Monochords

The monochord is still a musical instrument, for example the Ektar in India, and a metaphor of the hermetic tradition, see for example [James, Ch. 7]. But what we mean by monochord is a scientific instrument for the study of musical intervals and scales.

Experimental setup

For our experiments, it is useful to have on hand two monochords, or a duochord, and a stack of rulers.

Monochord

Each monochord should each have two fixed bridges (the nut and the head) and a movable bridge, or fret. The length is typically one meter but longer is even better. The string to be sounded is between the fret and the nut. The two strings should be the same length, and tuned to the same note, which we will take to be the C below middle C, that is, a frequency around 260 Hz. We also will standradize our graphics with the string horizontal, and the head to the left. This conforms to a slide guitar, for example, played by a right-handed musician: sliding the fret with the left hand, and plucking with the right. Moving the fret to the right raises the pitch of the sounding part of the string, corresponding to the standard orientation of piano keyboards.

Rulers

The rulers all provide linear scales increasing from the nut to the head or vice versa, with intermediate fiducial marks against which the position of the fret may be read.
  • Modern ruler, 2-1-0 [Terpstra, p. 143]
    This ruler should be marked 0 (at the nut) 2 (at the top bridge) and 1 (in the middle). It is modern in the sense that it measures in the real number continuum, while the ancients used only rationals (fractions) and in fact, preferred integers.
  • Alternate modern ruler, 1-1/2-0
  • 4-3-2-1-0 [called 2-4, Terpstra, p. 145]
  • 6-5-4-3-2-1 [called 3-6, p. 145]
  • 8-7-6-5-4-3-2-1-0 [called 4-8, p. 145]
  • 6-12 [pp. 151-153]
  • 12-24 [p. 155]
  • 24-48 [p. 149]
    • and many others for advanced lessons. Rulers may be made by folding paper. See [McClain, p. 169].

    References

    The best little reference I have seen is Terpstra (see Bibliography). See also Fideler (follows directly after Terpstra in Alexandria 2) and McClain.
    Revised 12 December 2001 by Ralph Abraham