HANDMADED INSTRUMENTS
Monochord
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A Brief History of the Monochord
The monochord consisted
of a single string stretched over a sound box, with the strings held taut
by pegs or weights on either end. It used a moveable bridge to change pitch,
and was usually plucked. A later instrument of the same principle was played
with a bow, called the "trumpet marine" (Adkins, New Grove). It
was used as an instrument as early 300 BC by Euclid (Ripin, New Grove),
and as a scientific instrument by Pythagoras as early as the 6th century
BC No one knows when it first appeared, as its origins extend into prehistory.
The monochord's impact as a scientific instrument is possibly more profound
than its musical importance. Pythagoras' study of ratios on the monochord
led philosophers to believe that these ratios also governed the movement
of planets and other cosmic matters (Ptolemy). This provided the bridge
between the world of physical experience and numerical relationships, giving
birth to mathematical physics. In addition, this elevated music to one of
the highest intellectual pursuits. Furthermore, since the "perfection
of sounds" could now be revealed by numbers, all simple numeric ratios
could be visualized as sounds. Kepler's "harmony of the spheres"
is based on this, as well as harmonically resounding architecture. If the
visible proportions of a building can be expressed in numeric ratios, then
their relationships can be "heard" as chords. Like the "golden
section" of architecture, musical harmony "imposes order in the
hearts and minds of men by virtue of their simple, natural relationships"
(Harnoncourt). This also helped support the baroque idea that music was
a reflection of the divine order (unless you were a minstrel, perhaps).
The monochord was later used as a teaching tool in the 11th century by Guido of Arezzo (fl. ~991/2-1033). By laying out the notes of a scale on a monochord, he was able to teach choir boys how to sing chant and also to detect incorrect chanting. The tones intervals used in chants were M2, m2, m3, P4, and P5. These six intervals were the "consonantiae", and (according to Guido) no chant uses any other intervals. Guido admits one could find more on the monochord if "art (did not) restrain us by its authority" (Palisca).
Music theorists have used the monochord since the time of Pythagoras to dissect the fabric of music. After Guido, the most important European theorist was probably Marchetto of Padua (fl. 1305-19). He was a leading composer of his day, and taught choir boys as Guido did. With the support of his patronage, he published his Lucidarium (1317-18), which contributed to musical philosophy, semiotics, numerology, and mathematics. He then published the Pomerium (1318-19) which covered more technical matters such as tuning, modality, melodic analysis, etc (Gallo, Vecchi). The most unique aspect of his tuning was his proposal that each whole tone be divided into 5 parts to allow for better tuning of intervals. These innovations influenced music theorists for almost 300 years (Rahn) After Marchetto came Gioseffo Zarlino, who proposed in his Institutione harmoniche, dividing the monochord into 6 parts, instead of the usual 4. Thus, for the first time, one was able to generate every consonant interval. He then extrapolated that there must be 6 species of voices (unisone, equisone, consone, emelle, dissone, and ecmele), as well as 6 consonances (diapason, diapente, diatessoran, ditino, semiditino, and unisono). He also then derives 6types of harmony, or modes (doria, frigia, mistalidia, o lochrense, eolia, and ionia).
Zarlino's work influenced music theory until Bach's time and beyond. In Bach's Clavier-Ubung, the 1st volume contains 6 partitas, which is just one of many mathematical references in Bach's music to the theoretical thought handed down by Zarlino. J.P. Kirnberger, who was a student of Bach's, explains scales, intervals, etc., according to Zarlino's principles in his Die kunst des reinen satzes in musik (1771-79). Even J.P. Rameau, in his Traite de l'harmonie (1772), based concepts upon the monochord.
Finally, the monochord probably provided the inspiration for the creation of the clavichord, which later led to the harpsichord and then the piano-forte. Early clavichords were really just several monochords of varying lengths built together (Ripin). To many keyboardists, this is seen as the monochord's most important contribution, but when comparing that to the impact it had on the sciences of mathematics and physics, one must concede that its reach has been far greater.
Pythagora and the Monochord
The monochord is a musical
and scientific laboratory instrument dating back to ancient human history.
It was perhaps invented by Pythagoras about 550 B.C. The history of western
science begins with Pythagoras and the Pythagoreans, a secret school which
only transmitted its findings orally. This geometrical body of thought was
essentially laid down by Plato in his dialogue "Timaeus". With Pythagoras
"everything is number" - he tried to describe natural phenomena
mathematically, to find numerical ratios in them. Here, we are first of all
reminded of Pythagorean music theory, in which harmonious intervals are represented
as proportions of whole numbers: the octave 2:1, the fifth 3:2, the fourth
4:3. This corresponds to the lengths of the vibrating strings of the monochord.
These numerical ratios became axiomatic.