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II.3 Mental Reality II.3.1 (M Sept 22) Beyond physics and psychology

II.3 Mental Reality II.3.1 (M Sept 22) Beyond physics and psychology. René Descartes: compendium musicae (1618). 1596-1650. psychological foundation of music: 8 axiomatic rules e.g. music must be simple to please the soul. Ludwig van Beethoven op. 57 „Appassionata“

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II.3 Mental Reality II.3.1 (M Sept 22) Beyond physics and psychology

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  1. II.3 Mental Reality II.3.1 (M Sept 22) Beyond physics and psychology

  2. 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. Ludwig van Beethovenop. 57 „Appassionata“ • Vladimir Horowitz • Glenn Gould

  4. M.C. Escher: Balcony

  5. Tempo (e.g. M.M. ♩= 120) e(E) e E T(E) = (de/dE)-1 [♩ /min]

  6. John Cage: ASLSP (http://www.john-cage.halberstadt.de)

  7. notation: white keys = C-major scale 1 1/2 1/4 1/8 1/16 1/32

  8. tuning!!! MusicalInstrumentDigitalInterface MIDI: pitch symbols 0,1,2,... 127

  9. modern: frequency ratios in 12-tempered tuning 0 1 2 3 4 5 6 7 8 9 10 11

  10. very old: frequency ratios in Pythagorean tuning (2-, 3-based) 0 1 2 3 4 5 6 7 8 9 10 11

  11. 45/32 = 2-5.32.51 classical: frequency ratios in just tuning 0 1 2 3 4 5 6 7 8 9 10 11

  12. 10/ Plomp & Levelt 1965 1707-1783 counterpoint interval Leonhard Euler‘s gradus suavitatis function (2e.3f.5g) = 1 + (2-1)|e| + (3-1)|f| + (5-1)|g| = 1 + |e| + 2|f| + 4|g| Euler‘ssubstitution theory ? 0 1 2 3 4 5 6 7 8 9 10 11

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