¹ Although Samuel Barber, Henry Cowell, John Cage, Morton Feldman, Elliott Carter, Conlon Nancarrow, George Crumb, and George Perle composed string quartets, they do not rival the scope of Johnston's contributions. He composed his Quartet no.1 in 1951 and Quartet no. 10 in 1995.

² Ben Johnston, “Autobiographical Lecture,” filmed [April 2006], YouTube Video, 1:41:06, posted [November 2010], https://www.youtube.com/watch?v=slXIOTTYpHY. Composition faculty at the University of Illinois—including Lejaren Hiller, Herbert Brün, Salvatore Martirano, and James W. Beauchamp—developed compositional methods with algorithms, computers, and various electronic devices.

³ “Kepler Quartet's Website,” http://www.keplerquartet.com/index.html.

⁴ In five-limit just intonation, like most Western music tunings, the prime-numbered harmonics up to the fifth harmonic produce all the frequencies. Likewise, seven-limit, eleven-limit, and thirteen-limit just intonations point to the prime-numbered harmonics up to the seventh, eleventh, and thirteenth harmonics as the foundation of all the frequencies. Partch created his eleven-limit just intoned system and built several instruments on its basis. See Harry Partch, Genesis of a Music, 2nd ed. (New York: Da Capo, 1974).

⁵ The manuscripts of the quartets are located in the Ben Johnston Papers, an extensive archive of Johnston's materials at Northwestern University Library.

⁶ Partch's terms otonality and utonality refer respectively to a collection of pitches of a harmonic series analogous to major tonality in the common period harmony, and a collection of pitches of a subharmonic series (an exact inversion of a harmonic series) analogous to minor tonalities. Partch designed a two-dimensional diagram called “tonality diamond,” where one dimension presents the otonalities and the other dimension the utonalities. See Partch, Genesis of a Music.

⁷ Kyle Gann, liner notes to Ben Johnston: String Quartets Nos. 6, 7, & 8, Kepler Quartet, New World 80730-2, CD, 2016.

⁸ Partch Quartet no.7 manuscript, Ben Johnston Papers, 1939–2003, Northwestern University Music Library. Kepler's is the first recording of Quartet no. 6 since the New World String Quartet's 1983 performance released by CRI.

⁹ Johnston, “Autobiographical Lecture.”

¹⁰ Ibid.