The Devil's Chord: The conspiracy to open the portal of consciousness and mystery of the octave

Infinite light, infinite presence, infinite love.

Just wanted to drop in to give big ups to my man God and J-cisslac (he likes to be called that).

reply to post by UncleV


UncleV you can read what what I wrote previously on Hertz and quote me for anything you're confused about. I'll be happy to respond to any specific "cluttering" you claim I have done. Here is my statement against Hertz on an ATS thread in 2010

Don L. Hotson has a fascinating analysis of Dirac's quantum field equation that Hotson then applies to a macroquantum octaves resonance model -- pdf of part one here

So the fundamental issue I've been emphasizing since the OP is time-frequency uncertainty. This means that the closer something is measured in time then the frequency becomes inversely broader and unknown -- broadband of the whole frequency spectrum.

time-frequency uncertainty also means that the order you make the measure then changes the result. So if you measure time first you get a different value than if you measure frequency first -- and that is what non-commutative means versus standard math as commutative.

O.K. so you state -- keep it simple since we're talking about sound. But I'm not talking about "simple" sound -- I'm talking about the secret transformation of sound into other types of energy. So the harmonics are nonlinear.

O.K. for example -- sonoluminescence. pdf here

Single-bubble sonoluminescence [1] is a mysterious phenomenon. A small bubble of gas, usually air, is trapped at the center of a flask of liquid, usually water, by the application of an intense acoustic field. The frequency of the field is typically 25 or 30 kHz, and once per cycle, driven by the sound field, the bubble undergoes expansion and then rapid contraction....The sound wave, with a time scale of tens of microseconds, produces a contraction of the bubble measured in tens of nanoseconds, which in turn somehow generates a pulse of visible light whose duration has recently been measured to be tens of picoseconds [3].To quantize this model, we can express ~E and ~B in terms of a vector potential ~A, and endow the fourier coefficients of ~A with the appropriate commutation relations. Effectively this means that the coefficients a and b in the above expressions become quantum operators....1) the Casimir effect arises essentially from the coupling of the electromagnetic field to a boundary. When that boundary is moving, the field is coupled to a time-dependent source, which in and of itself leads to the production of energy; and 2) if this time-dependent coupling gives rise to unstable modes, as it does in our model, then an unexpectedly large amount of energy can be produced.

o.k. so Hertz is based on the frequency as inverse the time as the period -- or cycles per second.

Very simple right? But not true! Hertz was driven by the commutative relation but that is not the truth of harmonics.

de Broglie Wave Mechanics - In 1923, while still a graduate student at the University of Paris, Louis de Broglie published a brief note in the journal Comptes rendus containing an idea that was to revolutionize our understanding of the physical world at the most fundamental level. He had been troubled by a curious "contradiction" arising from Einstein's special theory of relativity. First, he assumed that there is always associated with a particle of mass m a periodic internal phenomenon of frequency f. For a particle at rest, he equated the rest mass energy mc² to the energy of the quantum of the electromagnetic field hf. That is, mc² = hf where h is Planck's constant and c is the speed of light. De Broglie noted that relativity theory predicts that, when such a particle is set in motion, its total relativistic energy will increase, tending to infinity as the speed of light is approached. Likewise, the period of the internal phenomenon assumed to be associated with the particle will also increase (due to time dilation). Since period and frequency are inversely related, a period increase is equivalent to a decrease of frequency and, hence, of the energy given by the quantum relation hf. It was this apparent incompatibility between the tendency of the relativistic energy to increase and the quantum energy to decrease that troubled de Broglie. The manner in which de Broglie resolved this apparent contradiction is the subject of the famous 1923 Comptes rendus note [Comptes rendus de l'Académie des Sciences, vol. 177, pp. 507-510 (1923)].

So yes normally subharmonics are based on the commutative Hertz value but what I'm saying is that before even "second" as time is established -- which is based on a symmetric distance value from Galileo -- before this is even true then the subharmonics of the Perfect Fifth and Perfect Fourth are actually quantum - nonlinear and non-commutative.

So the Perfect Fourth is not a harmonic but the Perfect Fifth is the third harmonic with the octave as C -- so it's C to G as the perfect Fifth. So then the frequency is the inverse of the wavelength so that the frequency is 3/2 and the wavelenth is 2/3. But with the Perfect Fourth this does not work because it is the complementary opposite of the Perfect Fifth -- so it is noncommutative.

O.K. so then you take the subharmonic of the Perfect Fifth so that the harmonic is 3 and so the subharmonic is 1/3 -- going the reverse direction of the octave. So this means it goes in the reverse time direction. So then the secret is that there are undertone subharmonics that increase in amplitude at the same time there are overtone harmonics of the perfect fifth -- but since they are noncommutative then there is an inherent resonance or push-pull that drives the resonance. It's a nonlinear feedback resonance.

Thanks for providing links.

O.K. again you have to agree that frequency is the inverse of wavelength. Hertz assumes that time is measured in wavelength -- if you want to say "second" this actually means wavelength as meter or feet or radian. So "second" refers to the period of time it takes for one full wavelength distance. Hertz already assumes a commutative symmetric relationship of wavelength. So 300 to 200 hertz "going backwards" is still 1.5 Hertz -- it's still a fraction of 300 over 200 Hertz. Hertz already assumes that sound has a speed as the square of the distance -- by the wavelength squared. So when you talk about Hertz what you really mean is this:

Yep, this is what I'm talking about. I do not have to agree to the above statement. What I agree to, as does the rest of the world, is that hertz=cycle per second. 1hz is one vibrational cycle per second and that's what I asked we stick to for the simplest understanding. We can argue whether a centimeter is this or that, but the rest of the world has a standard they agree with, let's use that. The same with the word 'second' in reference to time. How about we stick with good ol' 'One Mississippi'....

300hz to 200hz is not 1.5hz...it is 100hz difference, backwards or forwards.

You asked earlier -- sarcastically -- does time slow down if it is reversed? Yes -- the Perfect Fifth interval as the overtone harmonic 3/2 is a higher frequency -- and so the wavelength time is faster since it is smaller value -- 2/3. Now if the subharmonic of 3/2 frequency is 2/3 frequency or 1/3 frequency then it is the same music interval -- a Perfect Fifth but in the opposite direction of time so frequency is lower and the wavelength spreads out and time slows down. So now the wavelength is 3/2 as time but the frequency is 2/3.

This is part of the clutter. The sarcasm explained...you and I are playing guitars, I go C to a higher G and you go from the same C to a lower G at the same time. Did time change? No. It does not. You can explain it away but in reality, you and I experienced the same time frame. What you are arguing about, the same music interval in the opposite direction is an argument over music theory, not sound itself. Your argument is with the system, the physics of sound remain whether C should be called F or W# or Bb. It sounds like you should be creating your own tuning and theory system, the commonly accepted isn't going to change anytime soon.

Again, play a given note, let's say 100hz. That is the lowest note, the fundamental, all harmonics are built, by nature, upwards which we've discussed. There is no 'subharmonic' except in theory. You produce the fundamental, nothing lower without artificial means. That's is the definition of the fundamental. Again, this points to an argument with the theory, note naming system, etc. not the reality of sound.

reply to post by UncleV


O.K. so you mean two notes moving from 300 hertz to 200 hertz. The pitch interval is the ratio or fraction of the two frequencies which is why 300 hertz to 200 hertz as the Perfect Fifth is 1.5 as a fraction. So the subharmonics are not a "theory" but a real perception of listening as beats are subharmonics -- no one can deny that beats are not theory but real perception of sound. The model this thread is presenting is similar to Andrija Puharich's model of ultrasound having a subharmonic beat in the ELF frequency. I have noted the research of a quantum chaos biologist who states that the subharmonic of frequency has a significant increase in amplitude -- that's Dr. Brian Goodwin. So as frequency increases there are more beats due to the overtones being more out of tune.

Now if you have a nonlinear harmonic oscillator using the Perfect Fifth and Perfect Fourth as it's subharmonic inversion there is a quantum chaos driving of that system. I have documented this in this thread -- it's discussed in number theory. This is why the Golden Ratio is used in quantum chaos because it's the opposite of the low consonance harmonics -- using the "most irrational of irrational numbers" prevents the harmonic oscillations from having too much nonlinear feedback.

So this proves that the Perfect Fifth and Perfect Fourth have nonlinear feedback that increases the amplification. So you are claiming that subharmonic is theory because it's based on the geometric symbol of pitch perception and therefore is not needed for using Hertz. You ask me -- is an octave a doubling of Hertz or not? I have pointed out in the links I provided that this is precisely the "bait and switch" issue that was covered up.

So I'm talking about the very beginning of the creation of time and frequency in Western science. O.K. so to double the octave you have -- 100 hertz and then 200 hertz and then 400 hertz. But to get an equal tempered tuning the octave is not doubled by squared. So then by the Law of Pythagoras to get half of the frequency at twice the wavelength of the octave the octave value of 2 is then used to get the square root of two.

So you say -- ah but this is just theory and has nothing to do with Hertz. Again Galileo used "seconds" as time by measuring geometric length -- so that the speed as velocity increases as the square of the distance as acceleration. When the direction of the speed as velocity changes then there is deceleration of velocity. I have pointed out that Hertz frequency is determined by velocity divided by wavelength. O.K. consider the Doppler Effect of sound -- the frequency as Hertz changes due to the wavelength of the sound changing. When there is a change of direction with the sound going towards an object then the frequency increases due to the wavelength getting smaller. When the sound is going away from the object then the Hertz frequency goes down due to the wavelength getting bigger. Again this is not theory -- it is sound perception. People hear the Doppler Effect all the time. O.K. then there is also sound faster than the speed of light:here

In their experiment, the researchers achieved superluminal sound velocity by rephasing the spectral components of the sound pulses, which later recombine to form an identical-looking part of the pulse much further along within the pulse. So it’s not the actual sound waves that exceed c, but the waves’ “group velocity,” or the “length of the sample divided by the time taken for the peak of a pulse to traverse the sample.”

Again the "time" as seconds or whatever stays the same but the time as wavelength or phase is changed. O.K. so if you have a harmonic as the Perfect Fifth it is 3/2 as a pitch interval. O.K. so you start with 100 Hertz and so then the Perfect Fifth as part of the harmonic series is 300/200 Hertz. If you take the speed of sound and then divide by the Hertz frequency you get the wavelength for the Perfect Fifth music interval -- 1.71 is the wavelength of 200 Hertz and 1.14 is the wavelength of 300 Hertz. So then the lower frequency has the longer wavelength. So the Perfect Fifth music interval based on Hertz is 200/300 or 1.71/1.14 = 1.5 or 3/2 wavelength. That is the subharmonic of the harmonics series of 100, 200, 300 Hertz. Then if you reverse the Hertz as 300/200 Hertz then the wavelength is 2/3 or .666.

So they are both the Perfect Fifth music interval only one is the subharmonic, a Perfect Fourth to the octave.

So now you want to say -- but it doesn't matter what the geometric symbol is because it's all the same speed as seconds. The question is though in relation to the 100 hertz as the "root" frequency for the octave. So 200 hertz is the octave but 300 hertz is not the octave.

Originally posted by fulllotusqigong
reply to post by UncleV

 

O.K. so you mean two notes moving from 300 hertz to 200 hertz. The pitch interval is the ratio or fraction of the two frequencies which is why 300 hertz to 200 hertz as the Perfect Fifth is 1.5 as a fraction. So the subharmonics are not a "theory" but a real perception of listening as beats are subharmonics -- no one can deny that beats are not theory but real perception of sound.

If you look up "combination tone" on Wiki, you'll see that it's nonlinear phenomena in the ear that can produce such perception of sound. However, human ear is not designed to perceive 7Hz, so what is said about such psychoacoustic phenomena at 200Hz is irrelevant. There is no perception at 7Hz.

I am not saying this or that is a theory but that it seems to me your argument is more against western music theory and not the actual physics of sound. Just clarifying. I also do not deny, nor have I ever denied the concepts of beats as the difference between two frequencies. Again, just clarifying.

So this proves that the Perfect Fifth and Perfect Fourth have nonlinear feedback that increases the amplification. So you are claiming that subharmonic is theory because it's based on the geometric symbol of pitch perception and therefore is not needed for using Hertz. You ask me -- is an octave a doubling of Hertz or not? I have pointed out in the links I provided that this is precisely the "bait and switch" issue that was covered up.

First sentence - huh??? Second sentence, in the example I used, the subharmonic doesn't exist except in MUSIC theory (I added MUSIC because I should have been clearer in that statement). In other words there is no audible note below the lowest note, the fundamental of 100hz in my example. Yes, the beat difference, but it is not an audible 'subharmonic', it is perceived, a ghost note. In nature, whatever the lowest note is, the overtone series is higher than it. Third sentence - huh??? You've pointed out this and that but I don't know if you ever answered the question. Is it or not? You suggest it isn't by using the term 'bait and switch' but considering that the octave is the purest interval, I'd say it is hard to swallow this 'bait and switch' concept. 100hz and 200hz is perfectly harmonious, change either one by 1 vibration a second (hertz) and the harmony is disrupted, no longer perfectly in sync.

The doppler effect doesn't change the actual pitch of the source. It changes for the observer due to his motion and has nothing to do with anything because of that. Let's assume we're both sitting still and within a few feet of each other. Clutter.

The question is though in relation to the 100 hertz as the "root" frequency for the octave. So 200 hertz is the octave but 300 hertz is not the octave.

Never said 300hz is an octave of 100/200hz because of course it isn't. It is the fifth of 200hz and 100hz (octave up). Natural harmonic overtone series is as follows:

100hz - root note or fundamental.
200hz - perfect octave of root
300hz - fifth above root
400hz - next octave up from root
500hz - major third
and so on, as it moves up certain things are retain, some skew but overall the harmonics lessen and lessen audibly

Now if we start at the fifth (300hz) and go backwards to the root (100hz) I can see your point, as in a G down to a C is a fourth. However, starting with the root note, there is nothing to go down to, which is my point.

Just had a flash....when you say 'sub' as in subharmonics I think "low" as in subwoofers. Therefore, in my example there are no subharmonics as the root note is the lowest. But, are you referring to the 'sub' in subharmonics as in subset, a part of the whole, not necessarily lower in pitch? Please, a simple yes or no to this question is all that is needed to get us on the same page. Anything more than that (links, videos, half hour long diatribes) is clutter and I will burn virtual dog poop on your virtual doorstep.

Originally posted by UncleV

Just had a flash....when you say 'sub' as in subharmonics I think "low" as in subwoofers. Therefore, in my example there are no subharmonics as the root note is the lowest. But, are you referring to the 'sub' in subharmonics as in subset, a part of the whole, not necessarily lower in pitch? Please, a simple yes or no to this question is all that is needed to get us on the same page. Anything more than that (links, videos, half hour long diatribes) is clutter and I will burn virtual dog poop on your virtual doorstep.

YES.

a G down to a C is a fourth.

a G down to a C is a fifth, not a fourth.

O.K. UncleV -- please review this response I gave to you early on Feb. 16th

Notice how I wrote:

Only then can he get the frequency ratios to create both a Perfect Fourth and a Perfect Fifth that are not below the value of the octave frequency.

as I've mentioned the F to C is listed as 2/3x and the C to G is 3/2x. So it's the same "C" just like with the harmonic series but it is noncommutative. So it would appear that this is fine except that the fractions are the frequency -- not the wavelength! So the frequency of the first Perfect Fifth as 2/3x is actually the wavelength and then it is doubled to 4/3x as the Perfect Fourth frequency.

O.K. so I've stated 300 hertz over 200 hertz is G to C as 3/2x and 200 hertz over 300 hertz is C to F as 2/3x. The same "C" -- it's non-commutative with frequency as inverse to wavelength.

What that means is that the "root" frequency of the octave does not exist. Why? Because then 4/3x is C to F but 400 hertz over 300 hertz is C going down to G. Both are Perfect Fourth music intervals but for 4/3x it is the doubling of 2/3x -- with the 200 hertz as the octave as F not C. The root octave has changed.

O.K. I have shown to you that the hertz are wavelengths and that the are the same Perfect Fifth music interval -- hence my answer YES to your question. but again the pitch relation to the octave is non-commutative.

The whole point of this thread is that there is eternal energy creation due to the non-commutative relation of time and frequency. There is no "root" or material ground -- in reality there is no "zero" Hertz.

Time-frequency uncertainty means that A x B - (B x A) is greater than zero. This does not fit with the Hertz system of measurement because again this is before Hertz.

Sorry that this doesn't make sense to you -- because I am pointing out that the Western system does not make sense. I have clearly shown why it doesn't make sense.

Quantum logic is a mystery and it has to be accepted as a mystery. The truth is very simple but very radical.

There is no beginning or ending to sound -- it resonates as consciousness that is formless.

alternatively if is it zero frequency then it is infinite phase amplitude wavelength.

O.K. technology can not measure true zero frequency due to quantum time-frequency uncertainty which creates infinite energy from the zero-point vacuum energy.

Similarly, one could certainly point out the long history of experimental confirmation of linear acoustics and could cite successful measurements of the Doppler effect. Nevertheless, since the linear wave equation is not exact,one needs to carefully consider whether this equation is appropriate to use in solving acoustical problems of interest, particularly in problems that involve the presence of two primary waves which can interact nonlinearly to produce sum-and-difference frequency waves.

Even‐Order Subharmonics in the Peripheral Auditory System

On the one hand the quantum theory of light cannot be considered satisfactory since it defines the energy of a light particle (photon) by the equation E=hf containing the frequency f. Now a purely particle theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of light, to introduce the idea of a particle and that of frequency simultaneously. On the other hand, determination of the stable motion of electrons in the atom introduces integers, and up to this point the only phenomena involving integers in physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be considered simply as particles, but that frequency (wave properties) must be assigned to them also. (Louis de Broglie, Nobel Prize Speech, 1929)

From this ATS thread on Milo Wolff's wave model

Decoding the Human Body Field -- scribd book

Weird World of Quantum Physics May Govern Life

Originally posted by fulllotusqigong
From this ATS thread on Milo Wolff's wave model

Once again, I see that a nonsense thread is following a predictable nonsense path. It only takes so much time for village idiots like Milo to rear their ugly heads. Speaking of the Milo thread, here's what one Milo proponent wrote:

Everything below the atom is just subharmonic wave structures, the 'factors' if you will of the harmonic ratios of the stable atom.

Yeah, let's pile it up people, and hope that we look smart while talking important-sounding nonsense!

Decoding the Human Body Field -- scribd book

What a jewel! I was going to go over a few precepts of this book which are particularly idiotic, then I decided it's not worth my time. I admit that "internal ej4culation" (sic) which is practiced by Full of Lotus makes more sense than this.

reply to post by buddhasystem


You cavalierly brand challenges to your mainstream education "nonsense." It's only nonsense if you have a closed mind because you're resting on your laurels, thinking you have the authority of the mainstream to back you up. You don't.

Click here for more information.

reply to post by Mary Rose


Hey Mary -- Tom Bearden relies on Broken Symmetry as the secret to free energy creation -- this is just the time-frequency uncertainty principle seen from the perspective of classical physics.

O.K. that Decoding the Human Body Field book also states that photons are not the information carriers for holographic healing but rather electrons and if electrons then it would also be positrons. They rely on Milo Wolf's theory but Don L. Hotson's model of the electron-positron is the same as Milo Wolff since both rely on a time reversal as the imaginary dimension. In other words the 720 degree spin of the electron is due to it secretly also being a positron as negative energy and this is because of the IN/OUT wave spin as time reversal or phase change. This is not the standard use of the imaginary complex domain in electromagnetics as just 90 degree phase change with the real number domain because that uses the imaginary domain as a spatial domain. Relativity also uses time as a spatial domain. So the scalar time dimension is the formless ground of reality as consciousness -- it can not be visualized due to time-frequency uncertainty. At zero frequency the phase time wavelength is infinite and at infinite frequency the phase time wavelength is zero. There is no way to precisely measure the two at the same time so that making a measurement at a frequency of one million times a second causes the quantum entanglement to not collapse -- time is stopped. This is the Quantum Zeno Effect that slows down the decay rate of exponential decay of radiation.

Here's another unified field theory saying the fundamental reality is electron-positrons

A free e-book based on Milo Wolff's phase-spin model of space resonance

Originally posted by fulllotusqigong
reply to post by Mary Rose

 

Hey Mary -- Tom Bearden relies on Broken Symmetry as the secret to free energy creation -- this is just the time-frequency uncertainty principle seen from the perspective of classical physics.

Ah, I was right about the pattern -- in a thread that's basically promotes quack science, it's only a matter of time before it becomes a toxic dump of MOST of quack science. First Milo, then Tom. Soon it will be Reich. Maybe Rodin again. ##snipped##

I'm going to step out of this thread once again. I have to thank Full Lotus for the one word answer, it does clear up some things though I still don't agree with or even understand much of what you are talking about. We can chalk that up to a lot of things.....lol

G to C is a fourth but in the scenario I gave, yes it is a fifth.

reply to post by UncleV


I'll miss you. You have contributed a lot. I hope you come back!

reply to post by Mary Rose


I will keep a watch on it, I just feel, in a due respect, that there is so much being thrown around, some worthy of investigation and some, well, not so much. Plus, it is so long that I'm having a hard time remembering what I said, yet alone anyone else.

Peace and taco grease

reply to post by UncleV


This Hertz issue was returned to after I had come across the power chord distortion creating subharmonics from the Perfect Fifth. Here it is again

Non linearities can give you great sound, in the right places, and preferably in a way that you can control them, they don't always sound good. As an extreme example, take lots of distortion on a guitar. You play a single note, it sounds fat and sustains forever... great You add a fifth, you have a really ballsy sounding power chord.. great Now you add a third.... UGH!!!

So the 200/300 Hertz interval is 66 Hertz while the 300/200 hertz interval is 150 hertz. So that 66 Hertz is F to 100 Hertz as C -- a Perfect Fifth subharmonic. 150 Hertz is the Perfect Fifth as C to G. The same C and so it's non-commutative. Now your question was is there a doubling of octaves or not with frequency. If the natural harmonics are used then the octave doubling does not line up with the Perfect Fifth/Perfect Fourth doubling. Is the octave not connected to the fifth?

So then UncleV you said that actually I'm just trying to make a different scale than equal-tempered. Actually in order to have the Perfect Fifth line up with the Octave then it has to go against the natural harmonics.

The music I'm talking about is either modal music that is not equal-tempered or else it is just 1-4-5 harmonics.

The whole concept of a scale is an attempt to equalize the notes within the octave but this is not possible -- why? Because number is not symmetric -- the number 1 resonates into 2 but when the third harmonic is added then a new whole is created. Subharmonics are undertones as 1/N and just as valid as overtone harmonics -- both are created - they have a complementary opposite relation to the octave.

So then the subharmonic becomes the new "octave" or root note so that for 2/3x as F to C it is the F that is doubled as the octave to create 4/3x as C to F, now the Perfect Fourth.

So an octave is made up of a Perfect Fifth and Perfect Fourth that are non-commutative. If we invert the fraction from 3/2 it is C to G but from 2/3 it is C to F. If we invert the geometric symbol it is C to G as 3/2 but G to C is 4/3.

If it is 4/3 as C to F then the Hertz is doubled from 66 Hertz of 2/3x C to F subharmonic so that the 4/3x is 132 Hertz.

Pythagorean Tuning

So this goal to "contain" the Perfect Fifths into the Octave is based on the commutative property of algebraic geometry. It is a very basic concept at the root of the Greek Miracle -- in contrast to say the Chinese not using a phonetic language and instead a pentatonic scale.

A "root frequency" -- why? Because this assumes that sound is defined by a visual wavelength or string - instead of sound being something we listen to as perception. For the same reason Archytas could not use the Perfect Fifth subharmonic as 2/3x -- it had to be doubled to 4/3x to hide the non-commutative relation. By doing so Archytas also changed the doubling of the octave into a squaring relation -- so that 3/2 is doubled to 9/4 and then halved back to 9/8 as the major second which is then cubed as the tritone or the Devil's Interval -- the square root of two.

So the Pythagorean Tetrad was 1:2:3:4 with the octave as 2 being part of the complementary opposites of the Perfect Fifth harmonic as 2/3. This had to be switched -- this is the bait and switch aka the changing order of infinity. So that is why the subharmonic is taken of 3/2 and then that subharmonic is doubled as 4/3.

The equation used by Archtyas, from Babylon, was arthimetic mean times harmonic mean = geometric mean squared. For the Pythagorean Tetrad this means if A = 1 and C = 2, the octave, then B = 3/2 for the arithmetic mean (A + C divided by 2) and B = 4/3 for the harmonic mean or 2(AC) divided by A + C. Meanwhile B = the square root of two for the geometric mean or the arithmetic mean times the harmonic mean equals the geometric mean squared (3/2×4/3 = 2)....So 2:3 became 3:2 from A + C divided by 2 = B with A = 1 and C = 2 as the octave. This conversion of the complimentary opposite Tetrad perfect fifth of 2:3 into 3:2, as an arithmetic mean, then could be doubled, 9/4, and inverted back into the octave as 9/8, the major second interval and then converted to the geometric mean as three major second intervals or the square root of two also known as the “Devil’s Interval,” the tritone – C to F#.

So that is from my 2007 article How the West Lost Alchemy

reply to post by UncleV

So again if A is 1 and C is 2 as the string length or inverse ratio of the octave, then the arithmetic mean is 3/2 and the harmonic mean is 4/3 and the geometric mean squared is 2. Or mass equals the octave NOW as geometric mean with 4 times the weight creating an acceleration as velocity squared -- time as distance. This is, again, where Newton got his inverse square law. 4 times the weight stretches the string to twice the frequency - or an octave increase, thereby changing time to a measure of weight and distance (momentum) by utilizing Archytas geometric mean conversion of frequency as COMPLIMENTARY OPPOSITES. What had been frequency (A = 1 and C = 2) is now reduced to distance (A + C divided by 2) with the perfect fifth now converted to a logarithmic standard.

That's from the comments I posted to my article

So if A = 1 and C = 4 (the double octave) then B = 5/2 is the arithmetic mean while the harmonic mean is 8/5 and their product, the geometric mean is 4, which has the square root equaling two. This confirms that Archytas did not think of the octaves as a doubling but rather a SQUARING even though this clearly goes against the harmonic series.

The real clincher for this complimentary opposites argument is Simon Stevin's 17th C. conversion of Archytas' diatonic scale into equal-tempered tuning. Stevin relied on the octave defined as a starting value of 5000 with it's "double" as 10,000. Stevin then argues that half of the octave is the square root, or the tritone and so a third of the octave, or two major second intervals, the major third is therefore a cube root of two. This fully accepted modern basis for equal-tempered tuning -- that which you consider to be the truth -- is directly from Archytas' proof for doubling the cube, namely that if a cube has a side one then to double the volume to two the side must be cube root of two with the proportion 1:5/4::8/5:2. That's the exact equation Simon Stevin used -- only converted to logarithmics. As I discussed in my article above and in my previous blogbook chapter, the subject of several emails from math professor Joe Mazur, Archytas' source for the cube root of two is from Babylon's use of the equation, arithmetic mean x harmonic mean = geometric mean squared. So again Stevin ASSUMES the value of the cube root of two without discussing the ORIGINS of the square root of two and all this time no one has questioned that fact that the arithmetic mean x harmonic mean equation Archytas relied on to create geometric mean is based on the octave, not as a doubled value, but as a SQUARED valued. Again having arithmetic mean 3/2 x harmonic mean 4/3 = 2 with 2 as geometric mean squared so that 3/2 x 3/2 = 9/4, the major second above the octave or the 11th interval (with 4 as the octave "squared" not doubled) and then halved to the sixth root of two as 9/8, the major second, cubed as the tritone or the square root of two is the source for Simon Stevin's equal-tempered tuning. The cube root is then just double the sixth root -- or 10/8 as 5/4. So Simon Stevin used the geometric mean equation A/B = C/X with X=BC/A just as Archytas used the arithmetic mean equations with A = 1 and X = 2. Only with Archytas it's not said what "X" is -- so the Babylonian geometric mean is 6:8::9:12, ostensibly the same as Simon Stevin's A:B::C:X but this time reduced to either 2:3::2:3 or 3:4::3:4. Archytas, in solving for the square root of two excludes the START of the octave -- which again is now no longer doubled, as is the case in the harmonic series, but is squared. SIMON STEVIN CONVENIENTALLY IGNORES THIS HARMONIC SOURCE FOR THE SQUARE ROOT OF TWO. So Archytas converts this process that starts with 1:2 as 6:12 so that 6 would be A and X would be 12. Instead Archytas reduces this to a 3 term equation with no "X" so that A = 1 and C = 2 and then what had been 2:3 as 6:8 is now the RESULT of the octave as arithmetic mean (A + C divided by 2) equals 3/2. What had been 3:4 as 6:9 is now the RESULT of the octave as harmonic mean (2 x AC divided by A + C), thereby HIDING the complimentary opposite harmonics of 1:2:3:4 and replacing a doubling of the octaves with a squaring of the octaves (2 is now geometric mean squared with "half" of the octave now the square root of two as the tritone).

reply to post by fulllotusqigong


Your game of is an octave squared or doubled only works with the number 2. I know you're not saying a note of 400 Hz is squared to 1600 Hz as the next octave higher but can't see the signifigance for saying it's squared rather than doubled. It just seems like you're bent on pulling out something that isn't there. Can you understand why I would say that?