Table of Propositions

XX. One can learn to speak and pronounce well by means of Music. 28.
XXI. Explaining how the voice increases or weakens. 29.
XXII. Determining if a single man can sing two or three different parts at the same time, and if he can go higher or lower by some sort of artifice than he ordinarily does. 31.
XXIII. How one must build halls or galleries to hear everything said at one end from the other, even if they are very long and the voices are very weak: where one sees the relationship of the circle to the ellipse, whose measurements are explained. 32.
XXIV. How to measure the Ellipse, whose major diameter is equal to the semi-diameter of the firmament The sphere of the stars or the heavens, and any other proposed Ellipse. 32.
XXV. At what point on the major diameter of the Ellipse its foci are found, where the rays of sound and light reflect when they come from one or the other of said foci. 34.
XXVI. The two foci original: "focus" of the Ellipse and one of its diameters being given, find the other diameter; and its two diameters being given, find its two foci. 35.
XXVII. How Architects must build structures to aid sounds: where one sees that craftsmen do not trace the Ellipse when they describe their Oval. 35.
XXVIII. Explaining other ways that serve to describe the Ellipse. 36.
XIX. Likely a printer's error for XXIX Describing the Parabola to gather voices in the same place. 37.
XXX. Describing all sorts of Hyperbolas for the same subject. 39.
XXXI. Explaining the terms of Conic sections that can serve Architects and which are necessary for understanding their properties. 39.
XXXII. Through which organs musical passages and trills original: "fredons"; vocal ornaments or rapid runs of notes are made. 40.
XXXIII. Whether speech is more excellent than singing, and in what they differ. 41.
XXXIV. Whether the French method of singing is the best of all possible methods. 42.
XXXV. What the defects original: "vices" of the voice are, and if one can make a bad and inflexible voice sing music, such as was that of Louis XII King of France (1462–1515); he was famously unmusical, and his composer Josquin des Prez reportedly wrote a piece for him consisting of a single repeated note. See the 45th Prop. of the 6th book of Composition, which gives the qualities of a good voice.
XXXVI. Remedies for curing the defects of the voice and for preserving it. 45.
XXXVII. How one can learn to sing through all sorts of degrees and intervals without a Master. 46.
XXXVIII. How birds learn to sing and speak, and whether they receive any pleasure from it. 47.
XXXIX. Why all birds do not speak; why no four-legged animal speaks; whether their voices serve them as speech, and if there is a way to understand it. 49.
XL. How the serpent of Eden and Balaam’s donkey References to biblical miracles where animals spoke spoke, and in what manner God or the Angels speak. 53.
XLI. How those who counterfeit spirits Ventriloquists or those claiming to channel voices from a distance, and who seem to be very far away when they speak, form their words. 54.
XLII. Whether the preceding Sibilots original: "Sibilots"; a term for ventriloquists or "whistlers" who claim to speak for spirits offend God, and if they should be search-