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

Table of Propositions

VIII. The ordinary rule of Combinations teaches the number of Songs that can be made from a given number of different sounds, when the same number is always kept, and no sound is repeated twice or several times. 107. Wherein 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 six other notes as one wishes, while 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 Art of making Anagrams, wherein one sees a numerical table of all Songs of nine notes.
XI. How many different Songs can be made from a certain number of notes taken from another larger number, when they are all different, whether one observes the order of different places or does not; and when it is permitted to take them two by two, three by three, or four by four, etc. 131. Wherein one sees a subtle and useful table, and another of the Geometric progression from one up to 22, the remainder 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 any other number as one wishes, whether they are taken as all different within the same number, or all similar; or part different and part similar. 135.
XIII. A Song being given, to find the rank and order it holds among all possible Songs within a determined number of notes. 136.
XIV. How to read all sorts of letters and words original: "dictions" in any language or idiom whatsoever, when they are written by numbers or other characters serving as numbers; and how one can sing all sorts of Airs and notes signified by all sorts 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 of an equal number of notes taken from twenty-two. 141.
XVI. A number being given, to find the Song or word original: "diction" that holds the same rank among the Songs or words which have an equal number of notes or letters. 142. Wherein 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 taking eight of them from the 22 notes of the TrisdiapasonA musical range spanning three octaves, from the Greek "tris" (three) and "diapason" (octave)., and when it is permitted to repeat the same notes two, three, or several times in said Songs. 146. Wherein 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, such as