The Monochord
Physical Description
The monochord is an instrument used with scientific, experimental and pedagogical purposes. It consists of a single string, taut by the tips of a woodden plank with markings on some places where the string should be divided in sections in order to create different pitches. These markings represent the Gamut: the group of letters which correspond to pitches in the medieval musical notation system. These start from the G (Gamma in greek alphabet for the lowest of the notes) and then from A to F, there are seven letters in total; G A B C D E F. The name Gamut comes from the contraction of the first letter and the syllable that is connected with this first letter, which is Ut. There are six voices/syllables; ut re mi fa sol la, which form a hexachord -group of six notes- and are placed starting with ut from the G, from the C and from the F. There are three types of hexachord which depend in which letter the first syllable of the hexachord is placed; when starting on the G, we say it is a hard hexachord because the semitone mi-fa is placed on the letter B-C, and this B was thought as the hard B, the square B. Then, when placed on the C, we say it is a natural hexachord, because the semitone is not over a B, but over E-F. Finally, when it is placed over F, we say it is a soft hexachord because the semitone is placed over A-Bb, so including the soft B, the round B. This musical notation and solmnization information was placed in the monochord mainly when used with a music education purpose.
History
The history of the monochord is also the history of the first physico-mathematical law which is the demonstration on this instrument of the harmonic sound proportions[1]. It was presumably invented by Pythagoras although there is no consensus in whether he was the inventor or not. There have been many versions of this instrument depending on the year and the place in which it was built, and what the use was going to be. Boethius describes this ancient practice and clasifies the Greek monochord in three types: one with a movable bridge, one "dividing the monochord by length to demonstrate the three genres of tetrachords [these correspond to the Greek musical notation system] [2]", and one without any kind of division, only with the markings, to be divided with the finger and create a scale. In the low Middle Age and in the Renaissance Boethius findings and descriptions were strongly incorporated by men, so both the use of the instrument and the ways in which the proportions were calculated in ancient greek were taken into consideration when making and using the monochord for the teaching of chants.
The first type, then, was the one with a bridge. It was used mainly with scientific purposes to compare the length of the string with the pitch relationship of sounds.
In the Middle Age and Renaissance classrooms the most popular version was the third type. The string was pressed down with a finger in the different markings by the student in order to divide it. There are several description of how to build these and several methods on how the proportions should be calculated to mark the woodden plank.
The tuning of the monochord would depend in the way the wood was shaped and how long and tense the string was.
Harmonical science and pedagogical use
The learning already starts with the building of the monochord, when marking the wood plank with the Gamut. Although the proportions between the notes of the Gamut stay the same, the methods for marking the plank were different. The next big theorist who describes the building and use of the monochord after Boethius of the monochord is Pseudo-Odo in the 10th century in his “Dialogus de musica”. Odo uses the 9:8 proportion to mark the first step from Gamma ut to A re (figure 1). It repeats this step to find the second step from A re tu B mi (figure 2). After that, the 4:3 proportion is used to mark the fourth from Gamma ut to C fa-ut (figure 3) and the rest of the notes are built with the 4:3 proportion by fourths.
figure 1
Once the monochord is made, and the student has experimented how the string length has certain proportions that correspond to the pitches used in their music and the way in which these relate mathematically, the music could begin to be played using the single-string instrument.
When the boys mark some antiphon with these letters, they learn it better and more easily from the string than if they heard someone sing it; and they are able after a few months training to discard the string and sing by sight alone, without hesitation, music that they have never heard."
Pseudo-Odo
In the “Dialogus de musica”, then, Odo gives a very important place in music education to the monochord, since it is a tool that both contains theoretical (letters, syllables, proportions of intervals visualized) and practical (the sound) information.