Note: Please read the introduction first. The SOS foundation encourages alternatives to Equal Temperament. The choice for the Krystal tuning turns out to be a logic next step after two years of 9-based musical experience. Since the beginning of Febuary 2015 Sounds of Silence went on with the 12-based Krystal tuning, backed by the out-of-the-box insights given by the 'spirals of creation handbook'. It discloses information which is completely new to the public.
To understand the bigger picture it is very helpful to read and fully comprehend the text and implications below.
The 9-based tuning
The in 2012 newly created 9-based musical tuning is based on the philosophy of balance and cooperation, a derivative of the cosmic spiraling creation principle, better known as the Golden Mean ratio (1,618033...). This spiraling blueprint can be found everywhere in nature. By using our metric system numerically (9-based) a different outcome of the Golden Mean shows a hidden mathematical model of a closed order of repetition (see the calcutation below). It is the same perfection or order that nature shows in all its expressions. The nautilus shell is a well known example.
The Fibonacci-sequence, derived from the Golden Mean ratio is beautifully layed out in the video below.
Calculate and discover
The video above shows how the Golden Mean manifests as blueprint in nature. But what is exactly the relation with the number nine? Below again the same Fibonacci-sequence. Grab a pen and paper and fill in the final step to discover more then you would have thought. How does the sequence work? It is simple, count as follow, by adding up the previous number with the current number. For instance: 3+5=8. Then 5+8=13. Then 8+13=21. Then 13+21=34. Etc etc.
So from zero onwards: 0+1=1 / 1+1=2 / 1+2=3 / 2+3=5 / 3+5=8 / 5+8=13 / 8+13=21 etc. Or in a row:
These are the first 12 numbers. Between brackets you find the original number, but numerically counted 13 is (3+1) 4 again. You always get to the source number between 1 and 9. The next 12 continues like this (89+144=233=8 or 8+9=17=8):
Now discover order and repetition, based on a very old number sequence, rediscovered by people like Gert Kramer, Marko Rodin and Scott Onstott. Put on a piece of paper the two sequences of 12 numbers in two columns next to eachother. Which number after adding up the opposite number do you get each time? And... What happens if you continue counting after the 24th number? The cycle begins again: 1 1 2 3 5 8 13 21 34 etc.
Repetition in numbers becomes obvious, which proves the evidence of a closed order that nature uses as a blueprint in all its forms of expression. The image with the two triangles (connecting 3, 6 and 9) and the black ring with the same number sequence expresses exactly this closed, repetitive cycle.
And also science finds the edges of 'the Box' we live in. Scientists from South Africa claim that the Golden Mean may determine how things are shaped and linked in the universe. The number is not only used mathematically, but is also found in physics, chemistry, biology and the 'space-time typology'. The research is done by dr. Jan Boeyens from the University of Pretoria and dr. Francis Thackeray from the University of Witwatersrand in South-Africa. Read more in the South African Journal of Science article 'Number Theory and the Unity of Science' (2 pages).
A Revolution using Sound
"Revolution Number 9" is a recorded composition that appeared on the Beatles' 1968 self-titled LP release (popularly known as The White Album). The sound collage, credited to Lennon–McCartney, was created primarily by John Lennon with assistance from George Harrison and Yoko Ono. Lennon said he was trying to paint a picture of a revolution using sound. - wikipedia
“Everything is energy and that's all there is to it. Match the frequency of the reality you want and you cannot help but get that reality. It can be no other way. This is not philosophy. This is physics.” – Bashar.
Every tuning has its own frequency and subsequently created its own reality. How should we interpret these words? What will happen if the world of (classical) music chooses a different tuning? What reality did we evoke since 1700, when equal temperament was introduced? Did Lennon with his revolutionary intention knew more about the substance of sound? And was the number nine indeed the number for his envisioned freedom of mankind from its own illusion or 'uncleansed doors of perception'?
Sounds of Silence experimented extensively with this 9-based tuning, but was pushed to go beyond this closed number sequence. The results are no less then astonishing, with the beautiful Krystal sounds and its out-of-the-box mathematics.
Continue with step 3: the 12-based Krystal tuning ~ an intermezzo.