Table of Propositions

XX. That one can learn to speak and pronounce well by means of Music. 28.

XXI. To explain how the voice increases or weakens. 29.

XXII. To determine if a single man can sing two or three different parts at the same time, and if he can ascend or descend higher by some kind of artifice than he ordinarily does. 31.

XXIII. How halls or galleries must be built to hear at one of the extremities everything that is said at the other, even though they are very long and the voices are very weak: wherein one sees the reason for the circle in relation to the ellipse, whose measurements are explained. 32.

XXIV. How one must measure the Ellipse, whose major diameter is equal to the semi-diameter of the firmament, and any other proposed Ellipse. 32.

XXV. In what place on the major diameter of the Ellipse its focioriginal: "foyers"; the two points in an ellipse where sound or light rays originating from one are reflected toward the other. meet, at which the rays of sound and light reflect when they come from one or the other of the said foci. 34.

XXVI. The two foci of the Ellipse and one of its diameters being given, to find the other diameter; and its two diameters being given, to find its two foci. 35.

XXVII. How Architects must build structures to aid sounds: wherein one sees that craftsmen do not trace a true Ellipse when they describe their Oval. 35.

XXVIII. To explain other ways that serve to describe the Ellipse. 36.

XXIX. The original OCR reads "XIX," a printer's error for XXIX. To describe the Parabola to gather voices in the same place. 37.

XXX. To describe all sorts of Hyperbolas for the same subject. 39.

XXXI. To explain the terms of Conic sections that can serve Architects, and which are necessary to understand their properties. 39.

XXXII. By which organs the passagesRapid melodic ornaments or runs. and the trillsoriginal: "fredons"; vocal decorations common in 17th-century singing. of Music are made. 40.

XXXIII. To know if speech is more excellent than song, and in what they differ. 41.

XXXIV. To know if the French method of singing is the best of all possible methods. 42.

XXXV. What the vices of the voice are, and if one can make a bad and inflexible voice sing Music, such as that of Louis XIIKing Louis XII of France (1462–1515) was famously said to have a very poor singing voice; the composer Josquin des Prez reportedly wrote a piece for him consisting of a single repeated note.. See the 45th Proposition of the 6th book on Composition, which gives the qualities of a good voice.

XXXVI. The remedies to cure the vices of the voice, and to preserve it. 45.

XXXVII. How one can learn to sing by all kinds of degrees and intervals without a Master. 46.

XXXVIII. How birds learn to sing and to speak, and if they receive any pleasure from it. 47.

XXXIX. Why all birds do not speak; why no four-footed animal speaks; if their voices serve them as speech, and if there is a way to understand it. 49.

XL. How the serpent of Eden and the she-ass of BalaamA reference to the biblical story in Numbers 22, where a donkey is miraculously given the power of speech. spoke, and in what manner God or the Angels speak. 53.

XLI. How those who imitate spirits, and who seem to be very far away when they speak, form their words. This refers to the practice of ventriloquism, which was often associated with spirit possession or deception in this period. 54.

XLII. To know if the preceding Sibilotsoriginal: "Sibilots"; likely referring to ventriloquists or those who make whistling or hissing sounds (from Latin 'sibilare'). offend God, and if they should be—