Chapter 11 Further Reading: Pitch, Frequency & Musical Scales

Foundational Texts

Helmholtz, Hermann von. On the Sensations of Tone as a Physiological Basis for the Theory of Music (1863; English translation 1954, Dover Publications) The foundational text of psychoacoustics and music theory. Helmholtz's analysis of resonance, timbre, and consonance remains essential. His theory of consonance (simple frequency ratios produce fewer beating overtones) still underpins modern understanding. Dense but rewarding; read Chapters 10-14 for the direct treatment of scales and temperament.

Partch, Harry. Genesis of a Music (1949; 2nd ed. 1974, Da Capo Press) Part autobiography, part music theory manifesto, part acoustic physics treatise. Partch's rejection of equal temperament and his development of a 43-tone just intonation scale is the most comprehensive alternative to 12-TET ever developed by a single composer. Essential reading for Chapter 12 as well.

Jorgensen, Owen. Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament (1991, Michigan State University Press) An exhaustive historical and technical account of Western tuning systems. More reference than narrative, but invaluable for anyone who wants precise numbers and historical documentation.

Cross-Cultural Perspectives

Nettl, Bruno. The Study of Ethnomusicology: Thirty-Three Discussions (3rd ed., 2015, University of Illinois Press) The standard introduction to ethnomusicology. Chapter 5 (on scales and tuning in world music) and Chapter 7 (on universals in music) directly address the questions raised in this chapter. Nettl is careful, balanced, and genuinely comparative.

Blacking, John. How Musical Is Man? (1973, University of Washington Press) A short, provocative book by the ethnomusicologist who studied Venda music in South Africa. Blacking argues that music is a universal human capacity, and that all musical systems — however diverse — reflect deep cognitive universals. Essential counterpoint to purely acoustic accounts of scale universality.

Touma, Habib Hassan. The Music of the Arabs (1996, Amadeus Press) The standard English-language introduction to Arab classical music, including an accessible account of the maqam system, the quarter-tone division of the octave, and the aesthetics of Arab tuning. Chapter 3 is directly relevant to Section 11.7.

Jairazbhoy, N.A. The Rāgs of North Indian Music: Their Structure and Evolution (1971, Wesleyan University Press) The most rigorous analysis in English of the Hindustani raga system. Jairazbhoy traces the physical basis of the shruti scale and the historical evolution of raga categorization.

Psychoacoustics and Perception

Levitin, Daniel J. This Is Your Brain on Music (2006, Dutton) An accessible but scientifically careful account of music cognition, written by a neuroscientist who is also a record producer. Chapters 2 and 3 cover pitch perception, octave equivalence, and categorical perception at a level appropriate for undergraduates without neuroscience background.

Zatorre, Robert, and Salimpoor, Valorie. "Why Music Makes Our Brain Sing" (2013, The New York Times, June 7, 2013) A brief, accessible overview of the neuroscience of music pleasure. Available online. Good introduction to the brain basis of pitch and scale perception.

Pierce, John R. The Science of Musical Sound (1983, Scientific American Library) Chapter 4 covers scales and tuning with excellent mathematical clarity. Pierce was a physicist at Bell Labs, and his account combines acoustic rigor with musical understanding. Particularly good on the relationship between the harmonic series and scale construction.

The Blues and Microtonality

Oliver, Paul. The Story of the Blues (1969; revised 1997, Northeastern University Press) The comprehensive history of the blues as a musical form, with attention to its African roots, its development in the American South, and its spread to urban centers. Oliver's account situates the blue note within its full historical and cultural context.

Titon, Jeff Todd. Early Downhome Blues: A Musical and Cultural Analysis (2nd ed., 1994, University of North Carolina Press) A meticulous acoustic and cultural analysis of early recorded blues, including spectral analysis of pitch inflections and an anthropological account of the music's social functions. The most rigorous academic treatment of the blue note's acoustic properties.

Duffin, Ross W. How Equal Temperament Ruined Harmony (and Why You Should Care) (2007, W.W. Norton) An accessible, polemical account of equal temperament's historical rise and acoustic compromises. Duffin argues that pre-equal-temperament tuning systems produced better-sounding harmony for the repertoire of their time. Excellent for the ⚖️ debate on equal temperament.

Microtonal Music

Sethares, William A. Tuning, Timbre, Spectrum, Scale (2nd ed., 2005, Springer) The most rigorous modern treatment of the relationship between tuning systems and timbral spectra. Sethares demonstrates that consonance depends on the specific overtone structure of the instruments used, not just on abstract frequency ratios. This has profound implications for alternative tuning systems. Mathematically demanding but rewarding.

Xenharmonic Wiki (xenharmonic.wikispaces.com — content now mirrored on various sites) A community-maintained wiki covering hundreds of alternative equal temperament systems, including detailed analysis of 19-TET, 31-TET, 53-TET, and many others. Includes listening examples, theoretical analysis, and composition guides.

Video and Audio Resources

"Why Do We Have 12 Notes in an Octave?" — Adam Neely, YouTube A clear, musically informed explanation of why 12 notes emerged as the standard, with discussion of alternatives. Approximately 20 minutes. Highly recommended as a visual companion to Section 11.6.

"Twelve Tones" — Vi Hart, YouTube An entertaining, fast-paced animation explaining the relationship between the harmonic series and scale construction. Approximately 30 minutes. Unusual and creative in its approach.

"Harry Partch: The Dreamer Who Remains" — Betty Freeman, documentary film (1974) A short documentary following Partch in his studio, showing his instruments and his philosophy. Essential companion to Case Study 12.2.

Smithsonian Folkways Recordings The Smithsonian Folkways catalog (available online through many university libraries) includes extensive recordings of world music, including Arab maqam, Indian classical, Indonesian gamelan, and blues. Essential listening resource for the cross-cultural dimensions of this chapter.