Ink blot obscuring text in proposition X.

Table of Propositions

The 20 Propositions of the 1st Book on Instruments.

I. Determine how many species of sounds and musical instruments there are. 1.
II. Explain the material and the manner in which the strings of instruments are made. 3.
III. Determine if harmonic instruments were made in imitation of voices, or if the intervals of voices were regulated by those of instruments; and whether Art can perfect nature, or the contrary; and if one must judge artificial things by natural ones. 7.
IV. Which is the most pleasant sound of all the instruments, and which instrument one should use to regulate Harmonic intervals The mathematical distances between musical pitches that create harmony.. 9. Wherein one sees the Monochord of Ptolemy. The monochord is an ancient scientific instrument with a single string and a movable bridge, used to measure musical intervals. Claudius Ptolemy was a famous 2nd-century scholar who refined its use.
V. Demonstrate all the divisions of the Monochord, and consequently the entire science of music. 16.
VI. Demonstrate that the Monochord divided into 8 equal parts contains all the Consonances Musical intervals that sound stable and pleasant to the ear, such as the octave or fifth.. 19.
VII. Explain the simplest division of a string to make it produce Consonances and the Diatonic degrees The standard steps of a musical scale.. 20.
VIII. Explain the intervals, both Consonances and Dissonances, which are found in the residues of the Monochord string after the Diatonic degrees have been marked upon it. 21.
IX. Explain all the Consonances and Dissonances of the Monochord and the Perfect System The "Systema Perfectum" was the full range of notes used in ancient Greek music theory., whether one compares the whole string to the parts that make the Diatonic, Chromatic, and Enharmonic degrees, or compares each degree or sound with the entire string or with its remainder. In such a way that the Monochord and the Harmonic System are here considered in every way that can serve Harmony. 22.
X. Divide all sorts of strings, or straight lines, into as many equal parts as one wishes, without changing the opening of the compass by chance?. 25. See also the 17th proposition of the 4th book which follows.
XI. Determine the number of Aspects In astrology, "aspects" are the angular distances between planets; Mersenne compares these celestial relationships to musical intervals. by which the stars look upon the earth, and the Consonances to which they correspond. 27.
XII. Explain the figure of a particular Monochord and all its divisions. 32.
XIII. Explain the difference and the distance from one Consonance or Dissonance to another by means of the Monochord; and the manner of dividing the same string half by half to make all sorts of Consonances and Dissonances. 35.
XIV. Explain another Monochord of equality, to divide the neck of the Lute, the Viol, the Cittern A wire-strung instrument popular in the 16th and 17th centuries., and all other instruments played in 12 equal semitones This is an early description of "Equal Temperament," the tuning system used on modern pianos., and to create the Diapason The standard pitch or range of an instrument. and the tuning of Spinnets and organs. 37. See the 6th and 7th propositions of the 2nd book, and the 9th of the 4th book following.
XV. Determine how much the intervals of this Monochord of equality are smaller or larger than those of the Monochord which follows just proportions: and if the ear can perceive the differences. 39.
XVI. What is the force of all sorts of strings, of whatever length...