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The magic of frequencies
We have observed until now that matter moves and relates to matter through different polarity (-ve and +ve) and with the assistance of substances like water that is a carrier. We also know now that energy interacts with these moving atoms through the level of excitement that allows them to bond or not. This is interesting, still it does not explain life (yet). For that we have have to introduce a new variable: frequencies.
To illustrate the world of frequencies I am going to use the passionate environment of musicality. We all have particular feelings about music and it often plays a significant role in our lives, especially when we enter our world of emotions. We enjoy certain music and feel it to affect our mood and emotions. Music is considered by most of us as a kind of expressive language that vibrates through our being with its tones and lyrics.
But why do we like music so much?
What makes us like certain tones and not the other frequencies? These questions were asked also by Pythagoras back in 500BC. Pythagoras lived in the ancient Greece. He had a special passion for numbers and was convinced that most of the miracles of life could be explained through application of mathematics and the usage of whole numbers, the integers
0 – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9.
When he asked himself the “like” question of tones he started to study the frequencies that musical instruments and human voices produce and especially those that we enjoy most. He came to the remarkable conclusion that the tones of our music ladder (do – re – mi – fa – sol – la – si and again do) have a unique frequency relationship. It can be obtained by pressing a vibrating musical string at a particular tension and point. The frequency patterns appear to relate to each other when producing the different tones.
This was very remarkable. So the tones that find a liking in our ears are all related to each other in ratios. They could be calculated through ratios of 1:2 and 2:3 producing fragmented tones between do and the next do. Each “do” was represented by the next integer and the fraction in between by a particular division that represented the harmonic relationship of frequencies that could be obtained by applying the ratios found. The problem Pythagoras encountered was that his experiments led him to awareness but not quite to the solution because his maths got him to produce musical cycles that were always off by a little bit. This became known as the Pythagoras comma, a small adjustment required in the tone to get it right.
It still took over 2000 years for a new famous character to pick up the challenge that Pythagoras had initiated. It was Galilei, the father of the famous Galileo Galilei, who solved the enigma of the Pythagoras comma. He concluded that the best frequencies were in the following proportions (source: Ray Tomes, 1996):
do re mi fa so la ti do
1 9/8 5/4 4/3 3/2 5/3 15/8 2
This is very interesting. When we adjust these number to represent a whole number we get the following:
24 27 30 32 36 40 45 48
When we look closely we see relationships ( eg 24/30/36 = 4/5/6 and 32/40/48 = 4/5/6) recurring all the time. This means that every note relates to “do” with three mayor cords in ratios 4/5/6.
Wow! This is remarkable and exciting. It was assumed by all these people that these optimal musical ratios had a significance in the universe and our own living selves. But what were these relationships?
We will see in the next blog lecture