Guerino Mazzola (Fall 2015 © ): Honors Seminar II.3Mental Reality II.3.1 (M Sept 28) Beyond physics and psychology.

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Guerino Mazzola (Fall 2015 © ): Honors Seminar II.3Mental Reality II.3.1 (M Sept 28) Beyond physics and psychology

Guerino Mazzola (Fall 2015 © ): Honors Seminar René Descartes: compendium musicae (1618) psychological foundation of music: 8 axiomatic rules e.g. music must be simple to please the soul...

Guerino Mazzola (Fall 2015 © ): Honors Seminar Ludwig van Beethoven op. 57 „Appassionata“ Vladimir Horowitz Vladimir Horowitz Glenn Gould Glenn Gould

Guerino Mazzola (Fall 2015 © ): Honors Seminar M.C. Escher: Balcony

Guerino Mazzola (Fall 2015 © ): Honors Seminar T(E) = (de/dE) -1 [ ♩ /min] Tempo (e.g. M.M. ♩ = 120) E e e(E)

Guerino Mazzola (Fall 2015 © ): Honors Seminar John Cage: ASLSP (

Guerino Mazzola (Fall 2015 © ): Honors Seminar notation: white keys = C-major scale 1 1/2 1/4 1/8 1/16 1/32

Guerino Mazzola (Fall 2015 © ): Honors Seminar tuning!!! MusicalInstrumentDigitalInterface MIDI: pitch symbols 0,1,2,

Guerino Mazzola (Fall 2015 © ): Honors Seminar modern: frequency ratios in 12-tempered tuning

Guerino Mazzola (Fall 2015 © ): Honors Seminar very old: frequency ratios in Pythagorean tuning (2-, 3-based)

Guerino Mazzola (Fall 2015 © ): Honors Seminar classical: frequency ratios in just tuning /32 =

Guerino Mazzola (Fall 2015 © ): Honors Seminar Leonhard Euler‘s gradus suavitatis function 10/  interval ? Euler‘s substitution theory counterpoint  (2 e.3 f.5 g ) = 1 + (2-1)|e| + (3-1)|f| + (5-1)|g| = 1 + |e| + 2|f| + 4|g| = 1 + |e| + 2|f| + 4|g| Plomp & Levelt 1965

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