If NASA’s diagram of
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If NASA’s diagram of ‘inflation’ after the ‘Big Bang’ is accurate, then the ‘shape-rate’ of ‘time-space’ emerging during COSMIC INFLATION seems perfectly to match the emergence of the ‘Pythagorean Comma’ where initially the speed of inflation is faster than the speed of light, but slowing to 0.618 at the ‘Golden Section’ [GS], as at the end of the first cycle of ‘Perfect Fifths’ from the Trinity [Hemiola or 3 in 1 of ‘Stringularity’ ], which is rather what you would expect isn’t it? The detail of GS is here: - http://www.gci.org.uk/images/PCI.pdf
Transcript of If NASA’s diagram of
If NASA’s diagram of ‘in�ation’ after the‘Big Bang’ is accurate,then the ‘shape-rate’ of‘time-space’ emergingduring COSMIC INFLATIONseems perfectly to matchthe emergence of the‘Pythagorean Comma’where initially the speedof in�ation is faster thanthe speed of light, butslowing to 0.618 at the ‘Golden Section’ [GS], as at the end of the �rst cycle of ‘Perfect Fifths’ from the Trinity [Hemiola or 3 in 1 of ‘Stringularity’ ],which is rather what you would expect isn’t it?The detail of GS is here: -http://www.gci.org.uk/images/PCI.pdf
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
Well Tempered 5ths
Perfect 5ths
Pythagorean Comma
0.000
1.000
C - C1Octave100 to200 Hz
C1 - C2Octave200 to400 Hz
C2 - C3Octave400 to800 Hz
C3 - C4Octave800 to
1600 Hz
C4 - C5Octave1600 to3200 Hz
C5 - C6Octave3200 to6400 Hz
C6 - C7Octave6400 to
12800 Hz
Perfect 5ths
Well Tempered 5ths
(Gap) = ‘Pythagorean Comma’
Well Tempered Frequencies [Herz]
Pythagorean Frequencies [Herz]
C to G100 to
150 Herz
G to D150 to
225Herz
D to A225 to
337.5Herz
A to E337.5
to506.25
Herz
E to B506.25
to759.375
Herz
B to F#759.375
to1139.063
Herz
F# to C#1139.063
to1708.594
Herz
C# to G# 1708.594
to2562.891
Herz
G# to D# 2562.891
to3844.336
Herz
D# to A# 3844.336
to5766.504
Herz
A# to E# 5766.504
to8649.756
Herz
E# to B# 8649.756
to12974.634
Herz
C to G100 to
149.8307Herz
G to D149.8307
to224.4924
Herz
D to A224.4924
to336.3586
Herz
A to E336.3586
to503.9684
Herz
E to B503.9684
to755.0995
Herz
B to F#755.0995
to1131.3708
Herz
F# to C#1139.063
to1695.141
Herz
C# to G# 1695.141
to2538.8417
Herz
G# to D# 2538.8417
to3805.4628
Herz
D# to A# 3805.4628
to5701.7518
Herz
A# to E# 5701.7518
to8542.9751
Herz
E# to B# 8542.9751
to12800.000
Herz
7 Perfect Octaves
Correspondence 12800.000:12800.000Exact [& Well Tempered 5ths are .618] [ . . . and to think ‘Tritone’ - 6 equal semi-tones in a ‘Well Tempered’ row - was called ‘Diabolus in Musica’. This Well-Tempered adjustment created Bach’s 48 Preludes & Fugues. The whole canon of Western Music has been governed by it from that moment [1722] onwards].
Correspondence 12800.000:12974.632Inexact [Pythagorean Comma & Perfect 5ths are .666 - the sign of the devil . . . ? . . . ]
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
Well Tempered 5ths
Perfect 5ths
Pythagorean Comma
0.000
1.000
C - C1Octave100 to200 Hz
C1 - C2Octave200 to400 Hz
C2 - C3Octave400 to800 Hz
C3 - C4Octave800 to
1600 Hz
C4 - C5Octave1600 to3200 Hz
C5 - C6Octave3200 to6400 Hz
C6 - C7Octave6400 to
12800 Hz
Perfect 5ths
Well Tempered 5ths
(Gap) = ‘Pythagorean Comma’
Well Tempered Frequencies [Herz]
Pythagorean Frequencies [Herz]
C to G100 to
150 Herz
G to D150 to
225Herz
D to A225 to
337.5Herz
A to E337.5
to506.25
Herz
E to B506.25
to759.375
Herz
B to F#759.375
to1139.063
Herz
F# to C#1139.063
to1708.594
Herz
C# to G# 1708.594
to2562.891
Herz
G# to D# 2562.891
to3844.336
Herz
D# to A# 3844.336
to5766.504
Herz
A# to E# 5766.504
to8649.756
Herz
E# to B# 8649.756
to12974.634
Herz
C to G100 to
149.8307Herz
G to D149.8307
to224.4924
Herz
D to A224.4924
to336.3586
Herz
A to E336.3586
to503.9684
Herz
E to B503.9684
to755.0995
Herz
B to F#755.0995
to1131.3708
Herz
F# to C#1139.063
to1695.141
Herz
C# to G# 1695.141
to2538.8417
Herz
G# to D# 2538.8417
to3805.4628
Herz
D# to A# 3805.4628
to5701.7518
Herz
A# to E# 5701.7518
to8542.9751
Herz
E# to B# 8542.9751
to12800.000
Herz
7 Perfect Octaves
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
Well Tempered 5ths
Perfect 5ths
Pythagorean Comma
0.000
1.000 Perfect 5ths
Well Tempered 5ths
(Gap) = ‘Pythagorean Comma’
Well Tempered Frequencies [Herz]
Pythagorean Frequencies [Herz]
C - C1Octave100 to200 Hz
C1 - C2Octave200 to400 Hz
C2 - C3Octave400 to800 Hz
C3 - C4Octave800 to
1600 Hz
C4 - C5Octave1600 to3200 Hz
C5 - C6Octave3200 to6400 Hz
C6 - C7Octave6400 to
12800 Hz
C to G100 to
150 Herz
G to D150 to
225Herz
D to A225 to
337.5Herz
A to E337.5
to506.25
Herz
E to B506.25
to759.375
Herz
B to F#759.375
to1139.063
Herz
F# to C#1139.063
to1708.594
Herz
C# to G# 1708.594
to2562.891
Herz
G# to D# 2562.891
to3844.336
Herz
D# to A# 3844.336
to5766.504
Herz
A# to E# 5766.504
to8649.756
Herz
E# to B# 8649.756
to12974.634
Herz
C to G100 to
149.8307Herz
G to D149.8307
to224.4924
Herz
D to A224.4924
to336.3586
Herz
A to E336.3586
to503.9684
Herz
E to B503.9684
to755.0995
Herz
B to F#755.0995
to1131.3708
Herz
F# to C#1139.063
to1695.141
Herz
C# to G# 1695.141
to2538.8417
Herz
G# to D# 2538.8417
to3805.4628
Herz
D# to A# 3805.4628
to5701.7518
Herz
A# to E# 5701.7518
to8542.9751
Herz
E# to B# 8542.9751
to12800.000
Herz
7 Perfect Octaves
Starting at 100 Hz and rising 7 ‘Perfect Octaves’ (Hz Doublings), the value rises to 12800 Hz. However, rising 12 ‘Perfect Fifths’ (Hz Treblings), the value rises to 12974.634 Hz.
Though both progressions involve 84 semi-tone steps (12*7) the outcome values don’t ‘commute’. In the case, where, 7 Perfect Octaves do not equal 12 Perfect Fifths, the emerging Hz difference is the so-called ‘Pythagorean Comma’.
The effect of the Pythagorean Comma is that the further the music modulates from a ‘Key’ based on an instance where the Fundamental of 100:200 Hz is the Octave that equals the ‘Ton-ic Key’ (the ‘home key’), the more out of tune the music begins to sound. This is obvious with pre-tuned keyboard instruments such as the harpsichord, the piano and the organ.
To get ‘commutation’, a convention was adopted in the 18th Century where the ‘Perfect Fifths’ were ‘Well Tempered’. This meant a very slightly smaller Hz value than a ‘Pefect Trebling’ was used to ‘Well-Temper’ the Perfect Fifths, as in the table above (as a function of making each of the 12 semi-tone steps within the Perfect Octave exactly equal).
The benefit of this convention was the vastly rich and diverse development of freely modulating Western music that ocurred after adopting it. The rather theoretical cost of this was that within all the Perfect Octaves in play, a slight ‘out of tuneness’ was identically distributed between all Perfect Octaves within the range of the music in play.
However, a truly tantalizing property revealed on adotping this is how 0.618 - the Golden Section proportion - mani-fests in the emergence of the Pythagorean Comma (see page two) and also in the ‘Well Tempering’ of the Perfect 5ths (see last page) and also how this syntax is an analogue for the ‘big-bang/creation-inflation-evolution’ (see page one).
Golden Section 0.618
0.666Golden Section 0.382
8/12
0.583
7/12
0.618
The Meeting of the PERFECT FIFTH [8/12 or 0.666]the DIMINISHED FIFTH [7/12 or 0.583]
& the WELL-TEMPERED FIFTH [7.416407865/12 or 0.618]The GOLDEN SECTION - is the ‘irrational fraction’ 0.618033988749895 . . .
Within the ‘Perfect’ to the ‘Well-Tempered’ Order, what Moves are Golden Section ‘Fractals’ of What Doesn’t.
Perfect FifthDiminished Fifth
For my Friend Jelle . . . . 27 04 2013
0.382
0.000.080.170.250.330.420.500.580.670.750.830.921.00
1 2 3 4 5 6 7 8 9 10 11 12
0.38
20.
618
Dim
inis
hed
Fift
h
Perf
ect F
ifth
Well Tempered FourthWell Tempered Fifth
7.416407865/12
7.416407865/12
