Math, Mystery, Music, Nature & ‘The Well-Tempered Climate Accord’

Pythagoras’ famous ‘string experiment’ from around 530 BCE, demonstrated relativity where: - 

  • if a string of constant length and at constant tension (the Fundamental)
  • is divided into two 1/2 lengths, the rate at which each 1/2 vibrates doubles (the Perfect Octave) &
  • is divided into three 1/3 lengths, the rate at which each 1/3 vibrates trebles (the Perfect Fifth) &
  • the three in the time of two in the time of one is called in music a ‘Hemiola’.

Let us call this law 'Stringularity' - it sounds like this and gives rise to 'Phi', the ;'Golden Rate' . . .
In 2010 physicist Stephen Hawking stated the view that we can call this, ‘the first law of theoretical physics’.

In music this ‘First Law’ gives rise to ‘Perfect’ or ‘Pythagorean Tuning’. With the intervals between the notes within the octave being unequal (including the ‘semi-tones’ arising), it roots music played on an instrument that is tuned ‘Perfectly’, firmly in the key in which that instrument is tuned. At the time of ancient Greek music this gave rise to the 'modes' (Lydian, Phrygian etc).

Around 2,225 years later ‘Equal Temperament’ or ‘Well-Tempered’ tuning was consolidated in Western music. In 1722 J S Bach first published his ‘Well-Tempered Harpsichord’. It eventually comprised the ‘48 Preludes & Fugues’ (four in each of the 12 keys available within the 'Perfect Octave') and this required ‘Equal Temperament’ or ‘Well Tempered Tuning’, where the tuning of each of the 12 semi-tones of the Octave is tuned to be in equal steps.

In both of these tuning systems a ‘Perfect Octave’ is always a ‘Perfect Doubling’. However, in Well Tempered Tuning, a ‘Perfect Fifth’ becomes a ‘Well Tempered Fifth’, comprised of seven of the 12 Well Tempered or ‘equal’ semi-tones within the 'Perfect Octave' and this is marginally smaller than the ‘Perfect Fifth’.

Well-Tempered tuning removes the Pythagorean Comma, rooting the instrument equally in any key. This ‘Well-Tempered’ tuning remains the basis of Western music to this day. It shows that music can be written, played in and modulate between any of the twelve ‘keys’ available within the 'Perfect Octave'.

For exactly the same reason, Contraction & Convergence ‘well-tempers’ future rights to anthropogenic carbon emissions by embedding the principle of equal carbon rights per capita within a finite global carbon budget. Like an orchestra playing in in tune and in time together, this 'Well-Tempered Climate Accord’ enables the carbon-contraction-budget to be ‘performed’ at whatever rate (or in whatever key) that science requires. Crucially, any convergence rate to equal per capita rights that may be negotiated remains a function of the global contraction-rate chosen, thus removing the randomness of the political-economic model applied so far.

However, the ‘Pythagorean Comma’ has a much greater significance than has been realised until this time. It is measurable as the Hertz (Hz) or ‘rate’ difference or ‘gap’ that emerges between 2^7 (seven Perfect Octaves) compared with 1.5^12 (twelve Perfect Fifths). As we progress the Hertz values through this sequence, twelve Well-Tempered 5ths progressively diverge from twelve Perfect Fifths, the tiny deviations arising create a constant differential that is also audible and beautiful. But most remarkable of all, is that on completion of the cycle 2^7:1.5^12, this Hertz gap has given rise to a sequence of rate-values that feedback between zero and ‘Phi’ or 0.618 – a subtle ‘deviation’ with a subtle ‘derivation’ from ‘Stringularity’, its significance is marked.

Physicist Richard Feynman once remarkably described the ‘Fine Structure Constant’, a very close derivative of ‘Phi’, as ‘one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man’. Electro-magnetically, ‘Phi’ is present throughout nature at every scale of time & space. From the spiral of galaxies to the double helix of DNA, Phi is dynamically encoded in the self-structuring self-limiting growth patterns of sunflower seeds, pineapples, fir cones, the human cochlea and much else besides.
So perhaps one can ask is it this ‘Golden Rate/Ratio that drives musicians (especially perhaps string musicians) to measure the fine structure of frequency governed this way with such minute accuracy?

Further, is the ‘living music of Phi-the-rate’ that emerges from ‘Stringularity’, a key to resilience of ‘the Well-Tempered Climate Accord’, a methodology to collective global action to cut carbon emissions in time to keep in tune with the planet, other life-forms and ourselves? Often known as ‘Contraction & Convergence’, after thirty years this ‘C&C’ methodology remains remarkably robust.


Golden Section

Source Code

Phi Eternal

360/1.618 = 222.4969

Portmeirion Festival Presentation 03 09 2016
(Come to where the two rivers meet)

Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms:

"There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455.

My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.

Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.

You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!"

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