New PDF release: Transversal mappings and flows

By Ralph Abraham, Joel Robbin

Vintage textual content of 1967

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Example text

Knobloch Kircher explained the fourth part by saying that even somebody who does not know music will be taught to compose arbitrary songs by a new and easy aid that is by means of certain musical-arithmetical columns. I would like to begin by discussing the first part. Though Kircher mentioned Mersenne several times, he did not say any word that he repeated the explanations of his French predecessor, even using the number examples: Nine notes are selected out of n notes. He left aside, however, the most difficult problem of calculating the combinations and arrangements of certain types of repetitions.

5.

Vu. 2 The Sounding Algebra 31 To my knowledge, no other author ever calculated - without a computer, of course - a greater factorial. Mersenne listed the twenty-four different songs with four notes, the seventy-two different songs of three types of songs, consisting of four different notes, respectively, the sevenhundred-twenty different songs with six notes. Considering fourths like ut, re, mi, fa or re, mi, fa, sol or mi, fa, sol, la he enumerated the possible permutations in order to discuss which song might be considered as better or more pleasant or more agreeable.

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Transversal mappings and flows by Ralph Abraham, Joel Robbin


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