Mathematical theory of music by JEDRZEJEWSKI Franck

By JEDRZEJEWSKI Franck

Co-authors : Carlos Agon, Moreno Andreatta, Gérard Assayag, Georges Bloch, Costin Cazaban, René Guitart, Tom Johnson, Olivier Lartillot, Guerino Mazzola, Andreas Nestke, François Nicolas, Thomas Noll, Stéphan Schaub, Dan Tudor Vuza Code EAN : 9782752100276 assortment : Musique/Sciences Date of ebook : 2006 structure : 17 x 26 cm Language : French fabric : e-book Pagination : 316 type : technology of tune

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Representative **0000000000 *0000*000000 *0*000000000 *00*00000000 *000*0000000 *00000*00000 tt C2-1 C2-5 C2-2 C2-3 C2-4 C2-6 Maz. 1 4 5 6 7 Sets 0,1 0, 5 0,2 0,3 0,4 0,6 Sym. Groups < Mn,ii > < Mil,ii > {1,T7,MIO,II,MIO,II} {l,T5,M9,7,M9>ii} {1,T7,M8J5,M8)II} Hi | The last symmetry group is defined by ifa = {l9T3,Ts,T7iT9tTluMa,6} with a = 0,1,3,5,7,9,11. In the symmetric classification, there are six classes of 2-chords which are the same as in the dihedral classification. But there are only two classes of 10-chords represented by the following representatives.

L. The final cadence is written in this scale. 43 2. Taxonomy of Chords and Scales Paul Hindemith [Hindemith, 1940] classified the intervals by order of harmonic affinity. He obtained a series (C, G, F, A, E, E\>, A\>, D, Bb, D\>, B, Pji) which he used in the piano piece Ludus Tonalis as a structural element. The series is even printed in spiral form on the cover page. The intervals lead to a complete redefinition of tonalities. In the following table, the first column is the representative of the sets of the dihedral or cyclic classification, the second column is the number of the class set, the third gives the prime form of this pcset, the fourth column is the interval vector and the last give the complement of the set.

The last column of the following table gives the 3-partitions of twelve.

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