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

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

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Numbers as Pattern and Music

Chakra Tonality