The Universal Art of Music, Volume II

Whenever, however, 2, 2, 2, and 3 [notes] out of 9 are in the same position original: "situ eodem"; this refers to notes placed on the same line or space of the musical staff, meaning they have the same pitch., the number of permutations will be 7,560.

Whenever 2 and 3 out of 9 are the same, the number of permutations will be 10,080. The math here follows the formula for permutations of a multiset: 9! / (2! × 3! × 3!).

Whenever 2, 3, and 3 out of 9 are the same, the melody Melody (vox): Kircher uses the word "voice" to refer to a specific sequence of musical notes. will be changed 5,040 times.

When 3, 3, and 3 out of 9 are the same, the melody will be changed 1,680 times.

When 2, 3, and 4 out of 9 are the same, the melody will be changed 1,260 times.

When 2, 2, and 5 out of 9 notes are the same, the number of permutations will be 756.

When 4 and 4 out of 9 are the same, the number of permutations will be 630.

When 2 and 6 out of 9 are the same, the number of permutations will be 252.

When 4 and 5 out of 9 are the same, the number of permutations will be 126.

When 3 and 6 out of 9 are the same, the number of permutations will be 84.

When 2 and 7 out of 9 are the same, the number of permutations will be 36.

When all notes are in the same space, nothing is changed, as in:

A musical staff displays 9 diamond-shaped notes: 2 on the 1st line, 2 on the 1st space, 2 on the 2nd line, and 3 on the 3rd line. A C-clef is on the 2nd line and a flat sign is on the 3rd line. This illustrates the "2, 2, 2, and 3" scenario mentioned first.

A musical staff displays 9 notes: 2 on the 1st line, 3 on the 1st space, followed by 4 descending notes from the 4th line down to the 1st line.

A musical staff displays 9 notes: 2 on the 1st line, 3 on the 1st space, 3 on the 2nd line, and 1 on the 3rd line.

A musical staff displays 9 notes: 3 on the 1st line, 3 on the 1st space, and 3 on the 2nd line.

A musical staff displays 9 notes: 2 on the 1st line, 3 on the 1st space, and 4 on the 2nd line.

A musical staff displays 9 notes: 2 on the 1st line, 2 on the 1st space, and 5 on the 2nd line.

A musical staff displays 9 notes: 4 on the 1st line, 4 on the 1st space, and 1 on the 2nd line.

A musical staff displays 9 notes: 2 on the 1st line, 6 on the 1st space, and 1 on the 2nd line.

A musical staff displays 9 notes: 4 on the 1st line and 5 on the 1st space.

A musical staff displays 9 notes: 3 on the 1st line and 6 on the 1st space.

A musical staff displays 9 notes: 2 on the 1st line and 7 on the 1st space.

A musical staff displays 9 notes all on the 1st space, representing the case where no permutations are possible because all notes are identical.

From the preceding diagram it is clearly evident how many times each melody of nine notes can be changed. And although it might seem impossible to some that, for example, the second to last melody could be changed 36 times, it will nevertheless be known to be true as we say when the curious reader has examined it. And by this art, one will be able to easily recognize the permutations original: "mutationes" of any melody and of any number of notes; which, in a melody of 22 notes, run to 8,130,792,301,632,000 permu-