Section
Harmonics
The world as sound: intervals as ratios, the lambdoma and the harmony of the spheres.
- 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.
- 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.
- 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.
- 04The octaves of light: the rainbow around the throneVisible light spans almost exactly one octave, forty octaves above the tone F4. Newton's seven colours, the rainbow as a circle, the hexagram of colours, the colour cube as a stella octangula and why complementary colours are not an interval.
- 05Harmony 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.
- 06The 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.
- 07Provisional metaphysical reflectionsEnergy, time, space and matter as a fourness, assigned to the four start figures. A provisional look beyond physics.