During the development of my current procedural composition projects, I realized that I needed some way to create arbitrary tuning systems, or sets of frequencies in an intuitive way. This way I could understand and work better with tuning systems. This project is almost an accident. I merely defined a user interface that lets one place tone components in the screen; the horizontal axis representing the frequency, and the vertical axis representing the amplitude.

After rapidly creating this interface, I started having a lot of fun with it, and it became it's own exploration. I decided to capture the experience in a couple of videos called Harmonic sculptures

Go on and play! Sine desk (note that first click will not produce any sound, the second click should.)

Things that I learned or realized after programming this

  • It's actually quite interesting that if you offset a bunch of frequencies preserving the structure of relative frequencies in a linear fashion, you will get a perceptually changing harmony. It's an obvious fact since harmonic perception is on a logarithmic scale, but one is not instantly aware of this.
  • Mathematically perfect harmonies tend to blend in and form timbres, but if they are not perfect, they will tend to work more as separate waves. A harmony of imperfectly harmonized tones feel a bit more alive than a harmony of imperfect tones. I wonder if this is a consequence of growing up accustomed to equal temperament.
  • Some ways how one could modulate from one harmony to another (akin to harmonic modulation in music theory)
    • Select one common tone between the start harmony (H1) and the destination harmony (H2), and generate a transition harmony (T) based on perfect harmonics. Start by adding tones from T while removing tones from H1. When few enough tones (or none) of H1 are present, start adding tones from H2 and removing tones from T.
    • Produce a glissando of each tone, so that harmony 1 morphs artifically into harmony 2.
    • Transpose either harmony so that more than 2 tones coincide (or are close enough, also taking into account factors and ratios). Then start removing tones from start harmony while adding tones from destination harmony. An additional method needs to be thought of as to what tones to use for transit.