Frequency doubling is also important in Radio. Remember those long white 108 inch (2.75 m ) whip antennas for mobile CBs in the early 1970s? They were 1/4 wavelength antennas for radios that operated at 27 Megahertz on the 11 meter band. When the wavelength of an antenna just equals the wave length of the signal it is to radiate, the transfer of energy from the antenna into the air is the most efficient. Other lengths except for even harmonic or subharmonic lengths, reflect some of the energy back to the radio,- setting up Standing Waves that seriously degrade the energy transfer.

Harmonic frequencies play a vital role in both music and radio, yet color theory does nothing with harmonic frequencies. I suspect the reason for this lies in habit. Musicians and Audio engineers think about sound in terms of frequencies and decibels, almost ignoring wavelength. People who work with color think in terms of wavelength not frequency. Radio engineers have to think in terms of frequency and wavelength because they have to design both oscillators and antennas.

Color theorists have ignored Harmonics because Harmonics were not observed to play a major role in color mixing. Actually, harmonics do play a major role in color mixing when you consider the "invisible colors" completely ignored until now. Nature is consistent after all.

Now it is time to concentrate on the properties of the first harmonic frequency of both a radio wave, and a musical note. I am looking for a property of harmonic relationships that will enable me to correctly apply harmonics to Color theory. Consider the musical note C, and its first harmonic, C above C: What is C-ish about them? On a primative instrument the string that produces C above C is half the length of the string that produces C. Rather than using two strings, there are "frets" that can be used to shorten the string that produces C to 1/2, 1/4, and 1/8 its original length at will.