Table of Propositions

arithmetically and geometrically, as well as the Consonances. 121.
Corollary. Dissonances serve harmony, although they enter it only by accident. 122.
V. How many commas A comma is a very small musical interval, the difference between two nearly identical notes in different tuning systems. the minor and major tones contain, and in what sense one can say that the minor tone is larger than nine commas. 123.
VI. To determine how many commas the Octave has. 125.
VII. Whether the false Fifth A diminished fifth. surpasses the Triton An augmented fourth., and by how much: where several degrees and intervals that serve to understand the Diatonic genre are explained. 126.
VIII. Whether the Triton surpasses the Fourth by more than the Fifth surpasses the Semidiapente Another term for the diminished fifth.. 127.
IX. Two minor Thirds, which can be taken in the same place as the Semidiapente—namely from the mi of E-mi-la The note E, to the fa of B-fa B-flat, or from ♮ mi B-natural to F-fa F—are larger by one major comma than the false Fifth: consequently, they surpass the Semidiapente more than it surpasses the Triton. 128.
X. To determine if Dissonances are as disagreeable as Consonances are agreeable: where one sees why pain is more sensible than pleasure. 129.
XI. To explain the consonant and dissonant Harmonic intervals that cannot be expressed by numbers. 132.
XII. From which positions weights must fall to create such proportions and accords or discords as one wishes, when they meet opposite one another. 134.
XIII. To demonstrate that there is no difficulty in the Theory of Music, and that everything in it is done by the mere addition or subtraction of beats of air Mersenne uses "beats of air" to describe what we now understand as sound wave frequencies.: where one sees how sounds resemble light. 137.
XIV. To provide the summary of everything that has been said in the book of Consonances and Dissonances. 139.

20 Propositions of the book of Harmonic Genres, Systems, and Modes.

I. To explain what the Diatonic genre consists of, its species, and the one used now: what the scale of Guy Aretin Guido of Arezzo, the medieval monk who invented the modern musical staff and solfège. consists of, and what the Tetrachords A scale of four notes used in ancient Greek music theory. of the Greeks are. 141.
II. Namely, whether the Diatonic degrees are more natural and easier to sing than those of the Chromatic and the Enharmonic. 147.
III. The ratios of the Diatonic degrees can be explained by the length of the strings and by the number of their vibrations. One sees where the minor tone and the major tone must be placed. 150.
IV. To explain the Diatonic, Chromatic, and Enharmonic Genres so clearly that all Musicians can easily understand them and use them in their Compositions. 153.
V. To explain the use of the Octave which contains the three aforementioned Genres. 155.
VI. To explain the same System or Diapason The full range of an octave or the standard scale. by beginning it with C-sol-ut Middle C.. 157.
VII. One can start each musical note on each Diatonic degree of the two preceding Systems, in order to transpose all sorts of tones on the Keyboard of the Organ arranged according to the Diapason. 161.