Guerino Mazzola

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• Guerino Mazzola
• U ETH Zürich
• Internet Institute for Music Science
• guerino_at_mazzola.ch
• www.encyclospace.org

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Birkhäuser 20021368 pages, hardcover incl.
CD-ROM 128. / CHF 188. ISBN
3-7643-5731-2 English
www.encyclospace.org
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Ernst Tittel Der neue Gradus Lehrbuch des
strengen Satzes nach Johann Joseph Fux
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12 ? 3 x 4 z gt (z mod 3, -z
mod4) 4.u3.v lt (u,v)
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d(x,y) min. major/minor thirds from x to y
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180 inversion Refl. fourth circle 90minor
third chain 120major third chain
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Consonance-dissonance dichotomy
12 K? D disjoint, K D 6 K
0,3,4,7,8,9, D 1,2,5,6,10,11
(Marked) dichotomy (K/D)
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(K/D) is a strong dichotomy, i.e., there is
exactly one (invertible) symmetry ya.xb of the
torus which exchanges K and D, i.e.,y5.x2 This
is the autocomplementarity function AC AC(0)
2AC(3) 5AC(4) 8AC(7) 1AC(8) 6AC(9)
11AC2 Id
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Proposition Among the 34 classes of marked
dichotomies, there are 6 strong classes. The
distances among the members of one half (or the
other) of such a dichotomy are class invariants
and characterize these classes
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span
diameter
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K 12 e.0,3,4,7,8,9 consonances
D 12 e.1,2,5,6,10,11 dissonances
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?
punctus contra punctum vertical and
horizontal!
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g(K)
g(D)
punctus contra Punctum vertical and
horizontal!
g 12e 12econtrapuntal symmetry g ea
e.b.(u e.v)u 1,5,7,11
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Contrapuntal symmetries are local
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Allowed transition for the major scale
The Topos of Music Table O.2 pp.1217/18
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Paralles of fifths are always forbidden
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V(Event) (S/Sq,S/Sa,S/Sb) vigilance vector
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111
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Jonathan Winson Hippocampal Gate Hypothesis
Elton John and Diana
Music is a key to unconscious emotional contents
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K 0,3,4,7,8,9,11 (add leading note 11 to
consonances)
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K 0,3,4,7,8,9,11 class 60 ragas -gt
melakarta 72 scales mela scale Nr. 15
0,3,4,7,8,9,1class 61
Do counterpoint with the major dichotomy on
exotic scales! Write a counterpoint deformation
program (K/D)2(I/J)!
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D C-dominant triad T C-tonic triad
K
Unification