Cosmopoeia
Sections

Section

Harmonics

The world as sound: intervals as ratios, the lambdoma and the harmony of the spheres.

  1. 01The lambdoma – harmonics and the tetractysThe table of all tonal ratios. In harmonics it orders the intervals, in number theory the divisibilities, and in it the two readings of the tetractys meet.
  2. 02Space and time – the monochord in the lambdomaOne string, one movable bridge. On the monochord you can hear that pitch and string length are inversely related, like frequency and wavelength.
  3. 03All is number – all is frequencyTwo vibrations at right angles draw Lissajous figures. Place them in the lambdoma and waveforms, numbers and star polygons lie in the same places.
  4. 04Harmony of the spheres – star polygons in spaceConnect the positions of two planets over years and symmetrical star figures appear. Venus and Earth draw a fivefold rosette.
  5. 05The Tonnetz – Euler's triangular lattice of soundsFifths to the right, thirds diagonally upwards: Leonhard Euler arranged the notes in a lattice whose triangles are the major and minor chords. It is the same triangular lattice the tetractys is laid out on.
  6. 06Provisional metaphysical reflectionsEnergy, time, space and matter as a fourness, assigned to the four start figures. A provisional look beyond physics.