Table of Propositions

one might imagine; and if, once composed, it can be sung with all possible perfection. 103.

VIII. The ordinary rule of Combinations teaches the number of Songs The author uses "Chant" to refer to a melody or a sequence of musical notes. that can be made from a given number of different sounds, when one always keeps the same number, and does not repeat any sound twice or several times. 107. Where one sees a numerical table from one up to the Combination of 64.

IX. To provide all 72 Songs that can be made from the six common notes of Music—ut, re, mi, fa, sol, la—or from any other six notes one wishes, always taking the same number of notes in each Song. 110.

X. How many Songs can be made from any number of notes one wishes, when it is permitted to use two, three, or four similar notes, etc., and when one always keeps the same number of the same notes from which these Songs are composed. 129. From this comes the method original: "l’Air" of making Anagrams. Where one sees a numerical table of all the Songs of nine notes.

XI. How many different Songs can be made from a certain number of notes taken from another larger number, whether they are all different, whether one observes the order of different positions or does not; and when it is permitted to take them two by two, three by three, or four by four, etc. 131. Where one sees a very subtle and useful table, and another of the Geometric progression from one up to 22, the rest of which from 23 to 64 is in the sixteenth Proposition.

XII. How many different Songs can be made from a number of notes taken from whatever other number one wishes, whether they are all taken as different within the same number, or all similar; or partly different and partly similar. 135.

XIII. Given a Song, to find the rank and order it holds among all possible Songs within a determined number of notes. 136.

XIV. How one must read all kinds of letters and utterances in any language or idiom whatsoever, when they are written by numbers or other characters serving as numbers; and how one can sing all kinds of Melodies original: "Airs" and notes signified by all kinds of given numbers. 140.

XV. To find the rank and place of a given Song of as many notes as one wishes, among those that can be made from an equal number of notes taken from twenty-two. 141.

XVI. Given a number, to find the Song or utterance that holds the same rank among the Songs or utterances that have an equal number of notes or letters. 142. Where one sees two numerical tables of the Geometric progression from 23 up to 64, and that of the Varieties of twelve notes taken from 36.

XVII. To determine the number of Songs that can be made from any number of notes one wishes, when they are taken from a larger number of notes (for example, when one takes eight from the 22 notes of the Trisdiapason original: "Trisdiapason" - a musical system or scale spanning three octaves.) and when it is permitted to repeat the same notes two, three, or several times in said Songs. 146. Where one sees an ingenious and useful table of numbers.

XVIII. To determine the number of Songs that can be made from a number of notes, when there are different ones that are similar, like