¹ For the first study of a sizeable portion of Polansky's output, and a brief biographical sketch, see Giacomo Fiore, ‘The Just Intonation Guitar Works of Lou Harrison, James Tenney, and Larry Polansky’ (PhD diss., University of California, Santa Cruz, 2013), 135–219.

² ‘My way of working is to come up with fertile ideas and explore them a lot, usually playfully, since that's my nature as a musician. Sometimes I feel like the conceptualist in me is a kind of wholesaler to the musician – one gives the other raw stuff, and the other makes music out of it. Sometimes these two are the same person, and that's when the pieces, to me, are the best’. Polansky, ‘Answers to Questions of Paul Doornbusch; About Mapping’ http://eamusic.dartmouth.edu/~larry/misc_writings/talks/about.mapping.html, accessed 30 August 2013.

³ The majority of Polansky's works, along with several writings, computer programmes, sound recordings and photos, can be accessed on his personal website: <http://eamusic.dartmouth.edu/~larry/>. The choice of making this material publicly available (especially considering Polansky's ties with a composers' collective that publishes the same works) is a deliberate comment on publishing, accessibility and imprimatur.

⁴ The slow, regulated change at play in these pieces makes them a specialised subset of Polansky's so-called morphing pieces, which explore fine parametrical changes from a ‘source’ to a ‘target’ musical item. See pieces such as 51 Melodies (1991), Roads to Chimacum (1992), The Casten Variations (1993–4), and the Four Voice Canon series. For the theoretical groundwork, see Larry Polansky, ‘Morphological Metrics: An Introduction to a Theory of Formal Distances’, Proceedings of the International Computer Music Conference, Urbana, IL (San Francisco: Computer Music Association, 1987), pp. 197–205; and Polansky, Larry with Bassein, Richard, ‘Possible and Impossible Melody: Some Formal Aspects of Contour’, Journal of Music Theory, 36 (1992), pp. 259–84CrossRefGoogle Scholar.

⁵ Obviously, this criticism is predicated on the assumption that a successful modulation requires both ‘keys’ to have similar (or in some cases identical) degrees of intervallic consonance. In fact, there is nothing preventing modulations in just intonation systems, were one to find complex intervallic ratios acceptable or desirable. See Gann, Kyle, ‘Key Eccentricities in Ben Johnston's Suite for Microtonal Piano’, in Thirty-One, 1 (2009), 42–48Google Scholar, for a pointed discussion of this issue.

⁶ Notable examples include Nicola Vicentino's Archicembalo and Perronet Thompson's Enharmonic Guitar.

⁷ Partch, Harry, Genesis of a Music (New York: Da Capo Press, 1974), pp. 181–94Google Scholar.

⁸ Gann, ‘Key Eccentricities,’ pp. 42–8.

⁹ Harrison, describes his Free Style method in his Music Primer (New York: C.F. Peters, 1971)Google Scholar. For a broader analysis, see Miller, Leta and Lieberman, Fredric, Composing a World: Lou Harrison, Musical Wayfarer (Chicago: University of Illinois Press, 2008), pp. 116–21Google Scholar. In addition, a short but pointed review of the importance of Harrison's method appears in Polansky, Larry, ‘Item: Lou Harrison's Role as a Speculative Theorist’, in A Lou Harrison Reader (Santa Fe: Soundings Press, 1987)Google Scholar, 92.

¹⁰ In fact, it is exactly because of the tempering that recursive intervals ‘return’ to their starting point, closing the spiral of fifths of Pythagorean intonation into its more famous circular counterpart.

¹¹ Tenney, who was not particularly inclined to write about his own pieces, made an exception for Changes: see ‘About Changes: 64 Studies for Six Harps’ in Perspectives of New Music, 25 (1987), pp. 64–87Google Scholar. See also Brian Belet, An Examination of the Theories and Compositions of James Tenney (PhD diss., University of Illinois at Urbana-Champaign, 1990); and Fiore, ‘Just Intonation Guitar Works’, pp. 101–23.

¹² For a historical, theoretical and aesthetic exposition of Polansky's interpretation of this subset of intonation theory, see Polansky, Larry, ‘Paratactical Tuning: An Agenda for the Use of Computers in Experimental Intonation’, Computer Music Journal, 11 (1987), pp. 64–5CrossRefGoogle Scholar.

¹³ Polansky, liner notes to The Theory of Impossible Melody, New World Records 8064 (2009; originally issued as ART1004, 1989).

¹⁴ For all examples in this article I have chosen to employ the Helmholtz-Ellis microtonal notation devised by Marc Sabat and Wolfgang von Schweinitz. The benefits of this system include precision, transposability and the reliance on intuitive and discrete symbols. For a brief introduction to the symbols and a legend, see Sabat, ‘An Informal Introduction to the Helmholtz-Ellis Accidentals’, http://www.marcsabat.com/pdfs/legend.pdf, accessed 30 August 2013. Each example also includes harmonic numbers, for added clarity.

¹⁵ Recurrence of the number 17 and its multiples as tuning limits, titles and sectional lengths is, by Polansky's own admission, a symptom of a mild case of heptadecaphilia (Polansky, personal communication with the author, 26 July 2013).

¹⁶ Polansky clarifies his choice of terminology in ‘Paratactical Tuning’, p. 68: ‘I invoke the word paratact to describe a situation in which cause and effect are not unambiguously specified, but which are sometimes clarified by a larger context. A simple textual example might be the difference between “I feel so bad’ cause my baby left me this morning” (syntact) and “I feel so bad, my baby left me this morning” (paratact)'. As discussed earlier in the article, the adaptive tuning is more dependent on the immediate context rather than on a pre-existing set of rules, such as the definition of a scale.

¹⁷ A recording of this performance is available online at http://music.dartmouth.edu/~larry/mp3_files/freeHorn_performances/freeHorn_UCSC_April_2012.mp3 (accessed 31 August 2013). Amy Beal is Professor of Music and Ma'ayan Tsadka is a graduate student in music at U.C. Santa Cruz.

¹⁸ A tricone resophonic guitar retuned in just intonation was the instrument envisioned by Lou Harrison for his last finished composition, Scenes from Nek Chand (2002); several other composers, including Polansky, have since written music for this uniquely resonating instrument. For more on the guitar and its repertoire, see Fiore, Giacomo, ‘Reminiscence, Reflections, and Resonance: The Just Intonation Resophonic Guitar and Lou Harrison's Scenes from Nek Chand’, Journal of the Society for American Music, 6 (2012), 211–37CrossRefGoogle Scholar. Although originally tuned to a G fundamental, with the open strings tuned DADGAD, the JI resophonic guitar has been used in several performances of freeHorn, solo and in ensemble, through the employment of simple open-string tuning modifications. For the performance in question, the strings were tuned CFCGAC, or 3–1–3–9–5–3 (in harmonic series terms).

¹⁹ This structural device was first introduced in Choir (Empi's Solo) (1997), another ‘orchestration’ of the Psaltery idea co-composed with soprano Marie Pauline Esguerra. Available on Polansky, Change, ART1023.

²⁰ Polansky actually considers ‘Preamble’ to be part of the Psaltery set; however I have chosen to group it with other guitar pieces in which the instruments are retuned in real time for analytical purposes.

²¹ For Polansky's analysis of Tenney's method, see his ‘The Early Works of James Tenney’, Soundings 13 (1984), pp. 214–18Google Scholar; also ‘Confessions of a Lousy Carpenter’, in 1/1, 1 (1985), pp. 1, 10–14, in which Polansky explains his approach to writing for bowed strings using harmonic scordaturas, as exemplified in the early works Movement for Lou Harrison (1975) and Movement for Andrea Smith (1978). A study of Tenney's guitar writing in his Spectrum 4 is found in Fiore, ‘Just Intonation Guitar Works’, pp. 124–33.

²² The second movement had had its premiere shortly after its completion, by dedicatee John Schneider's ensemble Just Strings at the Japan–USA co-sponsored Interlink Festival in fall 1995.

²³ Polansky, Callier, Troch, et al. The World's Longest Melody (New World Records 80700, 2010). For a video of ‘Preamble’ being performed by Estelle Costanzo (harp), Julien Mégroz (tuning) and Flavio Virzi (guitar) in Basel on 18 October 2011, see http://www.youtube.com/watch?v=TuZlnjK8x7o, accessed 31 August 2013.

²⁴ toovviivfor can also be heard on New World Records 80700.

²⁵ Cellist and composer William Raynovich premiered the first movement of 3 Cello Tunes on 14 July 2013 at the Frequency new music series in Chicago, Illinois; he is currently preparing the remaining two movements for performance.