1 / 13

Exploring the Psychological Foundations of Music through Time and Frequency Ratios

Delve into the interplay of psychology and music from Descartes to modern times, investigating axiomatic rules, frequency ratios, and iconic compositions like Beethoven's "Appassionata." Learn about musical notation nuances, MIDI technology, and historical tuning systems, unraveling the essence of musical harmony and expression. Discover the mathematical beauty within musical intervals and Euler's groundbreaking theories, shaping the evolution of musical composition. Explore the intricacies of counterpoint and the quest for musical perfection through historical perspectives and contemporary innovations.

castilloedward
Download Presentation

Exploring the Psychological Foundations of Music through Time and Frequency Ratios

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. II.3 Mental Reality II.3.1 (Tu Sept 17) 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] slope

  6. John Cage: ASLSP (http://www.aslsp.org/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. MUTABOR by Rudolf Wille

  13. 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

More Related