Tuning Theory


Return to: MUSC 726T | Bibliography 

Balzano, Gerald J. "The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems." Computer Music Journal 4/4 (Winter 1980): 66-88. {JSTOR}

Boatwright, Howard. "Ives' Quarter-Tone Impressions." Perspectives of New Music 3/2 (Spring - Summer, 1965): 22-31. {JSTOR}

Burns, Edward. 2012/1982. "Intervals, Scales, and Tuning." In The Psychology of Music, 3rd ed, edited by Deutsch, Diana. ed. New York: Academic Press. {GB}

Carey, N. and D. Clampitt. 1989. "Aspects of well-formed scales." Music Theory Spectrum 11/2: 187-206. {JSTOR}

Carlos, Wendy. 1989. "Three Asymmetric Divisions of the Octave." Available online at: <>.

____________. 1987. "Tuning at the Crossroads." Computer Music Journal 11/1 (Spring 1987): 29-42. Cambridge, MA. {JSTOR}

Clark, Philip. 2013. "The tuning wars: ‘Equal temperament destroys everything." Gramophone (Wed., Dec. 4, 2013). {}

Crismani, Dylan. "The Symmetry of a Tonnetz: Un-Transposable Harmonic Modes, and Modes of Synthesized Inversional Symmetry." Xenharmonikon (Feb. 24, 2021). {Xenharmonikon}

Crocker, Richard L. 1963/1964. "Pythagorean Mathematics and Music." The Journal of Aesthetics and Art Criticism 22/2 (Winter 1963): pp. 189-198 {JSTOR}; 22/3 (Spring 1964): pp. 325-335.{JSTOR }

Cutting, Court B. 2018. "Microtonal Analysis of 'Blue Notes' and the Blues Scale." Empirical Musicology Review 13/1-2 (2018).  {EMR}

Doty, David B. 2018. "Musical Ratios: The Why, How and Wherefore." Sound American (SA 20) {SA}

Duffin, Ross. 2006. "Just Intonation in Renaissance Theory and Practice." Music Theory Online 12/3 (October 2006) {MTO; See also:}

Fineberg, Joshua. 2000. "Guide to the Basic Concepts and Techniques of Spectral Music." Contemporary Music Review 19/2: 81-113.

Fonville, John. "Ben Johnston's Extended Just Intonation: A Guide for Interpreters." Perspectives of New Music 29/2 (Summer 1991): 106-137. {JSTOR}

Gann, Kyle. 2009. "Key Eccentricity in Ben Johnston's Suite for Microtonal Piano." Thirty-One 1 (Summer 2009). {HFF}

_________. 2000. "Between U S: A Hyperhistory of American Microtonalists." New Music Box (September 1, 2000). {NMB}

_________. 1993. "La Monte Young's The Well-Tuned Piano." Perspectives of New Music 31/1 (Winter, 1993): 134–162. {JSTOR}

Gilmore, Bob. 1995. "Changing the Metaphor: Ratio Models of Musical Pitch in the Work of Harry Partch, Ben Johnston, and James Tenney." Perspectives of New Music, 33/1/2 (Winter- Summer 1995): 458-503. {JSTOR}

Grady, Kraig. 2014/2007. "An Introduction to Moments of Symmetry: Wilson's Theories for Generating Microtonal Scales of any Size Interval." Available online at: <>.

Haack, Joel K. 1999. "The Mathematics of the Just Intonation Used in the Music of Terry Riley."  Proceedings of the Bridges: Mathematical Connections in Art, Music, and Science Conference (1999): 101–110. {Bridges Archive}

Halperin, Tamar. 2009. "The Ongoing Quest for Bach's Temperament." The Juilliard Journal (March 2009). Available online at: <>.

Hero, Barbara and R. M. Foulkrod, 1999. “The Lambdoma matrix and harmonic intervals.” IEEE Engineering in Medicine and Biology Magazine 18/2 (March-April 1999): 61-73.

Ives, Charles. 1962. "Some Quarter-Tone Impressions." In Essays Before a Sonata, the Majority and Other Writings. New York: Norton. {GB}

Johnston, Ben. 1976. "Rational Structure in Music." In Maximum Clarity and Other Writings on Music, edited by Bob Gilmore. Urbanna, IL: University of Illinois Press. {JSTOR}

Keislar, Douglas. 1991. "Six American Composers on Nonstandard Tunings: Easley Blackwood, John Eaton, Lou Harrison, Ben Johnston, Joel Mandelbaum, William Schottstaedt." Perspectives of New Music 29/1 (Winter 1991): 176-211. {JSTOR}

Levin, Theodore and Michael Edgerton. 1999. "The Throat Singers of Tuva." Scientific American (September 1999). {JSTOR}

Liern, Vicente. 2005. "Fuzzy tuning systems: the mathematics of musicians." Fuzzy Sets and Systems 150 (2005): 35–52.

Lindley, Mark and Ronald Turner-Smith. 1993. "An Algebraic Approach to Mathematical Models of Scales." Music Theory Online 0/3 (June 1993). {MTO}

Milne, A., D. Bulger, and S. Herff. "Exploring the space of perfectly balanced rhythms and scales." Journal of Mathematics & Music 11 2/3 (Jul.-Nov. 201): 101-133. {Ebscohost}

Milne, A., D. W. Bulger, and W. Sethares. "Perfect Balance: A Novel Principle for the Construction of Musical Scales and Meters." MCM 2015 (June 2015).

Muzzulini, Daniel. 2020. "Isaac Newton's Microtonal Approach to Just Intonation." Empirical Musicology Review 15/ 3-4. {EMR}

Nicholson, Thomas and Marc Sabat. 2018. Fundamental Principles of Just Intonation and Microtonal Composition. Available online at: <>.

O'Donnell, John. 2006. "Bach's Temperament, Occam's Razor, and the Neidhardt Factor." Early Music 34/4 (November 2006): 625-633. {JSTOR}

Polansky, Larry. 2018. "A Few Words About Tuning." Sound American (SA 20) {SA}

Rahn, Jay. 1998. "Practical Aspects of Marchetto’s Tuning. Music Theory Online 4/6 (November 1998). {MTO}

Schweinitz, Wolfgang von. 2011. "Iannis Xenakis’ Contributions to 20th Century Atonal Harmony and to the History of Equal Temperament:: The Aristoxenean Sieve Theory, and the Ptolemaic Alternative Some Thoughts on Our Perception of Musical Intervals." Available online at: <>.

Scholtz, Kenneth P. 1998. "Algorithms for Mapping Diatonic Keyboard Tunings and Temperaments." Music Theory Online 4/4 (July 1998). {MTO}.

Schubert, Peter N. 2017. "Thomas Campion’s 'Chordal Counterpoint' and Tallis’s Famous Forty-Part Motet." Music Theory Online 24/1. (March 2018) {MTO}

Schulter, Margo. 2018. "Huh? Microtonal music? A guide for the perplexed." Untwelve. Available online at: <>.

____________. 1998. Pythagorean Tuning and Medieval Polyphony. Available online at: <>

Sethares, William A. 1994. "Adaptive tuning for musical scales." Journal of the Acoustical Society of America 96/1 (July 1994). Available online at: <>.

________________. 1993. "Relating Tuning and Timbre." Experimental Music Instruments 9/2 (December 1993). Available online at: <>.

Shinn, Randall. "Ben Johnston's Fourth String Quartet." Perspectives of New Music 15/2 (Spring-Summer 1977): 145–173. {JSTOR}

Temperley, David. 2000. "The Line of Fifths." Music Analysis 19/3 (October 2000). {JSTOR}

Walker, Elaine. 2017. "What is Xenharmonic Music?" New Music Box (August 3, 2017). {NMB}

Walker, Jonathan. 1996. "Intonational Injustice: A Defense of Just Intonation in the Performance of Renaissance Polyphony." Music Theory Online 2/6 (September 1996). {MTO}

Wibberley, Roger. 2004a. "Syntonic Tuning: A Sixteenth-Century Composer's Soundscape." Music Theory Online 10/1 (February 2004). {MTO}

______________. 2004b. "Syntonic Tuning: Creating a Model for Accurate Electronic Playback." Music Theory Online 10/1 (February 2004). {MTO}

Wild, Jonathan. "Genus, Species and Mode in Vicentino’s 31-tone Compositional Theory." Music Theory Online 20/2. {MTO}.

Wild, Justin and Peter Schubert. 2008. "Historically informed retuning of polyphonic vocal performance." Journal of Interdisciplinary Studies 2 (2008). {}

Willis, Laurence Sinclair. 2019. "Comprehensibility and Ben Johnston’s String Quartet No. 9." Music Theory Online 25/1. {MTO}

EMR - Empirical Musicology Review
GB - Google Books
HFF - Huygens-Fokker Foundation
MTO - Music Theory Online
NMB - New Music Box
SA - Sound American

Updated: February 27, 2024

Reginald Bain | University of South Carolina | School of Music