• 1

    A triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row.

  • 2

    James Murray Barbour, Tuning and Temperament: A Historical Survey(Mineola: Dover Publications, 1951), ch. 4.

  • 3

    Cris Forster, Musical Mathematics: On the Art and Science of Acoustic Instruments (San Francisco: Chronicle Books, 2010), section 11.46, p. 611.

  • 4

    For a great summary, see Ross W. Duffin, How Equal Temperament Ruined Harmony (and Why You Should Care) (New York, NY: W. W. Norton, 2007).

  • 5

    www.midi.org/articles/midi-history-chapter-6-midi-is-born-1980–83

  • 6

    Ibid.

  • 7

    www.midi.org/articles-old/microtuning-and-alternative-intonation-systems

  • 8

    www.microtonal-synthesis.com/MIDItuning.html

  • 9

    Reaper is the only exception, as far as I’m aware.

  • 10

    For an excellent discussion about this, see Douglas Keislar, Easley Blackwood, John Eaton, Lou Harrison, Ben Johnston, Joel Mandelbaum, and William Schottstaedt, »Six American Composers on Nonstandard Tunings,« Perspectives of New Music, 29(1) (1991), p. 176.

  • 11

    Alain Daniélou, Music and the Power of Sound: The Influence of Tuning and Interval on Consciousness (Rochester VT: Inner Traditions International, 1995), p. 247.

  • 12

    www.midi.org/articles-old/new-mma-members-and-new-mma-specs