant; the precursors to modern note shapes, indicating melodic contour and ornament without precise pitch.
• Staff — the five horizontal lines and four spaces on which musical notation is written; pitches are assigned to lines and spaces.
• Treble clef (G clef) — the ornate symbol that curls around the second line, designating that line as G4; used for higher-pitched instruments and voices.
• Bass clef (F clef) — the symbol with two dots straddling the fourth line, designating it as F3; used for lower-pitched instruments and voices.
• Alto clef / tenor clef — C clefs that place middle C (C4) on the third or fourth line, respectively; used by viola, trombone, bassoon.
• Ledger lines — short lines added above or below the staff to extend the range of notatable pitches.
• Grand staff — the treble and bass staves joined by a brace; used for keyboard music.

Notes and Rests

• Whole note / whole rest — four beats in 4/4; rest hangs below a line.
• Half note / half rest — two beats; open notehead with stem; rest sits on top of a line.
• Quarter note / quarter rest — one beat; filled notehead with stem.
• Eighth note / eighth rest — half a beat; filled notehead with a flag (or beam when grouped).
• Sixteenth note — quarter of a beat; two flags or beams.
• Dot — placed after a notehead to add half its value (e.g., dotted quarter = 1.5 beats). A second dot adds half of the added value.
• Tie — a curved line connecting two noteheads of the same pitch, extending the duration without re-articulating.
• Slur — a curved line over different pitches indicating legato performance.

Time Signatures and Meter

• Time signature — a fraction-like symbol (e.g., 4/4) where the upper number gives beats per measure and the lower number identifies the note value receiving one beat.
• Common time (C) — 4/4; four quarter-note beats per measure.
• Cut time (alla breve, ₵) — 2/2; two half-note beats per measure; music often feels faster at the same tempo.
• Simple meter — each beat divides into two (e.g., 2/4, 3/4, 4/4).
• Compound meter — each beat divides into three (e.g., 6/8, 9/8, 12/8); the beat note is a dotted value.
• Duple / triple / quadruple — two, three, or four primary beats per measure.
• Measure (bar) — a unit of time between two bar lines; contains the number of beats specified by the time signature.
• Barline / double barline / final barline — vertical lines separating measures; double = section boundary; final (thin-thick) = end of piece.

Key Signatures and Accidentals

• Sharp (#) — raises a pitch by one semitone.
• Flat (b) — lowers a pitch by one semitone.
• Natural (♮) — cancels a previous sharp or flat.
• Double sharp (x) / double flat (bb) — raises/lowers a pitch by two semitones.
• Key signature — sharps or flats placed at the beginning of each staff line indicating the home key; sharps are added in the order F-C-G-D-A-E-B; flats in reverse (B-E-A-D-G-C-F).
• Enharmonic equivalents — pitches that sound identical but are spelled differently (e.g., F# and Gb).

Pitch and Scales

• Just intonation — a tuning system in which intervals are tuned to pure whole-number frequency ratios (e.g., the perfect fifth as 3:2, the major third as 5:4); produces beatless consonances but requires retuning when changing keys, making it impractical for modulating tonal music.
• Overtone series (harmonic series) — the natural sequence of pitches produced above a fundamental frequency when a string or air column vibrates; the partials are integer multiples of the fundamental (f, 2f, 3f, 4f…), producing successively smaller intervals; the series underlies consonance/dissonance, timbre, and the origins of tonal harmony.
• Equal temperament — a tuning system that divides the octave into 12 equal semitones; each semitone is the ratio 2^(1/12) ≈ 1.0595, allowing music to be played in any key without retuning.
• Concert pitch — the standard reference pitch to which all instruments in an ensemble tune; internationally standardized as A4 = 440 Hz. Transposing instruments (e.g., B♭ clarinet) sound at a different pitch than written, so parts are transposed to match concert pitch.
• Semitone (half step) — the smallest interval in Western equal temperament; the distance between two adjacent keys on a piano.
• Whole tone (whole step) — two semitones.
• Octave — 12 semitones; the interval between two pitches with a frequency ratio of 2:1; they share the same pitch class.
• Chromatic scale — all 12 semitones within an octave; no tonal center.
• Major scale — seven-note scale following the interval pattern W-W-H-W-W-W-H; characterized by a bright, stable sound.
• Natural minor scale (Aeolian mode) — pattern W-H-W-W-H-W-W; darker character; the relative minor shares a key signature with its relative major (3 semitones higher).
• Harmonic minor — natural minor with a raised 7th degree; creates a leading tone and an augmented second between scale degrees 6 and 7.
• Melodic minor — raises both 6th and 7th degrees ascending; reverts to natural minor descending.
• Parallel major/minor — share the same tonic (e.g., C major and C minor).
• Relative major/minor — share the same key signature (e.g., C major and A minor).
• Scale degree names — 1 tonic, 2 supertonic, 3 mediant, 4 subdominant, 5 dominant, 6 submediant, 7 leading tone (or subtonic if one semitone below the octave in minor).
• Leading tone — the 7th scale degree when it is one semitone below the tonic; creates strong resolution upward.

Modes

• Ionian — identical to the major scale; bright and stable.
• Dorian — like natural minor with a raised 6th; common in jazz and folk.
• Phrygian — like natural minor with a lowered 2nd; dark, Spanish-influenced character.
• Lydian — like major with a raised 4th; dreamy, ethereal quality.
• Mixolydian — like major with a lowered 7th; common in rock and folk.
• Aeolian — the natural minor scale.
• Locrian — like natural minor with a lowered 2nd and 5th; rarely used as a tonal center due to the diminished fifth above the root.

Special Scales

• Pentatonic scale — five-note scale; the major pentatonic omits scale degrees 4 and 7 (1-2-3-5-6); the minor pentatonic omits 2 and 6 (1-b3-4-5-b7). Ubiquitous in folk, blues, and rock.
• Blues scale — minor pentatonic with an added flat 5 (the “blue note”).
• Whole-tone scale — all whole steps; six pitches, no leading tone; associated with impressionism (Debussy).
• Octatonic (diminished) scale — alternating whole and half steps; eight pitches; symmetrical, favored in 20th-century music.
• Microtonality — the use of intervals smaller than the semitone; examples include quarter tones (24-equal temperament), the 31-tone scale, and the natural microtonal inflections of non-Western traditions; composers include Wyschnegradsky, Hába, and Partch.
• Mandolin — a plucked string instrument of the lute family with eight strings arranged in four double courses, tuned G-D-A-E (like a violin); played with a plectrum using rapid tremolo to sustain melody; central to bluegrass and Italian folk music; used in classical works by Vivaldi and Beethoven; Bill Monroe popularized it in country/bluegrass.
• Ukulele — a small, four-stringed plucked instrument derived from the Portuguese cavaquinho; introduced to Hawaii in the 1880s by Portuguese immigrants; standard tuning G-C-E-A; became emblematic of Hawaiian music and gained global popularity in the early 20th century and again in the 2000s folk revival.
• Panpipe (pan flute) — a wind instrument consisting of a graduated series of stopped pipes (tubes closed at one end) bound side by side; the player blows across the open tops; named for the Greek god Pan; found across many world cultures; in Western art music associated with pastoral imagery; Zamfir popularized the Romanian variety internationally.
• Bongo drums — a pair of small, open-bottomed hand drums of Afro-Cuban origin, joined together and played between the knees; the smaller drum (macho) and larger drum (hembra) produce contrasting tones; central to Afro-Cuban and Latin jazz percussion.

Circle of Fifths

• Circle of fifths — a diagram arranging all 12 major (and parallel minor) keys by ascending perfect fifths clockwise: C (0 sharps/flats), G (1 sharp), D (2), A (3), E (4), B/Cb (5/7), F#/Gb (6), Db (5 flats), Ab (4), Eb (3), Bb (2), F (1 flat).
• Keys adjacent on the circle are closely related and share six of seven scale tones.

Intervals

• Interval — the distance in pitch between two notes; described by a number (1–8+) and a quality.
• Unison — two notes of the same pitch; perfect unison = 0 semitones.
• Minor 2nd — 1 semitone (half step); dissonant.
• Major 2nd — 2 semitones (whole step).
• Minor 3rd — 3 semitones; defines minor chords.
• Major 3rd — 4 semitones; defines major chords.
• Perfect 4th — 5 semitones.
• Tritone (augmented 4th / diminished 5th) — 6 semitones; divides the octave exactly in half; historically called diabolus in musica; maximally dissonant in common-practice harmony.
• Perfect 5th — 7 semitones; highly consonant, foundational to tonal music.
• Minor 6th — 8 semitones.
• Major 6th — 9 semitones.
• Minor 7th — 10 semitones.
• Major 7th — 11 semitones; strongly dissonant, resolves to the octave.
• Perfect octave — 12 semitones.
• Interval qualities — perfect (unisons, 4ths, 5ths, octaves), major/minor (2nds, 3rds, 6ths, 7ths), augmented (one semitone larger than perfect or major), diminished (one semitone smaller than perfect or minor).
• Compound interval — an interval larger than an octave (e.g., a 9th = an octave + a 2nd).
• Inversion of interval — flipping which note is on top; a major 3rd inverts to a minor 6th; numbers sum to 9; perfect stays perfect, major becomes minor, augmented becomes diminished.
• Consonance — intervals perceived as stable: perfect unison, 3rds, 5ths, 6ths, octave.
• Dissonance — intervals perceived as unstable and requiring resolution: 2nds, 7ths, tritone.

Harmony

Chords and Triads

• Arpeggio — the notes of a chord played in succession rather than simultaneously; can ascend or descend; notated with a wavy vertical line beside the chord.
• Triad — a three-note chord built in thirds: root, third, fifth.
• Major triad — major 3rd + minor 3rd above root (e.g., C-E-G); stable, bright.
• Minor triad — minor 3rd + major 3rd above root (e.g., C-Eb-G); stable, darker.
• Diminished triad — minor 3rd + minor 3rd above root (e.g., C-Eb-Gb); dissonant, unstable.
• Augmented triad — major 3rd + major 3rd above root (e.g., C-E-G#); ambiguous, unstable.
• Root position — the root is the lowest note.
• First inversion — the third is the lowest note; notated 6 in figured bass.
• Second inversion — the fifth is the lowest note; notated 6/4 in figured bass.

Seventh Chords

• Seventh chord — a triad with an added seventh above the root.
• Major seventh (Maj7) — major triad + major 7th (e.g., Cmaj7 = C-E-G-B); warm, jazzy.
• Dominant seventh (V7) — major triad + minor 7th (e.g., G7 = G-B-D-F); the most harmonically active chord, strongly pulls to the tonic.
• Minor seventh (m7) — minor triad + minor 7th (e.g., Cm7 = C-Eb-G-Bb).
• Half-diminished seventh (ø7) — diminished triad + minor 7th (e.g., Bø7 = B-D-F-A); used as the leading-tone chord in minor.
• Fully diminished seventh (°7) — diminished triad + diminished 7th (e.g., B°7 = B-D-F-Ab); symmetrical, used for drama and modulation.
• Third inversion — the seventh is the lowest note; notated 4/2 in figured bass.

Functional Harmony and Roman Numeral Analysis

• Roman numeral analysis — chords labeled by scale degree; uppercase = major (I, IV, V); lowercase = minor (ii, iii, vi); diminished with ° (vii°).
• Tonic (I) — the home chord; stable, restful.
• Dominant (V) — built on scale degree 5; creates the strongest harmonic tension; its tritone (leading tone and 4th) resolves to the tonic.
• Subdominant (IV) — built on scale degree 4; pre-dominant function; moves toward V or I.
• I-IV-V progression — the backbone of Western tonal harmony; underlies countless folk, pop, and blues pieces.
• Secondary dominant — a dominant seventh chord applied to a chord other than the tonic, temporarily tonicizing it; written V/x (e.g., V/V = a D7 chord in C major).
• Modulation — a change of tonal center (key); common types: pivot chord (a chord functioning in both keys), direct, and chromatic.
• Tonicization — brief application of dominant motion to a non-tonic chord without a full modulation.

• Picardy third — ending a minor-key piece or section with a major tonic chord; the raised third is the distinctive feature.

• Neapolitan sixth chord (N6 / bII6) — a major triad built on the lowered second scale degree, typically appearing in first inversion; functions as a pre-dominant chord leading to V; common in minor keys (e.g., in C minor: Db-F-Ab in first inversion).
• Italian augmented sixth chord (It+6) — an augmented sixth chord containing scale degrees b6, 1, and #4; the interval of an augmented sixth between b6 and #4 resolves outward by half step to the octave on the dominant.
• French augmented sixth chord (Fr+6) — an augmented sixth chord containing scale degrees b6, 1, 2, and #4; distinguished from the Italian by the added second scale degree; has a whole-tone character.
• German augmented sixth chord (Ger+6) — an augmented sixth chord containing scale degrees b6, 1, b3, and #4; enharmonically equivalent to a dominant seventh chord; approaches the dominant via a 6/4 chord to avoid parallel fifths.
• Modal mixture (borrowed chords) — the use of chords from the parallel minor in a major-key context (or vice versa); e.g., borrowing iv or bVII into a major-key progression; darkens the harmony without a full modulation.
• Figured bass — a Baroque notation system in which numerals below a bass line indicate the intervals (and thus chords) to be realized above it; the foundation of basso continuo practice.
• Basso continuo — the Baroque practice of a bass line performed by a melody instrument (cello, bassoon) and a chording instrument (harpsichord, organ, lute) that realizes the figured bass; the rhythmic and harmonic spine of most Baroque ensemble music.

Cadences

• Authentic cadence (V-I) — the strongest resolution; perfect authentic cadence (PAC) requires both chords in root position with the tonic on top in the melody.
• Imperfect authentic cadence (IAC) — V-I but without all PAC conditions (e.g., inverted chord or non-tonic melody note).
• Half cadence — ends on V; feels like a question mark; common mid-phrase.
• Plagal cadence (IV-I) — “Amen” cadence; softer resolution than authentic.
• Deceptive cadence (V-vi) — expected I is replaced by vi; creates surprise and continuation.
• Phrygian cadence — a half cadence in minor in which iv6 moves to V; named for its resemblance to the Phrygian mode’s descending half step; common in Baroque music as a way to end a slow movement before a following fast one.

Chord Extensions and Other Concepts

• Ninth, eleventh, thirteenth chords — extensions beyond the seventh; stacked thirds; common in jazz.
• Suspension — a non-chord tone held from the previous chord, creating dissonance that resolves stepwise downward (4-3 and 9-8 suspensions are most common).
• Pedal point — a sustained or repeated pitch (often the tonic or dominant) in one voice while harmonies change above or below it.
• Ostinato — a persistently repeated melodic, rhythmic, or harmonic pattern.
• Voice leading — the smooth, logical movement of individual parts; common-practice rules include resolving the leading tone upward and avoiding parallel perfect 5ths and octaves.
• Parallel fifths / parallel octaves — consecutive perfect fifths or octaves between the same two voices, moving in the same direction; forbidden in common-practice counterpoint because they destroy voice independence.
• Voice types (SATB) — the four standard choral parts: Soprano (highest female), Alto (lower female), Tenor (higher male), Bass (lowest male); four-part SATB writing is the standard model for common-practice harmony pedagogy.
• Coloratura soprano — a soprano voice with exceptional agility for rapid runs, trills, and ornamental figures; roles include the Queen of the Night (Magic Flute) and Lucia di Lammermoor.
• Mezzo-soprano — a female voice between soprano and contralto in range; warm middle register; roles include Carmen, Octavian (Der Rosenkavalier), and many Handel castrato parts transposed.
• Baritone — a male voice between bass and tenor; the most common male voice type; includes operatic roles such as Don Giovanni, Figaro, and Rigoletto.
• Cadenza — a virtuosic, often improvisatory solo passage, typically near the end of a concerto movement; in Classical concertos the orchestra pauses on a tonic 6/4 chord while the soloist displays technical brilliance before resolving to V and the final orchestral ritornello.

Rhythm and Meter

• Beat — the basic unit of pulse in music.
• Tempo — the speed of the beat, typically measured in BPM (beats per minute).
• Metronome — a device that produces a regular audible tick at a set BPM, used to keep steady tempo during practice; the mechanical pendulum version was patented by Maelzel in 1815.
• Syncopation — accenting a beat or part of a beat that is normally unaccented; displacing the expected pulse.
• Hemiola — a rhythmic device in which two groups of three are replaced by three groups of two (or vice versa), temporarily contradicting the prevailing meter.
• Polyrhythm — simultaneous use of two or more conflicting rhythmic patterns (e.g., 3 against 2).
• Polymeter — simultaneous use of two different time signatures.
• Downbeat — the first beat of a measure; the strongest beat.
• Upbeat (anacrusis) — a note or notes preceding the first full measure; begins before the downbeat.
• Fermata — a symbol (𝄐) indicating a note or rest is held beyond its notated value at the performer’s discretion.
• Rubato — flexible tempo; the performer subtly speeds up and slows down for expressive effect.
• Accelerando (accel.) — gradually getting faster. Ritardando (rit.) — gradually slowing down. Rallentando (rall.) — similar to ritardando.
• A tempo — return to the previous tempo after a deviation.

Tempo Markings (Italian, slowest to fastest)

• Largo — very slow and broad (~40–60 BPM).
• Grave — slow and solemn.
• Lento — slow (~45–60 BPM); slightly faster than Largo; emphasizes deliberate, unhurried movement.
• Adagio — slow and stately (~66–76 BPM).
• Andante — walking pace (~76–108 BPM).
• Moderato — moderate speed (~108–120 BPM).
• Allegretto — moderately fast; lighter than allegro.
• Allegro — fast and lively (~120–168 BPM).
• Vivace — lively and fast.
• Presto — very fast (~168–200 BPM).
• Prestissimo — as fast as possible.

Dynamics and Articulation

Dynamic Markings

• Pianissimo (pp) — very soft.
• Piano (p) — soft.
• Mezzo-piano (mp) — moderately soft.
• Mezzo-forte (mf) — moderately loud.
• Forte (f) — loud.
• Fortissimo (ff) — very loud.
• Sforzando (sfz) — a sudden, strong accent on a single note.
• Crescendo (<) — gradually getting louder.
• Decrescendo / diminuendo (>) — gradually getting softer.

Articulation Markings

• Legato — smooth, connected playing; often indicated by a slur.
• Staccato — short, detached notes; indicated by a dot above or below the notehead.
• Staccatissimo — extremely short and detached; indicated by a wedge.
• Tenuto — hold the note for its full value; slight emphasis; indicated by a horizontal line.
• Accent (>) — a stressed attack on a note.
• Marcato (^) — marked, emphatic attack; stronger than a regular accent.
• Portato — slightly separated but not fully staccato; tenuto dots under a slur.
• Pizzicato — plucking string instrument strings rather than bowing.
• Arco — return to bowing after pizzicato.
• Tremolo — rapid repetition of a single note or rapid alternation between two notes.
• Trill (tr) — rapid alternation between a note and the step above it.
• Mordent — a brief, single alternation between a note and the step below it (lower mordent) or above it (upper mordent / inverted mordent); notated with a wavy line, with or without a vertical slash.
• Turn — an ornament that moves from the note above the principal note, to the principal note, to the note below, and back; the inverted turn reverses the direction.
• Appoggiatura — an ornamental note (usually a step above or below) that takes time value from the main note and resolves stepwise; creates an expressive dissonance on the beat.
• Acciaccatura — a “crushed” grace note played as quickly as possible before the main note, barely receiving any time value; notated as a small note with a slash through its stem.
• Grace note — a small-sized ornamental note played quickly before the main note; a generic term covering both appoggiaturas and acciaccaturas.
• Glissando — a slide through all pitches between two notes.
• Vibrato — slight, rapid fluctuation in pitch for expressive warmth.

Musical Form

• Motive (motif) — the smallest recognizable melodic or rhythmic idea in a composition; a brief, distinctive cell that can be developed, varied, or combined to build larger structures.
• Leitmotif — a recurring musical theme associated with a specific character, object, place, or idea; closely associated with Wagner’s operas, where leitmotifs are woven through the orchestral texture to guide dramatic meaning.
• Binary form (AB) — two contrasting sections, each usually repeated; common in Baroque dances.
• Ternary form (ABA) — three sections where the first returns after a contrasting middle section; da capo arias.
• Strophic form — the same music repeats for each verse of a text; common in songs and hymns.
• Through-composed — new music for each section; no large-scale repetition.
• Rondo form — a recurring refrain (A) alternates with contrasting episodes: ABACA or ABACABA; common in final movements.
• Theme and variations — a theme is stated and then repeated in altered forms (varied harmonically, melodically, rhythmically, etc.); Beethoven’s Op. 111, Mozart’s “Ah, vous dirai-je maman.”
• Fugue — a polyphonic compositional technique; a subject (theme) is introduced in one voice, then imitated in successive voices at the fifth or fourth; includes countersubject, episodes, and stretto. Associated with J.S. Bach.
  • Subject — the main melodic idea of a fugue.
  • Answer — the subject transposed to the dominant key (real answer) or with slight adjustment (tonal answer).
  • Exposition — the opening section where each voice enters with the subject.
  • Countersubject — a melodic line that consistently accompanies the subject/answer in a fugue, heard simultaneously with subsequent voice entries.
  • Episode — a passage in a fugue between subject entries; typically develops motives from the subject or countersubject and moves through related keys.
  • Stretto — overlapping entries of the subject before the previous one finishes.
• Canon — strict imitation where one voice exactly copies another at a fixed time interval; a round is a type of canon (e.g., “Row, Row, Row Your Boat”).
• Ritornello form — a Baroque form in which a recurring orchestral refrain (ritornello) alternates with freer solo sections; the ritornello may return in varied keys and truncated forms; used extensively by Vivaldi and Handel in concertos.
• Ground bass (basso ostinato) — a short bass line repeated continuously while upper voices vary freely above it; foundational to the passacaglia and chaconne.
• Passacaglia — a set of continuous variations over a repeating bass line (or harmonic progression) in triple meter; Bach’s Passacaglia in C minor is the canonical example.
• Chaconne — closely related to the passacaglia; continuous variations over a repeating harmonic progression, often in triple meter; Bach’s Chaconne from Partita No. 2 in D minor and Purcell’s “When I am laid in earth” are standard examples.
• Sonata form (sonata-allegro form) — the primary form of the Classical period’s first movements:
  • Exposition — introduces the primary theme (tonic key) and secondary theme (dominant or relative major key), often ending with a cadence theme; may be repeated.
  • Development — themes are fragmented, transposed, and developed through various keys; harmonically unstable.
  • Recapitulation — return of both themes, now both in the tonic key.
  • Coda — an optional closing section extending the ending.
  • Slow introduction — an optional introductory section before the exposition.
• Concerto — a multi-movement work for soloist(s) and orchestra; the double exposition (in Classical concertos) presents themes first in the orchestra, then the soloist. The cadenza is an unaccompanied solo passage near the end of a movement.
• Symphony — a multi-movement orchestral work; the Classical four-movement plan is: fast (sonata form) – slow – minuet/scherzo – fast finale.
• Suite — a collection of movements often derived from dances (Baroque: allemande, courante, sarabande, gigue) or drawn from a larger work.
• Opera — a dramatic work combining vocal music, orchestral music, and staging; includes recitative, aria, and ensemble numbers.
• Overture — an orchestral introduction to an opera, oratorio, or play; may use themes from the work.
• Minuet and trio — a stately triple-meter dance form (ABA); the trio is a contrasting middle section; common third movement in Classical symphonies.
• Scherzo — a fast, often humorous triple-meter movement that replaced the minuet in Romantic symphonies (Beethoven); also ABA form with a trio.

Vocal Performance Terms

• A cappella — singing without instrumental accompaniment; from Italian “in the manner of the chapel” (referring to chapel choirs that performed unaccompanied); encompasses everything from Renaissance sacred polyphony (Palestrina’s motets) to barbershop quartets to contemporary collegiate groups; in pop contexts, multi-voice unaccompanied arrangements have been popularized by groups such as Pentatonix and via the Pitch Perfect films.
• Mariachi — a Mexican ensemble genre and performance tradition originating in Jalisco; typically features violins, trumpets, the vihuela (high-pitched five-string guitar), guitarrón (large fretless bass guitar), and guitarra de golpe; the ensemble performs son jalisciense, huapango, ranchera, and bolero ranchero repertoire; recognized by UNESCO on the Intangible Cultural Heritage list (2011); the charro costume (suit with embroidered jacket and wide-brimmed sombrero) is the iconic dress.

Forms and Genres

• Ballad — a narrative song or instrumental piece that tells a story; in art music, a single-movement lyrical piano piece (Chopin, Brahms); in folk and popular traditions, a strophic song recounting a tale.
• Ballet — a staged dance work with orchestral accompaniment; the music follows dramatic and choreographic action (Tchaikovsky’s Swan Lake, Stravinsky’s The Rite of Spring).
• Cantata — a multi-movement vocal work with soloists, chorus, and orchestra or continuo; the Baroque church cantata (Bach) alternates arias, recitatives, and chorales.
• Etude — a study piece designed to develop a specific technical skill; can be a concert work in its own right (Chopin’s Etudes, Liszt’s Transcendental Etudes).
• Fantasia (fantasy) — a free-form composition that does not follow a strict structural template; characterized by improvisatory passages, abrupt contrasts, and harmonic freedom.
• Madrigal — a secular polyphonic vocal work, typically for 4–6 unaccompanied voices; flourished in Renaissance Italy and Elizabethan England; famous for word-painting.
• Mazurka — a Polish folk dance in triple meter (3/4 or 3/8) with an accent on the second or third beat; elevated to an art form by Chopin.
• Motet — a polyphonic choral composition, usually sacred, without dramatic staging; distinct from the cantata in being a single, through-composed piece.
• Nocturne — a lyrical, introspective piano piece evoking the night; defined by a singing right-hand melody over a left-hand accompaniment pattern; associated with Field and Chopin.
• Operetta — a light, popular form of opera featuring spoken dialogue, romantic or comic plots, and accessible melodies (Offenbach, Gilbert and Sullivan, Lehár).
• Oratorio — a large-scale dramatic work for soloists, chorus, and orchestra on a sacred or epic subject, performed without staging (Handel’s Messiah, Haydn’s The Creation).
• Polka — a lively Bohemian couple dance in duple meter (2/4) with a characteristic short-short-long rhythmic pattern; popular in 19th-century ballrooms.
• Prelude — an introductory piece, or a self-contained short character piece; Bach’s preludes precede fugues; Chopin’s Preludes are independent miniatures.
• Program music — instrumental music that depicts or narrates an extramusical idea, story, or scene, often specified by a title or printed program note; contrasts with absolute music.
• Rhapsody — a single-movement work with an episodic, improvisatory structure, often drawing on folk or national themes (Liszt’s Hungarian Rhapsodies, Gershwin’s Rhapsody in Blue).
• Symphonic poem (tone poem) — a single-movement orchestral work in free form that illustrates a programmatic subject; pioneered by Liszt; examples include Strauss’s Don Juan and Smetana’s Má vlast.
• Tango — a partner dance and music genre that originated in the lower-class districts of Buenos Aires, Argentina, in the late 19th century, derived from the milonga and the habanera; typically accompanied by an orquesta típica centered on the bandoneón (a button accordion); danced in close embrace, chest to chest or at arm’s length, with syncopated rhythm. The singer-actor Carlos Gardel popularized the tango song, beginning with “Mi Noche Triste.” Astor Piazzolla, a virtuoso bandoneón player who studied with Nadia Boulanger, fused classical and jazz elements to create nuevo tango, writing Libertango, Adiós Nonino, and the four-movement Estaciones Porteñas (The Four Seasons of Buenos Aires). The dance has distinct regional forms, including Argentine, Uruguayan, and Finnish (the latter usually in a minor key, with an annual festival in Seinäjoki).
• Waltz — a smooth couple dance in triple meter (3/4) with a characteristic one-beat bass note and two-beat chord pattern; elevated to art music by Chopin and Johann Strauss II.

20th-Century and Advanced Theory

• Atonality — music that avoids a tonal center and the functional harmonic relationships of common-practice tonality; associated with Schoenberg, Berg, and Webern; not the same as random or disorganized pitch usage.
• Twelve-tone technique (dodecaphony / serialism) — a compositional method developed by Arnold Schoenberg in which all 12 pitch classes of the chromatic scale are arranged into a fixed ordered sequence called the tone row (or series); no pitch class may be repeated until all 12 have appeared; the row governs melodic and harmonic content.
• Tone row (twelve-tone row / series) — the ordered arrangement of all 12 pitch classes used as the basis of a twelve-tone composition.
• Prime (P) — the original form of the tone row; labeled P-0 through P-11 by starting pitch class.
• Inversion (I) — the tone row with all intervals inverted (reflected about the starting pitch); an ascending minor third becomes a descending minor third, etc.
• Retrograde (R) — the tone row read backwards.
• Retrograde-inversion (RI) — the inversion of the row read backwards; the fourth and final canonical transformation.
• Pitch-class set theory — a post-tonal analytical framework developed by Allen Forte that classifies groups of pitch classes (regardless of octave or order) by their intervallic content; sets are identified by prime form and Forte number (e.g., [0,1,4,6] = Forte 4-Z15); tools include the interval vector and set-class equivalence.
• Polytonality — the simultaneous use of two or more different keys; Stravinsky’s Petrushka chord (C major and F# major superimposed) is the canonical example.
• Bitonality — a specific form of polytonality using exactly two keys simultaneously.
• Serialism (total serialism) — an extension of twelve-tone technique in which serial organization is applied not only to pitch but also to rhythm, dynamics, articulation, and register; associated with Messiaen, Boulez, and Stockhausen in the post-WWII period.
• Sprechstimme (Sprechgesang) — a vocal technique midway between speech and song, indicated by an x notehead; the singer approximates the written pitch but immediately slides away; used by Schoenberg in Pierrot Lunaire.
• Prepared piano — a piano whose timbre is altered by placing objects (screws, bolts, rubber, felt) between the strings; invented by John Cage; produces percussive, metallic, or muffled timbres.
• Aleatoric (chance) music — music in which some element of composition or performance is determined by chance procedures; John Cage’s use of the I Ching (Music of Changes) is a central example; distinct from improvisation in that the performer may follow random instructions rather than personal choice.
• Minimalism — a style using simple, repetitive musical materials that evolve through gradual processes; associated with Steve Reich (phasing), Philip Glass (arpeggiated patterns), and Terry Riley; the technique of phase shifting (two identical loops played at slightly different tempos) is a hallmark of Reich.

Instruments

Classification (Hornbostel-Sachs)

• Idiophones — instruments that produce sound by the vibration of the instrument’s own body material, without a membrane or string; examples include the xylophone, marimba, cymbals, bells, and castanets.
• Membranophones — instruments that produce sound by a vibrating stretched membrane; examples include the drum, kettledrum (timpani), snare drum, and tabla.
• Aerophones — instruments that produce sound by a vibrating column of air; examples include flutes, oboes, clarinets, trumpets, and organs.
• Chordophones — instruments that produce sound by vibrating strings; examples include the violin, cello, piano, guitar, and harp.
• Electrophones — instruments that produce or amplify sound through electronic means; examples include the electric guitar, synthesizer, theremin, and electric organ.

Texture

• Timbre — the characteristic tone color or quality of a sound that distinguishes one instrument or voice from another at the same pitch and dynamic; determined by the blend of overtones (harmonics) present in the sound.
• Monophony — a single melodic line with no accompaniment (e.g., Gregorian chant).
• Homophony — a melody supported by chordal accompaniment; all voices move in the same rhythm (homorhythmic/chordal texture) or melody with accompaniment pattern.
• Polyphony — two or more simultaneous, independent melodic lines of equal importance.
• Counterpoint — the technique of combining independent melodic voices according to rules of voice leading; the adjective is contrapuntal.
  • Species counterpoint — a pedagogical system (Fux, Gradus ad Parnassum) progressing from note-against-note (1st species) to florid counterpoint (5th species).
  • Contrary motion — two voices moving in opposite directions; the strongest type of independent voice motion.
  • Oblique motion — one voice stays on a pitch while the other moves.
  • Parallel motion — two voices moving in the same direction by the same interval; parallel perfect 5ths and octaves are avoided in common practice.
  • Similar motion — two voices moving in the same direction by different intervals.
• Heterophony — simultaneous variations of the same melody in different voices.

Musical Systems in Comparative Perspective

The notation, tonal harmony, and formal vocabulary above primarily describe Western concert traditions. Comparative listening also requires concepts developed within other musical practices.

• Rāga and tāla — fundamental to both Hindustani and Carnatic classical music. A rāga organizes melodic material and its expressive character; a tāla organizes time through a recurring rhythmic cycle. Listen to how a performance develops a rāga through elaboration and improvisation, and identify the returning points of its rhythmic cycle.
• Maqām and taqsīm — a maqām is a melodic framework involving characteristic pitches, intervals, and melodic movement. Taqsīm is an improvised exploration, often by a solo instrumentalist. Regional practices differ: Iraqi maqam also names a particular vocal and instrumental tradition, while Central Asian Shashmaqam organizes repertoire into suites. These terms should be learned with performances from the relevant tradition.
• Gamelan — Indonesian ensemble music, especially associated with Java and Bali, and the instruments used to perform it. Ensembles commonly combine gongs, keyed percussion, drums, and other instruments. Listen for simultaneous melodic layers, interlocking parts, and recurring rhythmic patterns. Performance, tuning, instrument making, ceremony, and theater are connected parts of the tradition.¹

Selected Italian and Other Terms

• Da capo (D.C.) — repeat from the beginning.
• Dal segno (D.S.) — repeat from the sign (𝄋).
• Fine — the end; used with da capo or dal segno to indicate where to stop.
• Coda — a concluding section appended to a form.
• Exposition — opening section; also used for fugues (see above).
• Con brio — with vigor. Con moto — with motion. Con fuoco — with fire.
• Dolce — sweetly. Espressivo — expressively. Grazioso — gracefully.
• Cantabile — in a singing style.
• Sostenuto — sustained; held.
• Subito (sub.) — suddenly (e.g., subito piano = suddenly soft).
• Simile — continue in the same manner as marked.
• Ossia — an alternative passage provided for a performer.
• Divisi (div.) — divide; string sections split into separate parts.
• Tacet — silent; do not play for an extended passage.
• Col legno — with the wood of the bow (strings strike strings with the stick).
• Sul ponticello — bow near the bridge for a glassy, nasal tone.
• Sul tasto — bow over the fingerboard for a softer, flute-like tone.
• Mute (con sordino) — a device that dampens the instrument’s resonance; senza sordino = without mute.
• Attacca — proceed immediately to the next movement without a pause.