130 likes | 141 Views
II.3 Mental Reality II.3.1 (Tu Sept 17) 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“
E N D
II.3 Mental Reality II.3.1 (Tu Sept 17) 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 Beethovenop. 57 „Appassionata“ • Vladimir Horowitz • Glenn Gould
M.C. Escher: Balcony
Tempo (e.g. M.M. ♩= 120) e(E) e E T(E) = (de/dE)-1 [♩ /min] slope
notation: white keys = C-major scale 1 1/2 1/4 1/8 1/16 1/32
tuning!!! MusicalInstrumentDigitalInterface MIDI: pitch symbols 0,1,2,... 127
modern: frequency ratios in 12-tempered tuning 0 1 2 3 4 5 6 7 8 9 10 11
very old: frequency ratios in Pythagorean tuning (2-, 3-based) 0 1 2 3 4 5 6 7 8 9 10 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
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