N.A.S.A. has calculated planetary distances for two different time periods.I will be using the 3000 BC to 3000 AD values unless otherwise stated.
Although both of the above equations could be seen as pure coincidence, I find it remarkable that in correcting the music interval power equation to equal Phi squarerd then the resulting changes improve the other equation!
So without any changes the discrepancy was 1.000088909% and after the changes 1.00001185% this is amost a decimal place better.It might be fifty fifty as to it being higher or lower but being more accurate, on a discrepancy so low is something else. The 76th root of the discrepancy would correct the equation.
Here is another coincidence, which I can't find a use for but it is worth mentioning
Well 1.2 the minor 3rd, is by no means an obscure interval and I could use these values in model B or another model. The problem here is that I would have to use the whole thing as a power which would be even more obscure and complicated
I have finally found some new ideas to build another model which I will call model B. With this attempt I will be trying to avoid high mathematical powers of Phi but will be using three or more factors (planetary distances), in my search for Phi.
I will have to use more music intervals than just 1.875 and its counterpart 1.066666 in this model but for starters here is a value for Mercury that I am quite pleased with
So using my iterated values for Mars and Venus I have a Mercury value of .387096514 which varies by 1.000004949 from the original.Why 1.152? no other reason than it works well and it must be rememberd that in using music intervals as powers it is possible to multiply and devide them by other music intervals to atain the same result with the same values but in another more elegant form. Here is an equation I discoverd many years ago which I found to be of no use to me in model A but here it is in model B.
Using the original values this works extemely well, so that each factor only need be corrected by 1.000000322% but then the Mars Venus equations would not work exactly.Using the Mars and Venus values in model B, Saturn then has the value of 9.541783617 with a decrepency of 1.000029847% It must be noted that this value power 1.06666666 is Phi power 5 and given that 6 devided by 5 is 1.2 the minor third, then Phi power 6 is attained bz 1.2 x 1.066666 1.28. in the equation above Saturn becomes Phi power 3. The interval 1.5625 is the major third 1.25 twice,or squared! So having given Saturn a value the next three equations will allow me to define the other planets.
I will come to the discrepancies later but first to the problem of 1.65888 which is not a music interval! It is though, the product of two music intervals. 1.44 x 1.152 is one possible combination, so that the 1.152 root of both Uranus and Saturn would be Mars power 1.44 as in the Jupiter Saturn equation.On the other hand,the 1.44 root of both Uranus and saturn would result in Mars power 1.152. In searching for music intervals if I could not find 1.875 and 1.06666 then there seemed to be a preponderance of the minor third of 1.2 or it squared which is 1.44 or the other diatonic interval, (a rival for the half tone 1.0666666) the small chroma of 1.0416666.The problem with the equations above is also that I am not searching for Mars but Phi and what I realy need is Mars power 1.875, so that I can then replace it with the 1.875 root of Venus and find Phi squared! So here are the four big plantes presented in a different form.
Here the same equations in a different form.
Why these equations have come out a different size I do not know but I will fix it later.The Uranus Saturn music intereval is not a classical interval at all but the small chroma cubed.The other intervals are, but equally obscure, 2 devided by 1.06666 twice or squared is the one and 1.25 times 1.0416666 is the other. The more I work on model B the less sure I am as to exactly what equations to include.I will probablly end up with a model C an D as well.
This is very much a work in progress and three days ago I discoverd another coincidence which has given me food for thought. I had never used Phi itself as a power before but the square root of Phi to the power Phi power 4 is an exelent value for Jupiter. 5.202490525 with a discrepancy of 1.000001987%