Chapter 14 Further Reading: Harmony & Counterpoint

Foundational Texts

Helmholtz, Hermann von. On the Sensations of Tone as a Physiological Basis for the Theory of Music (1863; English translation by A. J. Ellis, 1875) The original source for the physical theory of consonance and dissonance based on beating. Helmholtz's analysis of the frequency-ratio basis of consonance remains foundational, even where modern psychoacoustics has refined his account. The later chapters on historical musical systems are particularly valuable for cross-cultural perspective. Challenging reading, but the first several chapters on the physics of tone are accessible to readers with basic physics backgrounds.

Fux, Johann Joseph. Gradus ad Parnassum (1725; translated by Alfred Mann, 1943) The most influential counterpoint treatise in history. Presented as a dialogue between a student and master (loosely based on Palestrina), it walks through all five species of counterpoint with examples and exercises. Haydn, Mozart, and Beethoven all studied from this text. Reading it as a primary source gives a vivid sense of how the rules of counterpoint were understood in the 18th century as both aesthetic norms and physical necessities.

Tymoczko, Dmitri. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford University Press, 2011) The most rigorous modern treatment of voice leading as a geometric problem. Tymoczko demonstrates that chord progressions can be represented as paths through mathematical spaces (orbifolds), and that the principle of efficient voice leading corresponds to shortest-path optimization in these spaces. Requires some comfort with abstract concepts but is written for a music-theory audience, not pure mathematicians. Chapter 3 on voice-leading geometry is particularly relevant to this chapter's themes.

Acoustics and Psychoacoustics

Plomp, R. and Levelt, W. J. M. "Tonal Consonance and Critical Bandwidth." Journal of the Acoustical Society of America 38(4): 548–560 (1965) The landmark paper that updated Helmholtz's beating theory using the concept of critical bandwidth. Plomp and Levelt showed that two tones within the same critical band produce roughness regardless of their precise interval, and that consonance/dissonance correlates with whether tones fall inside or outside the critical band. This paper remains the starting point for psychoacoustic theories of consonance.

Sethares, William A. Tuning, Timbre, Spectrum, Scale (Springer, 2nd ed. 2005) An accessible but technically serious exploration of how the timbre (overtone structure) of instruments interacts with tuning systems to determine what sounds "consonant." Sethares demonstrates that consonance is not absolute but depends on the specific instrument: a gamelan instrument's inharmonic timbre makes its non-standard tuning system acoustically "correct" for that timbre, even though it sounds "out of tune" by Western standards. This book is essential for understanding why gamelan music sounds coherent on its own terms.

Harmony and Music Theory

Rameau, Jean-Philippe. Treatise on Harmony (1722; translated by Philip Gossett, University of Chicago Press, 1971) The founding document of functional harmony theory. Rameau was the first theorist to argue systematically that chords (not individual voices) are the fundamental units of harmony, and that harmonic progressions follow from the physics of resonance. Some of his acoustic claims are incorrect by modern standards, but his theoretical framework — tonic, dominant, subdominant functions; fundamental bass; inversion — remains the foundation of all subsequent Western harmony theory.

Piston, Walter. Harmony (5th ed., revised by Mark DeVoto, Norton, 1987) The standard undergraduate harmony textbook for decades. Clear, systematic, well-exemplified. Less theoretically adventurous than Tymoczko but invaluable as a reference for the mechanics of functional harmony: chord construction, voice leading, modulation, secondary dominants, and non-functional harmonies. Worth reading in conjunction with primary score analysis.

Aldwell, Edward, Carl Schachter, and Allen Cadwallader. Harmony and Voice Leading (4th ed., Cengage, 2010) The more analytically sophisticated alternative to Piston, incorporating Schenkerian concepts of hierarchical harmonic structure. Particularly strong on voice leading and its relationship to large-scale harmonic motion.

Counterpoint and Fugue

Kennan, Kent. Counterpoint: Based on Eighteenth-Century Practice (4th ed., Prentice Hall, 1999) A clear, practical introduction to species counterpoint and its application to 18th-century style. Works through all five species with many examples and exercises.

Mann, Alfred. The Study of Fugue (Norton, 1965) An anthology of fugue treatises from Fux through 20th-century theorists, with extensive commentary. The historical range reveals how the understanding of fugue has evolved while the basic structural principles remained stable.

Wolff, Christoph. Johann Sebastian Bach: The Learned Musician (Norton, 2000) The definitive Bach biography, with extensive technical analysis of Bach's compositional methods. Chapters on The Art of Fugue and The Well-Tempered Clavier are particularly relevant. Wolff situates Bach's contrapuntal achievements in the intellectual context of Enlightenment "learned music" — music intended to demonstrate the complete rational structure of a compositional system.

Levine, Mark. The Jazz Theory Book (Sher Music, 1995) The standard reference for jazz harmony. Comprehensive coverage of chord construction, voice leading in jazz contexts, modal jazz, reharmonization, and extended harmony. More practically oriented than theoretically, but invaluable for understanding how jazz musicians think about harmony.

Szwed, John F. So What: The Life of Miles Davis (Simon & Schuster, 2002) A comprehensive biography with good coverage of the Kind of Blue sessions, their context, and their influence. Particularly useful for understanding Davis's articulation of his reasons for moving toward modal jazz.

Gridley, Mark C. Jazz Styles: History and Analysis (11th ed., Pearson, 2012) A comprehensive survey of jazz history with strong musical analysis. The chapters on bebop (chapter 9-10) and the cool/modal period (chapter 11-12) provide excellent context for understanding Davis's innovations.

Non-Western Harmony

Nettl, Bruno. The Study of Ethnomusicology: Thirty-Three Discussions (3rd ed., University of Illinois Press, 2015) The most comprehensive introduction to ethnomusicology for Western readers. Part III on "The Music of the World's Peoples" includes excellent overviews of Indian classical, gamelan, and other non-Western musical systems.

Sorrell, Neil, and Ram Narayan. Indian Music in Performance: A Practical Introduction (Manchester University Press, 1980) A focused introduction to Indian classical music — raga theory, rhythmic cycles, performance practice — written accessibly for Western musicians. Particularly good on the concept of the raga as a complete aesthetic framework that includes pitch, ornament, emotional character, and time of day associations.

Tenzer, Michael (ed.). Analytical Studies in World Music (Oxford University Press, 2006) Scholarly analyses of non-Western musical systems by specialists. Includes substantial essays on Javanese gamelan, Carnatic music, Afro-Cuban music, and other traditions. More technically demanding but authoritative.

Atonality and Serialism

Schoenberg, Arnold. Style and Idea: Selected Writings of Arnold Schoenberg (University of California Press, 1984) Schoenberg's own essays on his compositional methods, the origins of twelve-tone technique, and the relationship between style and historical necessity. Essential primary source for understanding serialism from the inside.

Leeuw, Ton de. Music of the Twentieth Century: A Study of Its Elements and Structure (Amsterdam University Press, 2005) A clear analytical survey of twentieth-century compositional techniques, including atonality, serialism, spectralism, and minimalism. Good balance of technical precision and historical context.