This Tonic:Dominant relationship gives rise to the basic functionality of music harmony.
In 2010 particle physicist Stephen Hawking stated the view that we can call this, ‘the first law of theoretical physics’.
The Derivation of Phi "Nature's most Beautiful & Best Kept Secret."
Stringularity also gives rise to 'Phi'. Given the significance of 'Phi', or the 'Golden Rate' discussed in more detail below, this derivation as a rate is simple, subtle and obvious, yet still "Nature's smallest, most beautiful and best kept secret."
'Stringularity' & 'Perfect Tuning'
In music this 'Stringularity' or ‘First Law’ gives rise to ‘Perfect’ or ‘Pythagorean Tuning’. With the intervals between the notes within the octave being different for the seven tones and ‘semi-tones’ arising, it roots music played on an instrument that is tuned ‘Perfectly’, firmly in the key of the scale in which that instrument is tuned.
At the time of ancient Greek music this procedure gave rise to the 7 'modes' (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian & Locrian) each one starting on a different one of the seven available notes in the scale, but while maintaining the order of the tones and semitones arising in the scale.
Well Tempered Tuning
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 eight of the 12 Well Tempered or ‘equal’ semi-tones within the 'Perfect Octave', so this ‘Well Tempered Fifth’ becomes marginally smaller than the ‘Perfect Fifth’.
Well Tempered Tuning and the Pythagorean Comma
Well-Tempered tuning is a response to the Pythagorean Comma that roots the instrument equally in any of the twelve keys available on each of the 12 semi-tones within the 'Perfect Octave'.
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'.
The Well Tempered Climate Accord
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 ‘created and performed’ at whatever rate (or in whatever key) that science requires; in other words as a complete UNFCCC-Compliant 'event' (vide Adair Turner UK Climate Act).
So the primary purpose of Well-Tempering the 'C&C' Climate Accord is practical. It is so that any convergence rate to equal per capita rights that may be negotiated, remains a self-structuring and self-limiting function of the global contraction-rate that the science requires. The stringularity law applies to this as double the rate halve the weight.
The ‘Pythagorean Comma’ has a much greater significance than has yet been widely realised. 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).
The Pythagorean Comma gives the derivation of 'Phi'
Physicist Richard Feynman once remarkably described the ‘Fine Structure Constant’ - 137.03597 - 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’.
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.... where the subtle ‘derivation’ from ‘Stringularity’ with a subtle ‘deviation’ to 'Phi' is also the reciprocal of 360°/Phi and a simple function of Stringularity: -
360/1.618= 222.4969 360-222.4969=137.5013
In other words 'Phi' is a simple function of the first three integers as per 'Stringularity', or the first law of theoretical physics.
Consequently, its 'origin' and derivation are not 'mysterious' at all.
However, as electro-magnetically, ‘Phi’ is evident throughout nature at every scale of time & space, this evidence of 'Phi' is often seen, heard and felt as 'awe-inspiring'. From the spiral of galaxies to the double helix of DNA, 'Phi' is dynamically encoded in the simple, subtle, self-structuring and self-limiting growth patterns of sunflower seeds, pineapples, fir cones, the human cochlea and much else besides.
All from the 'Hemiola' - truly awe-inspiring . . .
From zero to one; so what really happened at the Big Bang?
At the core 'Phi' and the First Law of 'non'-theoretical physics is the source of all we have: -
Some people ask, "what has music got to do with climate change?"
Perhaps instead one can ask, are ‘Stringularity' and the Golden Rate/Ratio what drive musicians and especially perhaps string-playing musicians, to measure the fine structure of frequency governed this way with such minute accuracy?
And as a consequence, is the ‘living music of Phi-the-rate’ that emerges from ‘Stringularity’, a key to the resilience of ‘the Well-Tempered Climate Accord’, a methodology for collective global action to cut carbon emissions in time to keep in tune with the planet, other life-forms and ourselves, failing which a catastrophe looms (Sir David King)
Often known as ‘Contraction & Convergence’ (C&C), after thirty years this Well-Tempered 'C&C-methodology' remains robust, widely supported and unchallenged at a fundamental level.
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!"
Richard Feynman, Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 0-691-08388-6.