Cycles Harmonics
First published: 2004
Brief summary
CRI’s harmonics page explains exact-multiple harmonic cycles and simple ratio relationships between cycles.
Article
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.
Additional summary
The remainder gives examples including sunspot and wheat cycles and describes harmonics as a general pattern across cycle research.
Source details and credits
- Source / publisher: Cycles Research Institute
- Source type: Webpage
- URL type: WWW
- Credits: Cycles Research Institute
- URL: https://cyclesresearchinstitute.org/subjects/cycles-harmonics/