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Barbera does note that Archytas used the Babylonian tetrachord, an extension of the tetrad, 6:8::9:12 whereby 8 is the harmonic mean and 9 is the arithmetic mean between 6 and 12 with the above changed meanings as discussed.236 So 1, 4/3, 3/2, 2 were converted to 6:8:9:12. So 8 x 9 = 72 (harmonic mean x arithmetic mean = geometric mean squared) and the square root of 72 in simplified radical form is 6 times the square root of 2 – or the equal-tempered logarithmic tritone music interval, the 6th semitone of the 12 note scale aka the Devil’s Interval. In other words 9/8, the major 2nd music interval, cubed, is the square root of two as the most dissonant music interval of the Western logarithmic scale.
As a clue to the secret musical solution we can see a close analogy between the Hippocratic continued proportion used for doubling the cube, A:X::X:Y::Y:2A and the tetrachord from Babylonian math, 6:8::9:12....Archytas applied his Babylonian equation
stating that the arithmetic mean times the harmonic mean equals the geometric mean squared in
order to double the cube. As Professor Borzacchini states:
According to this opinion the original, crucial problem for the Pythagoreans
because of the general role of music in the social and political establishment, was
the “cutting of the tone” (the interval between the fourth and the fifth, i.e. the ratio
8:9) in two ‘equal’ parts. In other words the problem was to find x such that 8:x =
x:9. Obviously 17/2 is too high, 33/4 too low, and so on. Archytas succeeded in
proving that in general it was impossible to cut a superpaticular ratio, i.e. to find a
x such that n:x = x:n+1 in the ancient Greek arithmetic (roughly we could say in
rational arithmetic). From this general result, for n=1, we get the irrationality of
the square root of 2. 237
If the cube root of two is the value for X and if the cube root of two was approximated as the music ratio 5/4, the major third music interval, then A:X::X:Y::Y:2A with A as 1 and 2A as 2 and X as the cube root of two gives the following result. By doubling the music octave to 4, so that Archytas could apply his geometric mean, the continued proportion of Hippocrates can also be
cubed so that A is 1 and 2A is 8 and the volume proportion for doubling the cube is 1:2::2:4::4:8.
Since the cube root of this equation means that X equals 5/4, the major third music interval as the
cube root of two, then the cube root of four, as Y, gives the harmonic ratio of 8:5, the
complementary opposite of 5/4 (the music interval the major third, 5/4, is inverted as the minor
sixth, 8:5). The secret of the sect music equation for the compounding proportions of the side
lengths is this:
A:X::X:Y::Y:2A = 1:5/4::5/4:8/5::8/5:2.
tone: D, 147.85 Hz
pitch data: equivalent chromatical a1 = 443,0 Hz
difference to 440 Hz. = + 11,9 cent
tempo: 69,3 / 138,6 bpm
color: blue
source
The archaic Egyptian instruments that have been unearthed, so far, are largely tuned to 432 hz.In ancient Greece (the school book original place for music) their instruments were predominantly tuned at 432 hz. Within the archaic Greek Eleusenian Mysteries, Orpheus is the god of music, death and rebirth, and was the keeper of the Ambrosia and the music of transformation (his instruments were tuned at 432 hz).
Originally posted by Templeton
Thanks for the post OP. I am intrigued, but much like others here I have a real hard time understand the lingo.
Is all of this ratio talk in relation to the major scale?:
1 : do
2 : ray
3 : me
4 : fah
5 : so
6 : la
7 : ti
(Thank you Sound of Music)
So when you say perfect 5th you are referring to do + so? And the perfect 4th is do + fah?
I love that!
Originally posted by galacticgirl
I have kept this experience to myself (and just a few family members) for so long - this thread seemed like the time to get it out there. My life totally changed from that day forward. My focus in life shifted to the power of vibrational energy - the unseen - rather than the material.
Originally posted by ThoughtForms
reply to post by fulllotusqigong
This is so nice to see man, good on you and thanks too. S+F
I have some information pertaining to your research I hope you will find helpful...
This chart shows how energy changes from one form to another as you increase its frequency so in theory you can play musical octaves of gamma ray's and different colours within light...
So the Perfect Fifth is 3:2 as C to G and the Perfect Fourth is G to C as 3:4 but this is noncommutative mathematics!
For Western symmetric logic C to G is 2:3 and G to C is 3:2.
Music and Euclid's algorithm combined gives:
plus.maths.org...
Interval: tone - 2 semitones = comma is corresponding with ratio:
9:8 / (256:243)² = 531441:524288 (about 81:80) (Pythagorean comma)
The same ratio is on page 2 of document below.
www.totallyratted.com...
Now check the Pythagorean Comma
Comma means in Greek, incision (means to receive = Rx)
www.greatdreams.com...
137 is related to the harmonic numbers 262144 and 531441
137 is called the Feynman constant and is related to an electron to emit or absorb a photon.
The Eye of Horus works exactly the same.
The 'Rx' symbol which is used by pharmacies and in medicine has its origins in the Eye of Horus.
www.greatscott.com...
Rx = receive = (Pythagorean) comma = incision (Greek)
Although 432 Pythagoran music is very harmonic,
protect yourself from the Eye of Horus (Pythagorean comma)
Originally posted by DenyObfuscation
reply to post by fulllotusqigong
Do you believe 5/4 is the cube root of 2? Also,
So the Perfect Fifth is 3:2 as C to G and the Perfect Fourth is G to C as 3:4 but this is noncommutative mathematics!
I can't see why you expect it to be commutative as presented. What similarity is there between Perfect Fifth and Perfect Fourth? In this example doesn't C ascend to G and then G to C an octave above the original C?
For Western symmetric logic C to G is 2:3 and G to C is 3:2.
If they're the same C and G wouldn't that be true?
Cymatics (from Greek: κῦμα "wave") is the study of visible sound and vibration
Originally posted by fulllotusqigong
reply to post by LightsideAssassin
Again this is all Western symmetric harmonics -- it can be found on any New Age harmonics website and in no way challenges Western mathematics or anything else.
Sure it looks cool -- but sound is not based on vision - but the West defines sound by vision which is the original problem causing the symmetric math against natural complementary opposite harmonics.