Numbers as Pattern and Music

2010-02-03T08:55:36.718Z

An attempt to develope a natural and intuitive graphic representation of the inherent structure of number based on factorization. Here from 1 to 16 presented with the corresponding tones from the harmonic series. The alienation to arithmetics - number theory - seems to reach new heights with the widespread doctrines of numerology which mildly spoken are naive and speculative. Nevertheless it is absolutely understandable that we feel an urge for a holistic approach to life by searching for correspondances between different areas of knowledge. But if without discrimination and reflection we sow our seeds, spread our equals signs with a light hand over fields of tonality, colour, astronomy, anatomys etc., the harvest will be poor: we will never reach a genuine and deep understanding.
A good place to begin the search for the foundations of a genuine holistic structure is the harmonic series, which incorporates and unites tonal frequencies, vowel sounds and number, i.e. music, phonetics and maths, three primary areas of knowledge, which are here reflected in a graphic structure.
It is not a 'number system' like our decimal system (based on the primes 2 and 5) or a sexigesimal system (primes 2,3 and 5), but an attempt to come close to the essence of the language inherent in the concept of numbers, a language of primes.and compounds - arithmethic (and musical) atoms and molecules.
The piano is not eqaully-tempered but tuned to the harmonic series which is basically the musical equivalent of counting: 1-2-3-4-5-6-...
Fundamental (no. 1)= 64 Hz, no. 2= 128 Hz, no. 3=192 Hz etc.
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

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Numbers as Pattern and Music

Octave spiral with the first 16 elements of the harmonic series