The Lineage of Music Theory — 2500 Years from Pythagoras to Set Theory and Jazz

Does Music Theory Have a “History”?

It does — 2500 years of it. And the crucial point is that music theory is not a single, monolithic “correct system”: it has been rebuilt from the foundations in each era. What the ancient Greeks meant by “music,” what “music” meant in Bach’s time, and what a jazz musician means by it differ in the very premises of their theory.

Just as the sister series [The Lineage of Mathematics] traced mathematics as a history of “people and discoveries,” this series traces music theory as a history of changing questions and answers. “What is consonance?” “How do we notate sound?” “Why do chords progress?” — this is the story of how each era answered.

Four Threads Running Through It

Four oppositions and problems run through the 2500 years. Every episode touches one of these four threads:

1. Number vs. Ear — Is music the “ratio of numbers” or the “judgment of the ear”? The oldest question, beginning with the opposition of Pythagoras (number) and Aristoxenus (ear), and repeating to the present
2. The evolution of notation — The development of the technology to write down sound is what made complex theory possible in the first place. Guido’s staff is the decisive turning point
3. Melody/counterpoint → harmony — From the “horizontal line (melody)” to the “vertical sonority (chord).” Harmonic theory was established by Rameau (1722), surprisingly recently
4. The temperament problem — The eternal trade-off between just intonation (mathematically pure but unable to modulate) and equal temperament (all keys playable but every interval slightly impure)

Seven Eras over 2500 Years

Period 1: Antiquity — Number vs. Ear (BCE)

Pythagoras found consonance in the integer ratios of string lengths (2:1 octave, 3:2 fifth). “Music is number.” But Aristoxenus countered, “it should be judged by the ear.” This opposition is the starting point of theory’s history.

Period 2: The Middle Ages — the Birth of Notation

Guido d’Arezzo (11th c.) invented the four-line staff and solmization (ut re mi fa sol la — the origin of “do re mi”). Being able to write sound accurately let complex polyphony and theory flower. The age of church modes.

Period 3: The Renaissance — Triads and Counterpoint

Zarlino distinguished major and minor triads and systematized the rules of counterpoint. Not yet “chord progression,” but counterpoint — beautifully layering multiple melodies — remained central.

Period 4: The Baroque — the Birth of Harmonic Theory (the greatest turning point)

Rameau’s Treatise on Harmony (1722) established the concepts of the fundamental bass and functional harmony. A paradigm shift from “melody (horizontal)” to “harmony (vertical).” Equal temperament spread at the same time (Bach’s Well-Tempered Clavier).

Period 5: The 19th Century — Functional Theory and Acoustics

Riemann’s functional harmony (T/S/D), Helmholtz’s acoustics (explaining consonance and dissonance physically). Number vs. ear reunited as psychoacoustics.

Period 6: The 20th Century — Analysis, Atonality, Mathematization

Schenker’s analysis (reduction to background structure), Schoenberg’s twelve-tone technique (the negation of tonality), Forte’s set theory (analyzing music with mathematics). Ethnomusicology relativized “Western theory is not universal.”

Period 7: The Present — the Rise of Practical Theory

Jazz theory (chord-scale, the Berklee method), popular-music theory (stock progressions), Neo-Riemannian theory, AI composition.

“Descriptive Theory” and “Prescriptive Theory”

Another question runs through the history — does theory describe music after the fact, or prescribe it in advance?

• Rameau’s harmony, Riemann’s functional theory = descriptive theory that analyzes masterpieces after the fact
• Twelve-tone technique, set theory = constructive theory that prescribes composition in advance
• Jazz/pop theory = a shared vocabulary extracted from practice

“Which comes first, good music or theory?” is the root problem of music theory’s history, and the answer sways from era to era.

Articles Planned in This Series

The following 11 articles (excluding the overview), in chronological order:

1. Pythagoras and Antiquity — number vs. ear, string ratios, the independent theories of China and India
2. The Middle Ages and Guido — the notation revolution, church modes, the origin of do-re-mi
3. The Renaissance and Zarlino — the distinction of triads, the systematization of counterpoint
4. Rameau and the Birth of Harmonic Theory — the 1722 turning point, fundamental bass and functional harmony
5. The Story of Equal Temperament — just intonation vs. equal temperament, Bach’s decision
6. Riemann and Helmholtz — functional theory (T/S/D) and acoustics
7. Schenker and Analytical Theory — reducing a work to background structure
8. The Dissolution of Tonality — Schoenberg and the twelve-tone technique
9. Set Theory and the 20th-Century Mathematization — analyzing music with mathematics
10. Non-Western Music Theory — raga, maqam, the twelve lü, ritsu-ryo
11. Jazz and Popular Practical Theory — from chord-scale to the present

The Big Picture

Music theory is a history not of “things” but of “ways of thinking.” It sits exactly between the sister series [The Lineage of the Piano] and [The Lineage of the Violin] (instruments as things) and [The Lineage of Mathematics] (abstract concepts) — the story of how people have grasped the order of sound.

Swaying between number and ear, notation and improvisation, description and prescription, music theory has spent 2500 years drawing an ever-changing “map of the universe of sound.” The next article begins with its first step — the order of number Pythagoras found in a string.