Platonic Lambda

2010-02-03T08:56:22.889Z

Basis for this animation is Gregor Reisch' woodcut 'Arithmetica' from his work Margarita Philosophica (The Pearl of Philosophy), Freiburg 1503. It illustrates the Genesis from Platos dialogue Timaeus, where the Demiurg (world creator) uses the two continous four term proportions 1-2-4-8 and 1-3-9-27. They are so called geometric progressions (like the golden ratio) and they come together in the Lambda symbol. In the video the numbers are interpreted as frequencies whereas the ancients would have calculated string lengths (which would give the reverse side of the same structure) or fractions of string lengths which give the equivalent of the frequency structure. These two values are inversions of eachother. The chosen fundamental is C=64 Hz, the piano is in pythagorean tuning (tones generated by perfect fifths) A=432 Hz.
The musical perspective is followed by the geometrical: first by a look at the numbers represented by figures: the squares and cubes of 2 and 3.
After that follows a travel through dimensions from point via line, square and cube to hypercube, representing the fourth dimension. A pattern with resemblances of Eulers polyhedra formula reveals itself.
Conceived and presented by Skye Lofvander
More to be found (in danish) at: http://www.detspringendepunkt.net

Octave spiral with the first 16 elements of the harmonic series

2010-02-03T08:51:08.545Z

A musical animation of the first 16 elements of the harmonic series. The first 12 are the most commonly used by overtone singers, only very skilled singers can clearly accentuate up to no 16 or more. Here the tonal points are presented in the frames of an octave spiral structure which illustrates a fundamental principle in music:
The octave is a repetition of an already experienced quality on a new level.

The essence of the spiral figure is likewise:
1-2-4-8 are octaves of the fundamental;
3-6-12 are octaves of the perfect fifth;
5-10 are octaves of the just major third etc.

Proceeding through the spiral no. 1-16 the neighbouring intervals grow succesively smaller:
1:2=octave;
2:3=perfect fifth;
3:4=perfect fourth;
4:5=just major third;
5:6=just minor third;
6:7=septimal third;
7:8=septimal second;
8:9=major wholetone;
9:10=minor wholetone;
....;15:16=just halftone.

The sound should have been an overtone singing demonstration, but the piano is more precise. Please notice, that this is not common tempered tuning values but frequencies from the harmonic series with a fundamental of C=64 Hz (no. 1). The other frequencies are multipla of this tone (nx64 Hz).
The tonal axises represent divisions of a tonal circle of 360 degrees = 1200 musical cents.
Example: The 5-10 axis is situated at 115.8 degrees from the vertical axis corresponding to 386 cents.

More to be found (in danish) on http://www.detspringendepunkt.net

All Videos Tagged Proportions (Overtone Music Network) - Overtone Music Network

Platonic Lambda

Octave spiral with the first 16 elements of the harmonic series