After training as an economist, Edward R Dewey devoted his entire working life to the study of cycles. This was because, following the 1929 crash and resulting depression, he found that cycles were more useful for predicting economic events than any amount of economic theory that he had learned.
Some of the fundamental empirical laws of cycles found by Dewey and others over the years were:
- Certain common cycle periods appear in many seemingly unrelated disciplines.
- Cycles Synchrony is the observation that cycles of the same period often have the same phase.
- Cycles harmonic ratios is the observation that the common cycle periods are often related by ratios of 1:2 and 1:3 and their products.
- Cycles outside the earth are related to cycles on earth. This was a conclusion that he came to reluctantly because at first it sounds like astrology.
These individual observations will often appear in articles about cycles in this blog. In fact, astute observers not aware of these discoveries have often rediscovered parts of these laws for themselves.
For a more detailed explanation of these conclusions, there is no better reference than Dewey’s 1967 paper “The Case for Cycles”: http://www.cyclesresearchinstitute.org/dewey/case_for_cycles.pdf
One thing can be added to the harmonic relationships noted by Dewey. The referenced paper shows cycles arranged in two triangular shapes that meet at one vertex. These shapes and the ratios within them are exactly the same as Pythagoras’ Lambda which was Pythagoras’ way of representing the musical scale. Dewey does not seem to mention anywhere that his table is the same as Pythagoras’ so it is worth mentioning here.
Actually, long after Pythagoras, Galilei, the father of the famous Galileo, suggested that some of the notes in Pythagoras scale were better replaced by ratios that had a 5 in them. So for a major chord rather than having C-E-G be in the ratio 1 : 81/64 : 3/2 Galilei had the simpler 1 : 5/4 : 3/2 or simply 4:5:6. There were debates about these matters, and there are arguments for both. These other than 2 and 3 based ratios are most definitely real however, and can be seen in the ideal piano tuning shown here:
The 12 semitone octave copes well, with ratios involving 2, 3 and 5 but not with 7, 11 and 13 which fall into the cracks as shown here. However 17 and 19 again fit.