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Section 07
Harmonic Analysis
Build progressions, analyze function and tension, hear voice leading
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PROGRESSION
VOICE LEADING
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Section 08
Harmonic Innovators
Composers and musicians who expanded the language of harmony
Johann Sebastian Bach
1685 – 1750 · Baroque
Master of counterpoint and tonal architecture. The Well-Tempered Clavier explored all 24 major and minor keys, establishing equal temperament as the standard. His chorale harmonizations remain the textbook for voice leading.
Arnold Schoenberg
1874 – 1951 · Modern
Pioneer of atonality and the twelve-tone technique, in which all 12 pitch classes are used equally before any repeats. Led the Second Viennese School, dismantling centuries of tonal hierarchy.
John Coltrane
1926 – 1967 · Jazz
"Giant Steps" introduced Coltrane changes — rapid modulation through three key centers a major third apart. His sheets-of-sound approach and use of pentatonic superimposition revolutionized jazz harmony.
Dmitri Shostakovich
1906 – 1975 · Soviet
Wielded modal harmony, dark chromaticism, and bitter irony as tools of coded political expression. His symphonies and string quartets achieve emotional intensity through tonal ambiguity and unexpected dissonance.
Duke Ellington
1899 – 1974 · Jazz
Redefined jazz orchestration with extended harmonies, blue notes, and what he called the "jungle sound." Used instruments as tonal extensions of his harmonic palette, composing directly for specific players.
Steve Reich
1936 – present · Minimalist
Developed phasing and process music where harmonic change emerges from rhythmic displacement. Works like "Music for 18 Musicians" create shimmering harmonic fields from interlocking diatonic patterns.
Herbie Hancock
1940 – present · Jazz/Fusion
Bridged acoustic jazz harmony with electronic textures. Known for quartal voicings, pentatonic substitutions, and the MIDI harmony expansion of the 1980s. Masterwork: "Maiden Voyage."
Jacob Collier
1994 – present · Neo-Soul
Re-harmonization genius who applies negative harmony, micro-tonal tuning, and unconventional quartal voicings. Capable of modulating to half-step keys mid-phrase, treating harmony as a continuous, fluid spectrum.
Section 09
Glossary
Essential vocabulary of music theory
Cadence
A harmonic or melodic formula that creates a sense of resolution or pause — the musical equivalent of punctuation.
Chord
Three or more pitches sounded simultaneously. The fundamental building block of harmony.
Chromatic
Relating to notes outside the diatonic scale — all 12 pitches of the octave, moving by semitones.
Consonance
Intervals and chords perceived as stable, pleasant, or resolved — the acoustic result of simple frequency ratios.
Diatonic
Belonging to the seven notes of a given major or minor scale, as opposed to chromatic alterations.
Diminished
An interval or chord quality that is one semitone smaller than minor/perfect. The diminished 7th chord divides the octave into four equal parts.
Dominant
The fifth scale degree and its chord. Creates strong tension that resolves back to the tonic — the engine of tonal harmony.
Enharmonic
Two notes with the same pitch but different spellings (e.g., C# and Db). Enharmonic equivalents enable modulation.
Harmony
The combination of simultaneously sounding pitches; the study of chord structures and their relationships over time.
Interval
The distance in pitch between two notes, measured in semitones and named (unison, 2nd, 3rd … octave).
Inversion
A chord or interval where a note other than the root appears in the bass, altering its stability and color.
Leading Tone
The seventh scale degree — one semitone below the tonic — creating strong upward pull toward resolution.
Mode
A scale derived by starting on a different degree of a parent scale. The seven diatonic modes each have a distinct color.
Modulation
The process of changing from one key to another within a piece, creating harmonic motion and narrative.
Pedal Point
A sustained or repeated bass note held beneath changing harmonies above — creating tension or drone effects.
Pentatonic
A five-note scale found across world music traditions. The major pentatonic omits scale degrees 4 and 7, eliminating leading tone tension.
Pitch Class
All pitches with the same name across all octaves, treated as equivalent. There are 12 pitch classes in equal temperament.
Resolution
Movement from a dissonant or tense harmony to a consonant or stable one — the satisfaction of harmonic expectation.
Scale
An ordered sequence of pitches within an octave, defined by its pattern of whole and half steps.
Semitone
The smallest interval in Western equal temperament — one half step, the distance between adjacent keys on a piano.
Tonic
The first and central degree of a scale — the "home" pitch, the point of rest and resolution in tonal music.
Tritone
An interval of six semitones (three whole tones) — the most dissonant interval, dividing the octave exactly in half. Historically called "diabolus in musica."