by Ray Tomes

Harmonics Theory: Outstanding Harmonics

This blog series from FSC Science Director Ray Tomes shares the fundamentals of physics in layman's terms, showing how present theory must inevitably lead to all waves losing energy and forming harmonically related waves. The end result is a very specific detailed structure that matches the observed universe and explains many previously mysterious observations. This series was previously published.

Outstanding Harmonics

To further delve into the pattern of the harmonics, it is necessary to solve the problem of detrending the upward sweep of C(H), which grows ever faster with increasing H. For example, the harmonic 34560 has no less than 622592 ways of being factorised, so if it were placed on the graph of C(H)/H above, it would be at 18.01... which is way out the top and past your ceiling. And further up there are numbers with 36 digits that have a number of ways of being factorised that has 57 digits, so it would be more than out of the graph, it would be out past Sirius!

I might add as an aside that it takes a bit of computer time to calculate these harmonics. When I was doing this in the early days of the Harmonics theory I had this new fast computer with an 80286 chip in it that could calculate harmonics up to 15 digits or so if left alone for a few days. With the advance in computer speed and a few programming and mathematical tricks it is now possible to calculate beyond 50 digit harmonics. It doesn't do all of them, only the strong ones and the other ones necessary to calculate the strong ones.

In has taken some considerable effort to find a formula that detrends this sweeping growth. After using a variety of techniques to separate the different parts of what is going on, in March 2004 a formula that fitted the trend in the strongest harmonics was found. It works reasonably well up to fifty digit harmonics but might require a little tinkering beyond there. The trend in C(H) for the outstanding harmonics is estimated as Cest(H) = (H^1.7323)/(10.18^sqrt(log10(H)). The following graphs have been detrended by dividing C(H) by this Cest(H). This leaves two other parts of the variations in C(H) untouched. They are the variations in C over several octaves of H, and the detailed patterns within the octaves.

The result of this detrending is that we are free to look for the effects that are visible to us in the energy patterns of the universe because we will be comparing the energy at similar scales and not trying to compare galaxies to atoms which is beyond the present scope.

One other thing will be done to allow the musical pattern to be more easily seen, and that is to use a log scale for the harmonic number H, meaning that each doubling of H will take the same horizontal space. This will also avoid the graph going past Sirius in the horizontal direction. A doubling of H is what is called an octave in music, or going up from one note such as C to the next C. Now let's look at our harmonics in terms of whether they are outstanding harmonics in their range for harmonics from one to a million on a log scale.

It is clear that as the harmonic number gets higher the complexity increases. The number of weak harmonics grows very rapidly and although the strong harmonics stand out very much from these weak ones they are much further apart. There is less complexity among the strongest harmonics, with ratios of 2, 3, 4, 6, 12 and 3/2, 4/3, 5/4, 9/8 and others being frequently present between strong harmonics. These are the musical ratios. This diagram is nothing more or less than an enormous chord spanning some 20 octaves and including within it all the commonly known musical chords and scales. This aspect will be examined in detail later.


Detrended Strength of Harmonics vs. Log(10) Harmonic Number