Chakra Tonality

2010-02-03T08:53:02.303Z

In the tanric tradition the chakras are often depicted as lotuses with a variable number of petals. The most commonly refered to series is 4-6-10-12-16-96-972, but it is important to realize that history has seen many different systems and that the written sources to the concepts are much later than most spiritually orientated people tend to believe. Nothing explicit is written about chakras neither in the vedas nor the Bhagavad Ghita nor the Yoga Sutras. The concept became well established during the time of mughal rule of India, which many of the aesthetically appealing diagrams derive from.
What is necesarry is reflections about the cultural context of chakras, also mathematically, instead of understanding their structure as something absolute, an authoritative revelation.
The above mentioned number sequence curiously belongs to the basic sexagesimal calculation system, which thrived in Mesopotamia thousands of years BC. It is based on the prime numbers 2, 3 and 5 which from a musical perspective through the harmonic series are equivalent with octave, perfect fiffth and just major third respectivly (NB! in the written order!).
In these ancient cultures music, arithmetics, geometry and astronomy were evidently parts of a holistic approach which all in all may seem less speculative than modern new age imaginations.
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.

Please notice that the piano in the sample is not tuned equally tempered but in just tuning, which preserves the pure music of the integers!
The chosen frequency for the starting point, the 4 of the root chakra is C=32 Hz. The ending major seventh, close to eight octaves above our starting point, should actually be one octave higher than here.
More to be found (in danish) at: http://www.kortlink.dk/7ccw

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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Chakra Tonality

Octave spiral with the first 16 elements of the harmonic series