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

2. Guerino Mazzola (Fall 2015 © ): Honors Seminar René Descartes: compendium musicae (1618) 1596-1650 psychological foundation of music: 8 axiomatic rules e.g. music must be simple to please the soul...

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

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

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

6. Guerino Mazzola (Fall 2015 © ): Honors Seminar John Cage: ASLSP (http://www.john-cage.halberstadt.de) http://www.john-cage.halberstadt.de

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

8. Guerino Mazzola (Fall 2015 © ): Honors Seminar tuning!!! MusicalInstrumentDigitalInterface MIDI: pitch symbols 0,1,2,... 127

9. Guerino Mazzola (Fall 2015 © ): Honors Seminar modern: frequency ratios in 12-tempered tuning 01234567891011

10. Guerino Mazzola (Fall 2015 © ): Honors Seminar very old: frequency ratios in Pythagorean tuning (2-, 3-based) 01234567891011

11. Guerino Mazzola (Fall 2015 © ): Honors Seminar classical: frequency ratios in just tuning 01234567891011 45/32 = 2 -5.3 2.5 1

12. Guerino Mazzola (Fall 2015 © ): Honors Seminar Leonhard Euler‘s gradus suavitatis function 10/  interval 1707-1783 ? 0 1 2 3 4 5 6 7 8 9 10 11 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