The Universal Art of Music, Volume II

Two systems of musical notation on five-line staves with a C-clef on the third line. The bars are numbered 19 through 30, continuing a sequence from the previous page. Each bar contains five notes in various permutations on two pitches (the second line and the second space of the staff). System 1: bars 19, 20, 21, 22, 23, 24. System 2: bars 25, 26, 27, 28, 29, 30.

You see, therefore, that the proposed melody Melody (vox): Kircher uses the word "voice" to refer to a specific sequence of musical notes. can be changed only thirty times, and this is because of two pairs Pair (binarios): Groups of two identical notes. of notes existing on the same or different pitches Pitch (chorda): Literally "string," referring to the specific line or space on the musical staff..

Another example. If, furthermore, a certain melody consists of nine notes, which has three notes occurring on each of two different pitches, arranged in whatever way, as in the following example:
A small inset musical staff showing two bars of musical notation with nine notes each, illustrating repetitions of pitches on three different lines or spaces.
what is the sought variation? You will proceed thus: since three notes are the same on two different pitches, they belong to "combination 3" This refers to 3 factorial (3!), which is $3 \times 2 \times 1 = 6$., for which you will find the corresponding number 6 in the first table; therefore, multiply 6 by itself to get 36 as your divisor. For by this number, the combination of 9—that is, 362,880 This is 9 factorial (9!).—divided by 36, will give 10,080, which are the sought variations of the proposed melody. If indeed there were a melody of 7 notes with two sets of three Sets of three (ternarijs): Groups of three identical notes., the melody would change 140 times. But so that the curious reader may perceive the matter through visual proof original: "demonstratione oculari", let us give an example with a small number. Let there be, then, a melody of six notes, of which three are on the first pitch and the other three are on the second pitch, differing by a whole tone; the variation of the proposed melody is sought. Divide, therefore, the combination of 6 Which is 720., that is:

Four systems of musical notation on five-line staves with a C-clef on the third line. The bars are numbered 1 through 20. Each bar contains six notes, with three notes on the second space (pitch B) and three on the second line (pitch A), shown in all possible permutations of those two sets. System 1: bars 1, 2, 3, 4, 5. System 2: bars 6, 7, 8, 9, 10. System 3: bars 11, 12, 13, 14, 15. System 4: bars 16, 17, 18, 19, 20.