Table of Propositions

...of the Unison, as if from their origin. 30. See the elevations to God. Mersenne frequently links the physical properties of music to spiritual contemplation.

VIII. To know whether the smallest ratios and the smallest Harmonic intervals come from the largest, or vice versa. 34.

IX. To determine if the chord whose ratio is two to one is rightly named the Octave, or if it should rather be called something else—for example, the Diapason. 39. original: "Diapason"; from the Greek "dia pason," meaning "through all notes."

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

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

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

XIII. Why strings that are an Octave apart make one another tremble and sound; how much more strongly those of the Unison tremble than those of the Octave; how much more strongly the touched strings tremble than those that are not; and how much sweeter the Unison is than the Octave. 52. This refers to the phenomenon of sympathetic resonance.

XIV. The Octave multiplied to infinity does not change its lowest term. 55.

XV. Why, of all the doubled or multiplied Consonances, only the Octave remains a Consonance. 58. Wherein 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 being doubled or multiplied, it becomes a Dissonance. 60.

XVIII. All the replies or repetitions of the Fifth are agreeable, the first of which is three to one, and the second six to one, and so on with others, of which the lowest 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 Greek term for the interval of a Fifth. is sweeter and more powerful than the Diapason. 66.

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

XXII. The Diatessaron original: "Diatessaron"; the 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 of a string, and its ratio can just as well be called sub-sesquitertial as sesquitertial. 68. Term: "Sesquitertial" refers to the ratio 4:3 (where the larger number is 1 and 1/3 of the smaller).

XXIV. One finds the Diatessaron on a single 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. In the 17th century, the status of the Fourth as a "perfect" consonance was a subject of significant debate among theorists.

XXVI. How much sweeter the Diapente is than the Diatessaron; 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 and Semiditone original: "Diton & Sesquiditon"; the Ditone is a Major Third, and the Semiditone or Sesquiditone is a Minor Third. come from the third bisection of a...