THE MONOCHORD
The harmonist's instrument for experimenting and measuring is the monochord: the one-stringed instrument (το μονόχορδον, from μονος [monos] = one, and χορδή
[chorde] = string). In its simplest form, it consists of a board with a
string of given length stretched on it between two bridges. For
practical reasons, I envisage a thirteen-stringed monochord (for the
analysis of a self-contained chromatic scale of twelve notes), with
each string 1200 millimeters long. Thus the name “one-stringed” is,
strictly speaking, no longer correct and would be better replaced with
“sonometer,” “phonometer” (both meaning sound-gauge) or “polychord”
(many-stringed). However, since all thirteen strings have the same
length, thickness, and tension, and therefore give the same tone, we
are in effect dealing with one and the same string. For this reason,
and also for reasons of historical sentiment, we will retain the term
“monochord.”
§1a. Building a Monochord
One can easily build one's own monochord, or have it built by a
carpenter or piano maker. I recommend making the chest out of planed
spruce boards 123 cm long, 26 cm wide, and 10 cm high, firmly glued
together.

Figure
So that the chest will not bend under the relatively high tension in
the strings, it is advisable for the upper soundboard to be 1 cm thick,
and the lower one at least 2 cm thick. The thin headboards on each end
should be reinforced with strong wood blocks 3-4 cm thick at the points
where the nuts will be fixed. A thickness of 1 cm should suffice for
the boards on the sides. On each side board, cut two sound holes about
4-5 cm in diameter. At each end of the top board, affix a brass nut 1.5
cm high, 1.5 cm wide, and 26 cm long, at an exact right angle to the
length of the chest, so that between the two nuts there is a distance
of precisely 120 cm (1200 mm). This precision is essential for precise
tone analysis. Bridges for insertion beneath the strings, 11 mm high
and with the cross section pictured in Fig. 1, should be cut from a rod
of ash or hardwood, smoothed down by a carpenter. The insertion of the
bridges must not result in the strings being pulled too taut; they
should be just tight enough for the two divided parts of the string to
sound clearly, without buzzing. If necessary, file small notches in the
bridges. Place the 13 steel strings at equal distances from one another
and fasten them, with ordinary piano tuning pins, onto the string
boards at the head and foot of the monochord. With these pins, they can
be tuned to the exact same note (here middle c)
with the aid of a tuning fork. The easiest and simplest way to make the
strings sound is to pluck them. But the sound is better if the string
is struck with a small felt-covered wooden hammer, which can be made
easily.
§1b. Dividing the Strings on the Monochord
For measuring divisions along a string 120 cm in length, it is best to
use strips of millimeter paper 120 cm long, which can be fastened with
pins under the strings between the brass nuts. Since we will be
examining many different tone ratios, we will need a supply of
replaceable paper strips, on which we will note the locations in
question with lines and the appropriate tone and number signs. The
methods of division will be specified in each case.
§1c. Historical Remarks
The monochord is one of mankind's most venerable tools for scientific
research, with a history going back into impenetrable antiquity. Its
significance first comes to light with the Pythagoreans, who by means
of the monochord made the discovery-an epoch-making one for Western
scientific thought-that qualities (in this case, the hearing of tones)
can be traced to quantities (measurement with numbers). “Modern natural
science was born as empirical Pythagoreanism,” writes W. Windelband in
his Lehrbuch der Geschichte der Philosophie
(1935, p. 326). However, it should not be forgotten that for the
Pythagoreans, the tracing of the qualitative to the quantitative, or as
we harmonists would say, the path from tone to number, was only one
aspect of this discovery. The other aspect was the transformation of
quantity (string lengths on the monochord) into quality, i.e., of the
measurable into the perceptible, the physical into the psychic, the
number into the tone. For the ancients, this was a phenomenon at least
equally wondrous, evoking their astonishment to a similar degree.
Because of this dual aspect, the monochord soon became a kind of
universal experimenting tool, a “canon” for psychophysical, scientific,
and aesthetic investigations in the broadest sense. The monochord
survived into the Middle Ages, though its use was increasingly
restricted to investigations in music theory, and it finally served
merely as an aid to precise intonation for choral singers, thereby
becoming the direct precursor of the clavichord, harpsichord, and
eventually the piano. Thus the monochord is, on the one hand, the
prototype of the precise experiment in the natural sciences in the
West, and on the other hand, the direct forerunner of that very
instrument-the piano-to which all music is so greatly indebted for its
enormous development.
§1d. Bibliography
Regarding the monochord, the best work, mainly historical and with further bibliographical sources, is Sigfrid Wantzloeben, Das Monochord als Instrument und als System, Halle, 1911. See also A. von Thimus, Das harmonikale Symbolik des Alterthums, I, 29-30; H. Kayser, Vom Klang der Welt, 20, 50ff., 61, 78, 115, 149, 170; Abhandlungen, 87-88; Grundriß, 47, 54, 58, 64. [See the end of this book for full details of Kayser's works.]