The Universal Art of Music, Volume II

Musical notation is shown on a five-line staff using square and diamond-shaped notes. It illustrates six different variations of a four-note melody, numbered 7, 8, 9, 10, 11, and 12.

Musical notation on a five-line staff shows six variations of a four-note melody, numbered 13, 14, 15, 16, 17, and 18.

Musical notation on a five-line staff shows six variations of a four-note melody, numbered 19, 20, 21, 22, 23, and 24.

You see, therefore, that in this combination no note is found twice on the same degree original: "gradu". In music theory, a degree refers to the specific position or pitch on the musical scale., but that there are 24 entirely different variations.

Combinatorial Problem II.

This problem is solved without any difficulty by using the preceding Combinatorial Table II. Let there be, first, a melody Melody (vox): Kircher uses the word "voice" to mean a musical phrase or sequence of notes. of six notes, two of which are the same—that is, they sit upon the same pitch Pitch (chorda): Literally "string," referring to the specific line or space on the staff representing a tone. F. What is the combination of this melody? Divide the combination of a set of six original: "senarij". A senary is a group or set of six. (namely, 720) by the combination of a set of two (the binary), and the quotient, 360, will give the sought-after combination; for the proposed melody can be rearranged that many times. Alternatively, using the preceding table: look for VI in the first column, and the shared corner in the second column will give 360, the sought combination, as before.

Musical notation displays a staff with six notes. Two of these notes are placed on the same line, which is labeled with the letter F to indicate their shared pitch.

Again, let there be a melody of four notes, of which two are the same. The combination is sought; therefore, divide the combination of a set of four original: "quaternarij". A quaternary is a group of four. (namely, 24) by the combination of a set of two (2), and the quotient will give 12 as the sought combination, as is clear in the example.

Musical notation on a five-line staff shows six variations of a four-note melody where two notes share the same pitch (F). The variations are numbered 1 through 6. Beneath the staff are the markings "B" and "3 from G."