The Feminine Principle

The 'feminine principle' comes from the 'HEMIOLA'

Picture Credit Surya Therapy
"Everybody's got a mother." Professor Ian Douglas; Manchester University

In 2017, we are approaching the 'event horizon' of irreversibility with climate change. In December 2017, Jeremy Mathis, Director of NOAA's Arctic Programme said,
"the environment is changing so quickly . . . there is an almost runaway effect . . . we can't quite get a handle on what this new state is going to look like."

However, the UK Government refuses to align its carbon reduction target with the Paris Climate Agreement

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The 'Hemiola' may sound very 'abstract, but at a human scale, this 3-2-1 HEMIOLA is much more musically: -

* familiar & fun than you might think
* fundamental & formative than you might think

On-screen demonstration of the HEMIOLA over three octaves of 'Stringularity'

Below is an audio-visual of a strings tuned over three octaves of G Major. 'Gold buttons' are harmonics of G Major; Blue buttons are the steps in between. To explore both hearing
and seeing them being in-tune & in-time, in any chord and in any key, touch on-screen buttons once - gold and/or blue - to start them and again to stop them vibrating & sounding.

Harmonies can be 'heard' & 'seen' as in Pythagoras famous string experiment. This demonstration is much more likely that of Pythagoras than the square on the hypotenuse equalling the
sum of the squares on the other two sides in a right angled triangle of Euclidean space-dependency. It is also much more significant because of its four-dimensional 'space:time'-dependency'.

MUSICAL 'INTERVAL'

RATIO
What you 'See'

RATE (Hz) What you 'Hear' & also 'See'
decreased by a factor of 100 for visibility

G0

Fundamental

1:1 Length

1:1 Herz

G1

One Perfect Octave

1:2 Length

2:1 Herz

D1

One Perfect Octave & a Perfect 5th

1:3 Length

3:1 Herz

G2

Two Perfect Octaves

1:4 Length

4:1 Herz

B2

Two Perfect Octaves & a Major 3rd

1:5 Length

5:1 Herz

D2

Two Perfect Octaves & a Perfect 5th

1:6 Length

6:1 Herz

F2

Two Perfect Octaves, a Perfect 5th & a Minor 3rd

1:7 Length

7:1 Herz

G3

Three Perfect Octaves

1:8 Length

8:1 Herz

The inverse relationship between String Length Ratios & Herz Rates is clear to see.

To animate the device below for 'G Major' in 'root position', following the invariable law stringularity law (above),
touch the buttons in the animation below - once for 'on' and once again for 'off'. To make the proportionality
of the string's visual vibration rate cognitively easier to grasp, it has been decreased by a factor of 100.

With this device, many harmonic combinations are demonstrable as are the tensions & resolutions in the progressions
of these. After Millennia it is still the basis of the music we make & will always be for as long as we or whoever make music.

Well Tempered Tuning

The normalization of the Pythagorean Comma with Well Tempered Tuning of previously 'Perfect' 5ths means that,
12 of these Well Tempered 5ths now commute with 7 Perfect Octaves, enharmonically, notated so F# now is literally the same frequency as Gb etc;

With 'Well Tempered Tuning' all the notes in the top row notated in '#s' are the same as the notes in the bottom row notated in 'bs'

Dbb

Abb

Ebb

Bbb

The 'Cycle of Tempered 5ths' also becomes a 'circle' of 12 so-called 'Dominant 7ths', where C7 resolves to F7, which resolves to Bb7 and so-on, like this;

Bb7

Eb7

Ab7

Db7

Gb/F#7

Tempering the 5ths also entails making all the semi-tones within the octave equal to each other. The effect of this is 'normalising', making all keys 'equally in tune'.
This makes it possible to tune in, write in modulating between & playing in & modulating between all twelve keys.

Tempering is especially important with pre-tuned keyboard instruments & why J.S.Bach's wrote the '48 Preludes & Fugues of the 'Well Tempered Clavichord'.
It was really to demonstrate the viability of this all-important 'equality of keys'. However, as a 'necessity', this is what led to the flowering of the 19th Century repertoire.

This is what music has to do with Contraction and Convergence (C&C).
See 'speech' at the 20th of March at the Royal Courts of Justice

Back to the Feminine Principle

Imagine if we had stayed stuck with the dissonance of an F# major chord being played on a huge church organ',
where its pipes hadn't been pre-tuned with Well Tempered Tuning (St Matthew Passion)!