The 432Hz Tuning Theory Part 2.
More on the 432Hz tuning controversy! (you might do well to read my earlier post to get up to speed)
[# it's worth noting from the outset: the only scale you'll find that has C=256Hz and A=432Hz is PYTHAGOREAN - and virtually NO-ONE uses that temperament now, not even New Age 432ers!]
#Edit - Wed 7th May: Good news, everyone! I am very pleased to report that I have located the source of the disturbance. It's Amanda Bossman (I have deliberately avoided using their "real" name) - Charlatan, New Age Entrepreneur, 'Inventor' of the 432Hz Swindle, Trance Music Wanker-Shaman. Has at least half a dozen websites.
On another New Age site for $50 you can buy a "spiritual healing" tuning fork in any colour of the rainbow, supposedly at the frequency of ॐ (claimed to be 136.10 Hz.) and hold it over various parts of the body to balance your chakras with the "Cosmic Healing Force of Universal Vibration of the Heralded Adepts and Secret Masters of Ancient Wisdom or Whatever". Sorry, it's a "true" story, but I'll try to be serious.
Apparently, this figure represents the vibration of the Earth's orbital journey around the Sun. The website you can get this from (or the forks) uses incorrect data, so I've re-done the maths so you can see for yourself how it's done (this is conveniently left out which I found annoying) and you can therefore check the accuracy for yourself. I used wiki.
One Earth Year = 365.242190402 days. To covert to seconds (because Hertz is a measure of wavelength, a vibration at so many cycles per second) we need to multiply this by...
24 (hours in a day), 60 (minutes in an hour) and 60 (seconds in a minute)
365.242190402 × 24 ×60 × 60 = 31,556,925.250732 seconds in a year EXACTLY. We divide this number into 1 to get the cycles per second (Hertz) and because the result is so small we need to raise it 32 octaves (double it 32 times) for it to be an audible frequency that humans can vibrate (there's that word again) or at least HEAR. The answer?
136.1022119026, the 32nd harmonic of 0.0000000317 (the quotient).
Ok. So that's how the figure is arrived at. For the purposes of this argument we will assume that this value represents ॐ expressed as a mathematical term because science deals only with quantifiable phenomena and not intangible mystical (dare I say it.... ) vibrations.
So what's this got to do with the New Age Healing theory of 432Hz tuning? (I am not going to go any further into the Illuminati Conspiracy Theory about the Nazis introducing the "evil" 440 Hz tuning standard that the World uses for 12-TET, aka Twelve-tone Equal Temperament, other than so it can be referred to here, later) Well....
Firstly, 136.1Hz doesn't represent a musical note. Well, not one that we recognise - it's somewhere between a C and a C#. By lowering the reference point of A from 440 to 432Hz, it equates to C# exactly, but only in 12-TET, the Western system. Remember, where talking about esoteric concepts here, and all Oriental music, all music in Nature, all Hindu, Spiritual, Sacred Hymns, Chants, (you get my drift) they all use unequal divisions of the Octave by implementing ratios of simple integers. All notes of the Pure Tuning scale (PT) are generated from (and multiples of) 1,2, and therefore 3,4, and 5. I refuse to credit this to the name of the Pythagoras, it originates from the Śulba Sutra written two centuries earlier by Baudhayana. The Vedic system is the well-known right angle triangle with sides of 3-4-5. Multiples of these create the Pure Tuning perfect major chord notes of C=256 E=320 G=384) Without going into too much detail, a Major third is expressed as 5:4, a minor third as 6:5, a perfect fifth as 3:2 etc etc. Apart from the Octave, in the western 12-TET all of these notes are more or less out of tune, some as much as nearly a quarter of a semitone, or note; only the "perfect" fourth and fifth are 2% out, still not exact.
So what this means, is that in 12-TET the notes do not vibrate in synchronous resonance or harmonic frequency together. In fact the inharmonious clashing of unmatched-up wavelengths create an unpleasant effect called "beating", where the notes wobble out of phase with each other. AND THIS IS THE POINT I CAN'T STRESS ENOUGH.
When ratios are used to determine the intervals of where the notes are in a Pure Tuning or Just Intonation scale, all, and I mean ALL THE NOTES VIBRATE IN PERFECT HARMONY WITH EACH OTHER.
Surely if you advocate a tonal centre of pitch supposedly based on ॐ you would use the natural method of tuning and not Equal Temperament which is harsh and somewhat out of tune. I will now attempt to explain how this unfounded 432Hz theory falls apart and why we can still learn from it.
Using 136.1Hz as C# and the ratios to determine the value of A in Hertz, we find:
If C# is the Tonic, then A becomes the minor sixth (8:5) and A=435.52Hz not 432; and
If C# is the Major third, then calculating using A=432 (5:4) then C#=135Hz, not ॐ!
Furthermore:
12-TET: A432 gives C513.74, not 512; hence C512 gives A430.5;
PT: A432 gives C518.4, not 512; and similarly C512 gives A426.666
Totally disproving the "connection" of 256, 432 & 512 based on multiples of 8, the Earth's vibration (actually 7.83Hz is the Schumann frequency) that adherents of the theory claim - regardless of the temperament used.
Clearly, you can't have it both ways. Resonance vs Beating! The whole argument is supposed to be about frequencies vibrating in harmony! (incidentally, "Amanda Bossman" uses their invention "Harmonic Equal Temperament" which is nothing other than than fudged numbers - the previous calculation inconveniently yields the awkward value of 256.9Hz for C which is secretly rounded down without being disclosed)
Curiously however, I did manage to find a "Indian 22 Shrutis" Gandhar or Samvadini method in a totally new (not C=256) 240Hz tuning here which incorporates the most features without compromise - and importantly, doesn't need to resort to the western 12-TET system in order to "work", as the 432ers do. Without dispensing of 256 and 432, it uses what we know of as a 'B' but calling it a C at 240Hz instead, and generates the scale from there. 256Hz now becomes the second note C# and 432Hz is now A#. It approximates the ॐ as 135, it's only real shortfall if you're hung up on 136.10 being its "real value". Given the all-encompassing nature of Om I would've thought it can be chanted at any frequency with full benefit, but that doesn't sell tuning forks!
So there you have it! In a nutshell, whoever came up with the 136.1/432 idea was probably using Western 12-TET, sitting at either a keyboard instrument or a computer keyboard, trying to use the "magic" of numbers without realising (or deliberately covering up) that the contrary systems cancel each other out. Of course, by all means all musicians can tune however they want, but 432ers who believe they are harnessing cosmic energy through the magic power of numbers whilst simultaneously clashing frequencies with Equal Temperament should understand that they are fooling themselves. And probably a lot of gullible New Age "groupies" as well.
Edit:
I think 'Bogdan' sums it up very well in their April 7th 2014 comment here at humansarefree.com
"Only after having a pure tuning system that can support resonance and is in tune with the nature and the universe, only then we can talk about a "standard frequency" for the fundamental tone. Until then, as long as we're still using equal temperament, all the claims about the divinity of 432 Hz are left-brain fantasies. All we do know, through the observations made by Maria Renold using acoustic instruments, is that lowering the standard frequency a few Hertz WHILE CHANGING THE TUNING SYSTEM to other than equal temperament has certain effects, which we all can notice.
More info: at humansarefree.com here
-and: here
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