Table of Propositions

I. To explain an easy method for learning and teaching how to read and write Music. 332. It is the invention of Monsieur des Argues. Gérard Desargues (1591–1661) was a renowned mathematician and architect; here, Mersenne refers to Desargues's proposal for a simplified musical notation using numbers.
II. To explain another method for learning to sing and to compose without ordinary notes, by means of the letters of the Alphabet alone, without mutations. 342. Original: "muances." This refers to the complex traditional system of shifting between "hexachords" (six-note scales) used in Renaissance music education.
III. To explain all the characters necessary to easily write and compose all kinds of Music, whether for voices or for all kinds of instruments. 347. Where one sees two compositions by du Caurroy in 7 and 8 parts, note-against-note; and the Perfect Harmonic Hand of the Gamut. The "Hand" refers to the Guidonian Hand, a mnemonic device used to help singers find their pitches; the "Gamut" is the full range of notes in the musical system.
IV. To learn to compose Music correctly in a short time. 351.
V. To explain the manner of knowing if a voice is good, and the qualities it must have. 353.
VI. To explain the manner used to train voices for the cadence, and to make them capable of singing all kinds of Airs. 354. Where one sees a warning for Masters who teach singing. In the 17th century, a "cadence" often referred specifically to a vocal ornament, such as a trill, rather than just the end of a musical phrase.
VII. To explain the characters necessary to signify all the particulars of the Airs that one desires to perform with every kind of perfection, and the manner of properly performing cadences and tremblemens. 358. "Tremblemens" were vocal ornaments similar to modern trills or shakes.
VIII. To explain the method of making good melodies for all kinds of subjects and letters. 360.
IX. To discover the skills that serve to compose good melodies. 362. Where one sees a specific warning for this subject.
X. Accents are so great in number that it is almost impossible to explain them all. 365.
XI. Accents reveal the country one is from, and sometimes the temperament and the mood. 366.
XII. The accent is a modification of the voice, by which one expresses the passions of the soul naturally or with artifice. 366. Mersenne views "accents" as the rhetorical and emotional inflections used in singing to move the listener.
XIII. Each affection of the soul has its own accents, by which it expresses its different degrees. 367.
XIV. One cannot express the Accents of the passions without new characters. 369.
XV. All the Accents of the 3 passions need nine different characters to be marked, namely 3 for the 3 degrees of anger, and two other sets of three for love and sadness. 370.
XVI. To determine if these Accents can be expressed and performed while singing Music. 371.
XVII. To show the utility that Preachers and other Orators can derive from the Accents of each passion. 373. Mersenne connects musical theory with rhetoric, suggesting that public speakers can use musical principles to better influence their audiences.
XVIII. Rhythmics establishes and regulates movements, their sequence, and their mixture to excite, increase, maintain, diminish, and appease the passions. 374. Where one sees 27 examples of movements or metrical feet. "Rhythmics" (Rythmique) refers to the study of musical meter and time, often modeled on the poetic feet of Greek and Latin verse.