Table of Propositions

...from the Unison, as if from their origin. 30. See the elevations to God. These "elevations" likely refer to spiritual reflections or prayers intended to lift the soul, a common feature in Mersenne's scientific works where he connects music to the divine.

VIII. To know if the smallest ratios The mathematical relationship between two notes, such as 2:1. and the smallest harmonic intervals come from the largest, or the contrary. 34.

IX. To determine if the chord whose ratio is two to one is correctly named the Octave, or if it should rather be called something else, for example, Diapason original: "Diapason"; the ancient Greek term for the interval of an octave, meaning "through all [the notes].". 39.

X. To determine if the ratio of the Octave is double, quadruple, or octuple. 43.

XI. From where the Octave takes its origin, and whether it comes from Sound or from the Unison. 47.

XII. The Octave is the sweetest and most powerful of all the Consonances Harmonious intervals that sound stable and pleasing to the ear. after the Unison, even though it is the most distant from it. 49.

XIII. Why strings that are an Octave apart cause each other to tremble and sound; how much more strongly those of the Unison tremble than those of the Octave; how much more strongly those that are touched Plucked or played. tremble than those that are not; and how much sweeter the Unison is than the Octave. 52.

XIV. The Octave, multiplied to infinity, does not change its smallest term In music theory, this refers to "octave equivalency," where doubling the frequency repeatedly (2:1, 4:1, 8:1) maintains the same relative identity of the note.. 55.

XV. Why, of all the doubled or multiplied Consonances, only the Octave remains a Consonance. 58. Where one sees the manner of multiplying ratios and chords.

XVI. The first and easiest division of the Octave produces the Fifth, the Fourth, the Twelfth, and the Fifteenth. 60.

XVII. The Fifth, whose ratio is three to two, is the third of the Consonances; but when doubled or multiplied, it becomes a Dissonance. 60.

XVIII. All the repeats or repetitions of the Fifth are agreeable, of which the first is three to one, and the second is six to one, and so on with the others, in which the smallest term always remains. It is also determined by how much the Fifth is less sweet than the Octave. 61.

XIX. To determine if the Fifth is sweeter and more agreeable than the Twelfth. 62.

XX. To determine if the Diapente original: "Diapente"; the ancient Greek term for the interval of a Fifth. is sweeter and more powerful than the Diapason The Octave.. 66.

XXI. A string, being touched, causes the one at the Fifth to tremble, but it causes the one at the Twelfth to tremble more strongly. 67.

XXII. The Diatessaron original: "Diatessaron"; the ancient Greek term for the interval of a Fourth. is the fourth Consonance, whose sounds have a ratio of four to three. 67.

XXIII. The Fourth comes from the Octave or from the second bisection A division into two equal parts. of a string, and its ratio can just as well be called sub-sesquitertial as sesquitertial original: "souz-sesquitierce" and "sesquitierce"; technical Latin-derived terms for the 4:3 ratio.. 68.

XXIV. One finds the Diatessaron The Fourth. on the same string divided into seven equal parts, by placing the bridge at the fourth part. 69.

XXV. To determine if the Fourth should be placed among the number of Consonances. 70.

XXVI. How much the Diapente The Fifth. is sweeter than the Diatessaron The Fourth; and why the latter is not as good against the Bass as the former. 72.

XXVII. The Fourth is so sterile that it can produce nothing good, neither by its multiplication nor by its division. 74.

XXVIII. The Ditone A Major Third. and the Semiditone original: "Sesquiditon"; a Minor Third. come from the third bisection of a