Key Formulas & Frameworks
Pitch (frequency) → Duration (rhythm) → Dynamics (volume) → Timbre (tone color) → Texture (layers) → Form (structure)
The six elements of music
C → G → D → A → E → B → F# → C# → G# → D# → A# → F → C
Clockwise = add sharp; Counter-clockwise = add flat. Relative minors are 3 semitones below major.
Natural Minor Scale: W-H-W-W-H-W-W
Harmonic Minor: W-H-W-W-H-WH-H (raised 7th)
Melodic Minor (ascending): W-H-W-W-W-W-H
Major Triad: Root + Major 3rd + Perfect 5th (1-3-5)
Minor Triad: Root + Minor 3rd + Perfect 5th (1-b3-5)
Diminished: Root + Minor 3rd + Diminished 5th (1-b3-b5)
Augmented: Root + Major 3rd + Augmented 5th (1-3-#5)
Seventh chords: Major 7 (1-3-5-7), Dominant 7 (1-3-5-b7), Minor 7 (1-b3-5-b7)
Unison: 0 | Minor 2nd: 1 | Major 2nd: 2 | Minor 3rd: 3 | Major 3rd: 4
Perfect 4th: 5 | Tritone: 6 | Perfect 5th: 7 | Minor 6th: 8 | Major 6th: 9
Minor 7th: 10 | Major 7th: 11 | Octave: 12
4/4 (Common Time): 4 beats per measure, quarter note gets one beat
3/4 (Waltz): 3 beats per measure, quarter note gets one beat
6/8 (Compound Duple): 6 eighth notes per measure, felt in 2
Simple meters: beat divides by 2. Compound meters: beat divides by 3.
Medieval (500–1400) → Renaissance (1400–1600) → Baroque (1600–1750) → Classical (1750–1820) → Romantic (1820–1900) → 20th Century (1900–2000) → Contemporary (2000–present)
Intro → Verse → Chorus → Verse → Chorus → Bridge → Chorus → Outro
Verse: tells story, different lyrics. Chorus: repeated hook, main message. Bridge: contrast, builds tension.
Core Concepts
Melody, Harmony, and Rhythm
Melody is a sequence of pitches perceived as a single entity — the "tune." Harmony is the vertical aspect of music — chords and their progressions. Rhythm is the temporal organization of sound — beat, meter, tempo. Together with dynamics (loudness/softness), timbre (tone color), and texture (monophonic, homophonic, polyphonic), they form the complete musical experience.
Musical Form and Structure
Form is the architecture of a musical piece. Common forms: Binary (AB), Ternary (ABA), Rondo (ABACA), Sonata-Allegro (Exposition-Development-Recapitulation), Theme and Variations, Fugue (subject, answer, countersubject). Form creates expectation, tension, and resolution — the narrative arc of music.
Music Psychology and Perception
How humans perceive and respond to music. Pitch perception — frequency (Hz) mapped logarithmically. Consonance and disonance — simple frequency ratios (2:1 octave, 3:2 perfect fifth) sound consonant. Emotional responses — major = happy, minor = sad (culturally influenced). The Mozart effect — temporary spatial reasoning improvement from listening to Mozart (debunked as general intelligence boost). Music activates reward centers (dopamine release).
World Music and Ethnomusicology
Music varies dramatically across cultures. Indian classical — raga (melodic framework) and tala (rhythmic cycle), improvisation within strict rules. West African — polyrhythm, call-and-response, drum language. Gamelan (Indonesia) — interlocking patterns, bronze percussion. Japanese — pentatonic scales, ma (silence/space). Flamenco (Spain) — cante (song), toque (guitar), baile (dance). Ethnomusicology studies music in its cultural context.
Music Technology and Production
Modern music production involves: Recording (microphones, audio interfaces, DAWs — Digital Audio Workstations like Pro Tools, Logic, Ableton). Mixing — balancing levels, panning, EQ, compression, reverb. Mastering — final polish for distribution. MIDI (Musical Instrument Digital Interface) — digital control of instruments. Synthesis — subtractive, additive, FM, wavetable, granular. Sampling — using recorded sounds as raw material.
Music and Society
Music serves social functions: Identity — subcultures defined by music (punk, hip-hop, EDM). Protest — Bob Dylan, Nina Simone, Public Enemy. Ritual — religious music, national anthems, wedding songs. Economic — music industry ($25B+ global), streaming economy, live events. Therapeutic — music therapy for dementia, depression, PTSD. Political — censorship, propaganda, cultural diplomacy.
Worked Examples & Case Studies
Example 1: Chord Progression Analysis
Progression: I-V-vi-IV in C Major = C-G-Am-F
Analysis: (1) I (C): Tonic — home, stability. (2) V (G): Dominant — tension, wants to resolve. (3) vi (Am): Relative minor — emotional depth, deceptive resolution. (4) IV (F): Subdominant — departure, openness. Resolution: IV → I (plagal cadence, "Amen") or V → I (authentic cadence).
Usage: This progression (or variants) appears in hundreds of pop songs: "Let It Be" (Beatles), "No Woman No Cry" (Marley), "Someone Like You" (Adele), "Counting Stars" (OneRepublic). Its effectiveness: familiar yet emotionally flexible.
Example 2: Rhythmic Analysis — Polyrhythm
Example: 3:2 polyrhythm (hemiola) — three notes in the time of two.
Notation: Left hand: quarter note, quarter note, quarter note (3 beats). Right hand: dotted half note (2 beats). Both start together, realign after 6 eighth notes.
Musical Effect: Creates tension and forward momentum. Common in: African drumming, Bach (Brandenburg Concerto No. 3), Stravinsky (Rite of Spring), jazz (Elvin Jones), progressive metal (Tool, Meshuggah).
Example 3: Sonata Form Analysis — Mozart's "Eine kleine Nachtmusik"
Exposition: Primary theme (G major, assertive) → Transition (modulates) → Secondary theme (D major, lyrical) → Closing section.
Development: Themes fragmented, sequenced through distant keys (G minor, C minor, etc.), increased tension through instability.
Recapitulation: Primary theme (G major) → Transition (stays in tonic) → Secondary theme (G major — now in tonic!) → Coda.
Key Insight: The secondary theme's return in the tonic key provides resolution — the "homecoming" that defines sonata form's dramatic arc.
Case Study: The Beatles — Musical Innovation
Background: Liverpool band (1960–1970) — John Lennon, Paul McCartney, George Harrison, Ringo Starr. Best-selling band in history (600M+ units).
Musical Evolution: (1) Early (1962–1964): Merseybeat — simple I-IV-V progressions, love songs ("She Loves You"). (2) Middle (1965–1966): Studio experimentation — "Rubber Soul" (folk rock, sitar), "Revolver" (tape loops, backward guitar, Indian influences). (3) Late (1967–1970): "Sgt. Pepper" (concept album, orchestral, psychedelic), "Abbey Road" (medley, Moog synthesizer). Innovations: Popularized concept albums, studio as instrument, music videos, Eastern philosophy in Western pop, sampling techniques. Impact: Transformed popular music from singles to art form; influenced every subsequent genre.
Case Study: Hip-Hop Culture — From Bronx to Global
Origins: 1973, Bronx, NY — DJ Kool Herc's back-to-school party at 1520 Sedgwick Avenue. Breaks (isolated drum breaks) + MCing (rhythmic spoken word) + Breaking (dance) + Graffiti (visual art) = Four elements of hip-hop.
Evolution: (1) 1970s: Block parties, Sugarhill Gang's "Rapper's Delight" (1979) — first hip-hop hit. (2) 1980s: Golden age — Run-DMC, Public Enemy (political), N.W.A. (gangsta rap). (3) 1990s: East Coast vs. West Coast (Tupac vs. Biggie), jazz rap (A Tribe Called Quest). (4) 2000s: Mainstream dominance — Eminem, Kanye West. (5) 2010s–present: Trap (Future, Migos), SoundCloud rap, global dominance. Impact: Most consumed music genre globally; influenced fashion, language, politics, social justice movements (Black Lives Matter).
Practice Problems
Problem 1: What are the notes in a G major scale? What is the relative minor of G major?
Answer: G-A-B-C-D-E-F#-G. Relative minor: E minor (3 semitones below G, or the 6th degree of the scale).
Problem 2: Build a D minor triad. What are the intervals from the root?
Answer: D-F-A. D to F = minor 3rd (3 semitones). D to A = Perfect 5th (7 semitones).
Problem 3: What is the difference between simple and compound meter? Give an example of each.
Answer: Simple: beat divides into 2 (4/4, 3/4, 2/4). Compound: beat divides into 3 (6/8, 9/8, 12/8). Example: 4/4 = simple quadruple. 6/8 = compound duple (two beats, each divided into 3 eighth notes).
Problem 4: What is a I-IV-V-I progression in F major? Name a song that uses this progression.
Answer: F-Bb-C-F. Songs: "Twist and Shout" (Beatles/Isley Brothers), "La Bamba" (Ritchie Valens), "Wild Thing" (The Troggs).
Problem 5: What is the difference between monophonic, homophonic, and polyphonic texture? Give an example of each.
Answer: Monophonic: single melody, no accompaniment (solo chant, "Happy Birthday" sung alone). Homophonic: melody with chordal accompaniment (most pop songs, hymns). Polyphonic: multiple independent melodies (fugue, Bach's "Art of Fugue", round like "Row Your Boat").
Problem 6: What is syncopation? How does it create rhythmic interest?
Answer: Syncopation = accenting normally weak beats or off-beats. Creates surprise and forward momentum by subverting expectations. Essential in: jazz (swing), funk (James Brown), reggae (skank), Latin music (clave rhythm).
Problem 7: What is the difference between major and minor keys? How do they affect emotional perception?
Answer: Major: major 3rd above root (4 semitones), generally perceived as happy/bright. Minor: minor 3rd above root (3 semitones), generally perceived as sad/dark. Emotional associations are partly cultural — some cultures associate minor with joy. Mode mixture (borrowing from parallel major/minor) adds complexity.
Problem 8: What is a plagal cadence? How does it differ from an authentic cadence?
Answer: Plagal: IV-I (subdominant to tonic). Gentle, "Amen" resolution. Authentic: V-I (dominant to tonic). Strong, conclusive resolution. Deceptive: V-vi (dominant to relative minor). Surprise, delays resolution. Half: ends on V (any chord to dominant). Inconclusive, creates expectation.