PyConZA 2013: "Harmonies and Hues" by David Fraser

Mapping music to colours in Python.

Transcript

1. Harmonies and Hues Pythonic explorations of tones colourful and musical David Fraser PyConZA 2013 http://frasergo.org/projects/harmonihue/
2. Introduction • Will there be a finale? • Children learning. Stupid coloured notes. • I did use Python to do all this
3. Musical Maths • Twelve-tone scales
4. Musical Maths • Circle of Fifths – Pythagoras!
5. Harmonic Space a function hd that is a metric on the frequency space, which approximates the harmonic difference between two frequencies. The result should be low for frequencies that are close harmonies of each other, and high for frequencies that aren't. Principle Mathematical Formulation Notes are perfectly harmonious with themselves hd(a, a) = 0 Notes exactly an octave apart are equivalent hd(a, 2a) = 0 independent of direction (commutative) hd(a, b) = hd(b, a) constant for any interval - independent under transposition hd(a, b) = hd(ra, rb)
6. Harmonic Space • Circle of Fifths – Fifth is Closest Harmony • hd(a, b) = p(a) - p(b) (mod 12) (where p is the position in the circle of fifths) represents this distance
7. Geometry of Intervals • Pictures of the cycles • 1 Semitone at a time
8. Geometry of Intervals • Pictures of the cycles • 2 semitones at a time
9. Geometry of Intervals • Pictures of the cycles • The other ones
10. Relative Discordancy • How relatively discordant are different intervals? • In Western Music, roughly like this: 0 = d(0) < d(5) < d(4) < d(3) < d(2) < d(1) < d(6) • Using the circle of fifths generates this: 0 = d(0) < d(5) < d(2) < d(3) < d(4) < d(1) < d(6)
11. A Tuneful Torus
12. Color Spaces • RGB • Cubic
13. Color Spaces • HSV • Cylindrical
14. Color Spaces • Lab... • Weird
15. Cyclical Space Mappings • Circle of Fifths → HSV Hue Dimension
16. Fiddling around • Using Lab space and Delta-E on same SV
17. Better Differentiation
18. Sheet Music
19. Instruments of Colour