Harmonics might seem initially to be more connected with music than with cycles. However the in depth study of cycles in any area eventually leads the researcher to find the presence of harmonics of cycles. Harmonics are other cycles that fit an exact number of times into a fundamental cycle.
It is useful to distinguish between two different causes of harmonics. It is a mathematical fact that any repeating waveform that is not an exact sine wave will have harmonics present. An example is a wave like the sunspot cycle that has sharper peaks than troughs and faster rise than fall. Even if every cycle were the same, frequency analysis would show that exact frequency multiples of the main cycle were present.
Another type of harmonic that is found in cycles is when different time series show periods that are exactly related by simple ratios. For example, the sunspot cycle has a period of 11.08 years and the price of wheat shows a 5.54 year cycle, exactly half the sunspot period. This strongly indicates that something is going on.
Edward Dewey found that a particular pattern of harmonically related periods was present in commonly reported cycles periods. Dewey found many relationships with proportions 2 and 3 in cycle periods starting from a period of 17.75 years, in an enormous variety of different time series.
His table of periods in years is:-
142.0 213.9 319.5 479.3 ----- 71.0 106.5 159.8 ----- 35.5 53.3 x2 x3 ---- ---- \ / 17.75 \ / ----- 5.92 8.88 ---- ---- / \ 1.97 2.96 4.44 / \ ---- ---- ---- /3 /2 0.66 0.99 1.48 2.22 ---- ---- ---- 0.22 0.33 0.49 0.74 1.11 ---- ---- ---- ----
Underlined figures are commonly occurring cycles.
This same pattern of periods, or parts of it, has been found by a number of different researchers independantly each other, often using different data. There can be no doubt that it is a real fact of nature.
Gann, for example, used periods of 360, 180, 90, 45 days along with 120, 60, 30 days cycles. These periods overlap with Dewey’s table and continue the pattern, as 360 and 180 days are 0.99 and 0.49 years and 120 days is 0.33 years.
In the time of Gann, Dewey, Hurst and others that pattern must have seemed quite myserious, although Castles noted in Cycles magazine that the pattern of periods he found in the US stock market was none other than the musical scale. In fact, Pythagoras musical scale consisted only of ratios of 2 and 3.
Later on Galilei, father of the famous Galileo, showed that a ratio of 5 was also needed in music and in modern times a ratio of 7 is also recognised. Tomes showed that ratios of 5 and 7 could extend Dewey’s table to include most of the other common cycles that he had found. The connection between cycles and music runs extremely deep.
In the last few decades, the study of non-linear systems has become quite popular, and through non-linear systems we can understand why harmonics form. It is worth mentioning that known physical laws are non-linear, so that we should actually expect the formation of harmonics.
Consider a simple example. Suppose that the 11.08 year cycle in sunspots were to cause slight variations in temperature or rainfall on earth, or any other variables that affect the growth of crops. If crops are grown in locations that have, on average, the ideal conditions, then these solar variations will cause the conditions to vary alternately above and below the ideal. That means that the crop will have ideal conditions twice per cycle, and non-ideal conditions twice per cycle, but once in one direction and once in the other from the ideal. Therefore the growth of the crops will show a variation in a cycle that is twice as fast as the solar cycle. This is just the situation found with wheat.
Because the universe is so complex and so many things affect so many others, we can expect this pattern of harmonic formation to go through many steps as one thing affects another and then another. In this way it is possible to build up the whole pattern found by Dewey and others.
Tomes has developed the calculation of harmonics and uses a very simple premise:
The universe has a wave structure and this wave develops harmonically related waves and each of these does the same.
From this it is possible to calculate the wave structure of the universe which explain why galaxies, stars, planets, moons and cells, atoms, nucleons are all produced at the scales and frequencies that they are.
The periods and distance scales of all known structures are consistent with this Harmonics Theory and for students of cycles it provides a basis for uniting all of the understanding of cycles.