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Octave spiral with the first 16 elements of the harmonic series


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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