The Universal Art of Music, Volume II

Book VIII. The Miraculous Art of Music.

3 A musical staff displays 20 diamond-shaped notes on the lowest line in the first section and 2 diamond-shaped notes in the second. The number 20 is printed below the first section and 2 below the second. in this arrangement, they are permuted (mutantur): Referring to the mathematical calculation of how many ways these specific notes can be rearranged. 231.

4 A musical staff displays 19 diamond-shaped notes on the lowest line in the first section and 3 diamond-shaped notes in the second. The number 19 is printed below the first section and 3 below the second. in this arrangement, they are permuted 1,540.

5 A musical staff displays 18 diamond-shaped notes on the lowest line in the first section and 4 diamond-shaped notes in the second. The number 18 is printed below the first section and 4 below the second. in this arrangement, they are permuted 7,315.

6 A musical staff displays 17 diamond-shaped notes on the lowest line in the first section and 5 diamond-shaped notes in the second. The number 17 is printed below the first section and 5 below the second. they are permuted 26,334.

7 A musical staff displays 16 diamond-shaped notes on the lowest line in the first section and 6 diamond-shaped notes in the second. The number 16 is printed below the first section and 6 below the second. they are permuted 74,613.

8 A musical staff displays 15 diamond-shaped notes on the lowest line in the first section and 7 diamond-shaped notes in the second. The number 15 is printed below the first section and 7 below the second. they are permuted 170,544.

9 A musical staff displays 14 diamond-shaped notes on the lowest line in the first section and 8 diamond-shaped notes in the second. The number 14 is printed below the first section and 8 below the second. they are permuted 319,770.

10 A musical staff displays 13 diamond-shaped notes on the lowest line in the first section and 9 diamond-shaped notes in the second. The number 13 is printed below the first section and 9 below the second. they are permuted 497,420.

11 A musical staff displays 12 diamond-shaped notes on the lowest line in the first section and 10 diamond-shaped notes in the second. The number 12 is printed below the first section and 10 below the second. they are permuted 646,646.

12 A musical staff displays 11 diamond-shaped notes on the lowest line in the first section and 11 diamond-shaped notes in the second. The number 11 is printed below the first section and 11 below the second. they are permuted 705,432.

You see the arrangement of the notes; now let us provide at least a single example of the second series, so that the curious reader may see how the permutations original: "mutationes" ought to be made.