CU-Boulder PHYS 1240 - The Origin of the Chromatic Scale (38 pages)

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The Origin of the Chromatic Scale



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The Origin of the Chromatic Scale

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Lecture Notes


Pages:
38
School:
University of Colorado at Boulder
Course:
Phys 1240 - Sound and Music
Sound and Music Documents

Unformatted text preview:

The Origin of the Chromatic Scale Outline Revisit Lissajous Shapes Pythagoras Hypothesis The Magic of Integer Ratios The Circle of Fifths and the Chromatic Scale Imperfect Tuning and Compromise Equal Temperament Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes x y 1 1 1 1 Lissajous Shapes 1st harmonic and 1st harmonic 1st harmonic and 2nd harmonic Harmonic Visualization 1st harmonic and 3rd harmonic 344 0 Hz and 486 6 Hz Pythagoras Hypothesis The Magic of Whole Number Ratios monochord l1 l2 Pythagoras Hypothesis The Magic of Whole Number Ratios l2 l1 1 2 3 Pythagoras Hypothesis The Magic of Whole Number Ratios l2 l1 l2 l1 3 2 diapente Pythagoras Hypothesis The Magic of Whole Number Ratios l2 l1 l2 l1 l2 l1 2 1 diapson 3 2 l2 l1 diapente 4 3 diatesaron Pythagoras Hypothesis The Magic of Whole Number Ratios l2 l1 l2 l1 l2 l1 2 1 diapson 3 2 l2 l1 octave diapente 4 3 diatesaron perfect 5th perfect 4th Ratios Harmonics and Intervals Work out octave fifth third and fourth on board frequency Hz Make a scale with octaves 10000 1000 1 octave 100 10 0 2 4 6 8 10 12 frequency Hz Make a scale with fifths 10000 1000 100 10 0 2 4 6 8 10 12 fifths 7 octaves 12 frequency Hz Slide the some of the fifths down one octave 10000 1000 100 10 0 2 4 6 8 10 12 frequency Hz Slides fifths down again 10000 1000 100 10 0 2 4 6 8 10 12 Etc etc 10000 1000 100 10 0 2 4 6 8 10 12 frequency Hz Chromatic Scale 1000 octave 100 10 0 2 4 6 8 10 12 14 frequency Hz Chromatic Scale 1000 octave 100 2 1 10 0 2 4 6 8 f2 f1 2 02729 10 12 14 Oops frequency



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