1 Novalis, Schriften, ed. Friedrich Schlegel and Ludwig Tieck, 3 vols. (Berlin, 1837–46), iii, 236. Viktor Shklovsky, ‘Art as Technique’, Russian Formalist Criticism: Four Essays, trans. and with an introduction by Lee T. Lemon and Marion J. Reis (Lincoln, NE, 1965), 3–24. See also Terrence Hawkins, Structuralism and Semiotics (Berkeley and Los Angeles, CA, 1977), 62–7.

2 Walter Piston, Harmony (New York, 1941), 1–2.

3 I have explored these dual aspects in greater detail in ‘Beethoven's Function, Riemann's Functions: Tonality as Rule and Repertoire’, Music Theory Spectrum, 33 (2011), 109–23.

4 Friedrich Kittler and Matthew Griffin, ‘The City Is a Medium’, New Literary History, 27 (1996), 717–29; Kittler, Gramophone Film Typewriter, trans. Geoffrey Winthrop Young (Stanford, CA, 1999); Kittler, ‘Universities: Wet, Hard, Soft, Harder’, Critical Inquiry, 31 (2004), 244–56.

5 For a musicological exploration of this idea, see David Trippett, ‘Composing Time: Zeno's Arrow, Hindemith's Erinnerung, and Satie's Instantanéisme’, Journal of Musicology, 24 (2007), 522–80.

6 Friedrich Kittler, Discourse Networks 1800/1900 (Stanford, CA, 1990). Kittler's discourse networks have occasionally been described as Foucauldian epistemes transferred onto technological ground. I will return to this point; see note 51 below.

7 Sybille Krämer, ‘The Cultural Technique of Time Axis Manipulation: On Friedrich Kittler's Conception of Media’, Theory Culture and Society, 23/7–8 (December 2006), 93–109 (p. 106).

8 Franchinus Gaffurius, De harmonia musicorum instrumentorum opus, trans. Clement A. Miller (n.p., 1977), 35.

9 Gaffurius, De harmonia, 174.

10 For modern commentary, see for instance Frieder Rempp, ‘Bemerkungen zum Selbstverständnis der italienischen Musiktheorie im 16. Jh.’, Musiktheorie, 4 (1989), 100–12.

11 As Clement A. Miller points out, the enmity between the two goes back a long way. In 1489 Gaffurius had defaced Spataro's copy of Musica practica by his teacher Bartolomeo Ramis de Pareia by scribbling negative comments in the margin, which Spataro, understandably, took rather badly. See Gaffurius, De harmonia, 20.

12 Ibid., 204.

13 For a history of the monochord, see Cecil Adkins's monumental ‘The Theory and Practice of the Monochord’ (Ph.D. dissertation, State University of Iowa, 1963).

14 The figure of Pythagoras from Gaffurius's Theorica musicae is discussed in greater detail in my forthcoming article ‘Instruments of Music Theory’, which is in many ways the present article's sibling and counterpart.

15 On a practical level, it often proved difficult to find two strings that were in fact materially identical.

16 Johannes Kepler, Harmonices mundi (Linz, 1619). Kepler's multidisciplinary work on music was the subject of a recent exchange between Jonathan Owen Clark and Michael Fend: Clark, ‘The Voice and Early Modern Historiography: Reading Johannes Kepler's Harmony of the World’, Opera Quarterly, 29 (2013), 307–27; Fend, ‘Historical Alternatives to a Poststructuralist Reading of Johannes Kepler's Harmony of the World: Response to Jonathan Owen Clark’, ibid., 328–36.

17 Robert Fludd, Utriusque cosmi maioris scilicet et minoris metaphysica, physica et technica historia, 2 vols. (Oppenheim, 1617–21).

18 See Joscelyn Godwin, Robert Fludd: Mystic Philosopher and Surveyor of Two Worlds (Boulder, CO, 1979).

19 Creese coins this term after Raviel Netz, The Shaping of Deduction in Greek Mathematics (Cambridge, 1999).

20 David Creese, The Monochord in Ancient Greek Harmonic Science (Cambridge, 2010), 47.

21 See Joscelyn Godwin, Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music (Rochester, VT, 1993).

22 I take my cue from John Tresch and Emily Dolan's work, especially their ‘Toward a Critical Organology: Instruments of Music and Science’, Osiris, 28 (2013), 278–98. The discipline of music theory especially has a lot to learn from paying attention to organological aspects.

23 In ancient Greece, the aulos had also been used as a music-theoretical instrument, but was ultimately discarded because its sound production was subject to too many variables, such as breath control, embouchure, etc. See also Stefan Hagel, Ancient Greek Music: A New Technical History (Cambridge, 2009).

24 Gaston Bachelard, The New Scientific Spirit, trans. Arthur Goldhammer (Boston, MA, 1984), 13.

25 Mary McAllester Jones, Gaston Bachelard: Subversive Humanist (Madison, WI, 1991), 42.

26 Bruno Latour, Science in Action (Cambridge, MA, 1987); The Uses of Experiment: Studies in the Natural Sciences, ed. David Gooding, Simon Schaffer and Trevor Pinch (Cambridge, 1989); Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton, NJ, 2011).

27 On Actor-Network-Theory, see among many others Bruno Latour, We Have Never Been Modern (Cambridge, MA, 1993). Musicology has finally responded to ANT: see particularly Benjamin Piekut, ‘Actor-Networks in Musicology: Clarifications and Critiques’, Twentieth-Century Music, 11 (2014), 191–215.

28 Bill Brown, ‘Thing Theory’, Critical Inquiry, 28 (2001), 1–22. See also, among others, Jane Bennett, Vibrant Matter: A Political Ecology of Things (Durham, NC, 2010).

29 Davis Baird, Thing Knowledge: A Philosophy of Scientific Instruments (Berkeley and Los Angeles, CA, 2004).

30 Hans-Jörg Rheinberger, Towards a History of Epistemic Things (Stanford, CA, 1997).

31 I use the translation ‘blurriness’ as offered by Uljana Feest's review article ‘Remembering (Short-Term) Memory: Oscillations of an Epistemic Thing’, Erkenntnis, 75 (2011), 391–411, which is closer to the flavour of the original German than the term ‘vagueness’ that the official translation uses.

32 Timothy Lenoir, ‘Inscription Practices’, Inscribing Science, ed. Lenoir (Stanford, CA, 1998), 1–18 (p. 14).

33 Friedrich Kittler, ‘Zahl und Zeit’, Bild – Schrift – Zahl, ed. Sybille Krämer and Horst Bredekamp (Munich, 2008), 193–203 (p. 202).

34 Sybille Krämer, ‘Was haben “Performativität” und “Medialität” miteinander zu tun? Zur Einführung in diesen Band’, Performativität und Medialität, ed. Krämer (Munich, 2004), 13–31 (p. 23).

35 See Rheinberger, ‘Experimental Systems, Graphematic Spaces’, Inscribing Science, ed. Lenoir, 285–302 (p. 286).

36 The sometimes rocky history of these chorale editions has been described in the chapter ‘Inventing the Bach Chorales’ in Matthew C. Dirst, Engaging Bach: The Keyboard Legacy from Marpurg to Mendelssohn (Cambridge, 2012), 34–54.

37 The theoretical side of this chapter of Bach reception is illuminated by Thomas Christensen in ‘Bach and the Theorists’, Bach Perspectives 3, ed. Michael Marissen (Lincoln, NE, 1998), 23–45.

38 See Dirst, Engaging Bach, 46–7. The practice of using these chorales as teaching materials goes back to Bach's own teaching practice, as Johann Nicolaus Forkel relates in his seminal biography, Ueber Johann Sebastian Bachs Leben, Kunst und Kunstwerke (Leipzig, 1802).

39 See The New Bach Reader: A Life of Johann Sebastian Bach in Letters and Documents, ed. Hans T. David, Arthur Mendel and Christoph Wolff (New York, 1998), 384.

40 Johann Kirnberger, Die Kunst des reinen Satzes, 2 vols. (Berlin and Königsberg, 1774–9), i, 157; trans. from The New Bach Reader, ed. David, Mendel and Wolff, 367.

41 To cite just one example, Moritz Hauptmann, the first teacher of music theory at the Leipzig conservatoire in 1843, repeatedly underlined how fundamental four-part chorales were for all aspects of the composer's craft. See Briefe von Moritz Hauptmann an Franz Hauser, ed. Alfred Schöne, 2 vols. (Leipzig, 1871), i, 279–80; ii, 137, 157.

42 He explored this most thoroughly in his influential treatise The Nature of Harmony and Metre, trans. W. E. Heathcote (New York, 1991), though for our purposes the essay ‘Temperatur’ from his collection Opuscula: Vermischte Aufsätze (Leipzig, 1874), 16–51, is more pertinent.

43 Hauptmann, The Nature of Harmony and Metre, 24.

44 In the introduction to The Nature of Harmony and Metre, Hauptmann adamantly refuses to commit to the kind of scientific understanding of harmony that was in vogue at the time. Nonetheless, his commitment to a concept of nature (which is even highlighted in the title) – in this case the ‘nature’ of a quasi-Hegelian dialectic – is unaffected by this refusal.

45 Hauptmann, The Nature of Harmony and Metre, 25–6.

46 Hauptmann, ‘Temperatur’, 20. A detailed critique of this issue comes from Hugo Riemann, ‘Ideen zu einer Lehre von den Tonvorstellungen’, Jahrbuch der Musikbibliothek Peters (1914/15), 1–26 (p. 18).

47 In The Nature of Harmony and Metre he took the other way out of this quandary: rather than arguing for two kinds of D, as we saw in notes 43 and 45 above, he demoted the D minor triad to the status of a ‘diminished triad’, not a regular major/minor triad. This solution is logically consistent, though musically dubious.

48 It is worth bearing in mind that (non-equal-tempered) keyboard instruments with multiple options for specific tones had long existed, though by the nineteenth century they had become rare. See Patrizio Barbieri's magisterial Enharmonic Instruments and Music 1470–1900 (Latina, 2008). I am grateful to Martin Kirnbauer for reminding me of the importance of microtonal – or rather, ‘multitonal’ (‘vieltönig’) – keyboards. See his ‘“Vieltönigkeit” instead of Microtonality: The Theory and Practice of Sixteenth and Seventeenth Century “Microtonal” Music’, Experimental Affinities in Music, ed. Paulo de Assis (Leuven, 2015), 64–90.

49 See particularly his ‘Discourse Concerning the Unison’, trans. in Claude Palisca, The Florentine Camerata: Documentary Studies and Translations (New Haven, CT, 1989), 198–207.

50 This tension becomes particularly apparent in Hugo Riemann's Handbuch der Akustik (Berlin, 1891), which goes in great detail into different tuning systems, even though equal temperament was fully accepted by both musicians and theorists – including Riemann himself – as a necessity at the time.

51 Here I part company with Kittler, certainly the Kittler of Discourse Networks 1800/1900, who tends to view his Aufschreibesysteme as all-encompassing entities, modelled as analogous to the Foucauldian epistemes of The Order of Things (1966), which ruled exclusively and in strict temporal succession. What I have in mind here is closer to Foucault's later modified and more localized concept, in which ‘discursive formations’ may coexist in various power-knowledge systems. See Michel Foucault, Power/Knowledge, ed. Colin Gordon (New York, 1980), 197–8. The media-theoretical equivalent of this more circumspect concept is closer to Krämer's reframing of Aufschreibesysteme in the context of ‘cultural techniques’: see her ‘The Cultural Technique of Time Axis Manipulation’.

52 The piano clearly existed as a musical instrument before it assumed its role as a music-theoretical instrument in the context of common-practice theory. There are two preconditions for this change: (1) the implementation of equal temperament, and (2) our indifference to the specific timbre of the piano. I am grateful to Joseph Dubiel for helping me clarify this thought.

53 Guido of Arezzo, Micrologus, Hucbald, Guido, and John on Music: Three Medieval Treatises, trans. Warren Babb (New Haven, CT, 1978), 57–85.

54 Wolfgang Ernst especially tends to draw a sharp line between media archaeology and history. He explores the differences in numerous essays: see his Digital Memory and the Archive, ed. Jussi Parikka (Minneapolis, MN, 2012) and his recent Im Medium erklingt die Zeit (Berlin, 2015).

55 Friedrich Wilhelm Opelt, Über die Natur der Musik (Leipzig, 1834).

56 Anon., ‘A General Theory of Music’, The Harmonicon, 10 (1832), 168–70; Gottfried Wilhelm Fink, review of Über die Natur der Musik, Allgemeine musikalische Zeitschrift, 47/36 (1834), cols. 785–9; Carl Ferdinand Becker, ‘Theorie’, Neue Zeitschrift für Musik, 3 (1835), 121–3; Friedrich C. Schwiening, ‘Über Geist und Inhalt natürlicher Tonbewegung’, Cäcilia, 22 (1843), 69–72.

57 François-Joseph Fétis, ‘Opelt’, Biographie universelle des musiciens (2nd edn, Paris, 1867), vi, 372.

58 Charles Cagniard de la Tour, ‘Sur la sirène, nouvelle machine d'acoustique destinée à mesurer les vibrations de l'air qui constituent le son’, Annales de chimie et de physique, 12 (1819), 167–71.

59 Ernst Friedrich Chladni, Entdeckungen über die Theorie des Klanges (Leipzig, 1787); and see Peter Pesic, ‘Thomas Young's Musical Optics: Translating Sound into Light’, Osiris, 28 (2013), 1–39.

60 See for instance Ernst Robel, Die Sirenen: Ein Beitrag zur Entwicklungsgeschichte der Akustik (Berlin, 1891). For a media archaeology of the siren, see Philipp von Hilgers, ‘Sirenen: Loslösungen des Klanges vom Körper’, ZwischenRäume, 6 (2003), 103–21.

61 I have explored the wider context of this point in ‘Of Sirens Old and New’, The Oxford Handbook of Mobile Music Studies, ed. Sumanth Gopinath and Jason Stanyek, 2 vols. (New York, 2014), ii, 77–106.

62 Georg Simon Ohm, ‘Ueber die Definition des Tones, nebst daran geknüpfter Theorie der Sirene und ähnlicher tonbildender Vorrichtungen’, Annalen der Physik und Chemie, 59 (1843), 497–565. See also Benjamin Steege, Helmholtz and the Modern Listener (Cambridge, 2012). In some ways, Ohm's victory over his scientific opponent August Seebeck had the (unintentional) effect of retaining acoustics firmly in the realm of the ‘analogue’ and ignoring its ‘digital’ potential for years to come.

63 Anon., ‘A General Theory of Music’, 170. Kittler's influential Gramophone, Film, Typewriter must be mentioned here as the furthest-going effort to notate such ‘unmeaningful’ sounds.

64 Stockhausen's colleague at the Cologne Radio Studio, Herbert Eimert, points to the precedent of Opelt and his siren. See especially the entry ‘Impuls’ in Herbert Eimert and Hans Ulrich Humpert, Lexikon der elektronischen Musik (Regensburg, 1973), 142–4. This is one of very few references to Opelt in the literature. See Robin Maconie, Other Planets: The Music of Karlheinz Stockhausen (Lanham, MD, 2005), 519. I am grateful to Benjamin Steege for pointing this out to me.

65 See for instance Jonathan Goldman, ‘Cultural and Generational Querelles in the Musical Domain: Music from the Second World War’, Cambridge Companion to French Music, ed. Simon Trezise (Cambridge, 2015), 180–97 (p. 192).

66 See for instance Bill Friskics-Warren, I'll Take You There: Pop Music and the Urge for Transcendence (New York, 2005), 90.

67 Cowell's New Resources for Composition was published in 1930/1 but most of it was written much earlier, around 1915, at the same time as the Quartet Romantic. Cowell's work is explored in greater detail in my ‘Instruments of Music Theory’.

68 See for instance Aisthesis: Wahrnehmung heute oder Perspektiven einer anderen Ästhetik, ed. Karlheinz Barck, Peter Gente, Heidi Paris and Stefan Richter (Leipzig, 1990), and Gernot Böhme, Aisthetik: Vorlesungen über die allgemeine Wahrnehmungslehre (Munich, 2001).

69 See for instance Manfred Wagner, Die Harmonielehren der ersten Hälfte des 19. Jahrhunderts (Regensburg, 1974); Johannes Forner, ‘Leipziger Konservatorium und “Leipziger Schule”’, Die Musikforschung, 50 (1997), 31–6; and Mark Evan Bonds, ‘The Spatial Representation of Musical Form’, Journal of Musicology, 27 (2010), 265–303.

70 Friedrich Kittler, ‘Musik als Medium’, Wahrnehmung und Geschichte: Markierungen zur Aisthesis materialis, ed. Bernhard Dotzler and Ernst Martin Müller (Berlin, 1995), 83–99.

71 This definition is taken from Nietzsche contra Wagner, Friedrich Nietzsche, Kritische Studienausgabe, ed. Giorgio Colli and Martino Mozzinari, 15 vols. (Berlin, 1980), vi, 413–45 (p. 418). I have considered the music-theoretical response to this shift in perspective in ‘Mapping the Field: Music Theory and Philosophy’, The Oxford Handbook of Western Music and Philosophy, ed. Nanette Nielsen, Tomas McAuley and Jerrold Levinson (New York, forthcoming).

72 See also note 52 above.

73 Creese, The Monochord, 47.

74 Krämer, ‘The Cultural Technique of Time Axis Manipulation’, 97–8.