(click to enlarge)
All vibrating and oscillating bodies possess a signature
or complex series of sub and super harmonics
. These sets (or series) of relative frequencies (constituting its vibration signature
) are developed according to law
and arithmetic (addition, subtraction, multiplication and division) and are of two basic types of seemingly opposite qualities - harmonic
) and enharmonic
) not in their discrete pitches but in the relationships with the other notes of that series and outside of it. When harmonics are thusly derived from arithmetical methods they are called Summation
Tones and Difference
Tones. Other Resultant
Tones or harmonics derived arithmetically are "multiples" (times two, squaring or other quantities) and divisions or halves (divided by two, square root or other quantities). Because these signatures are created and governed by basic laws
of arithmetic they are not accidental or by happenstance. Keely
used the term "chord
" in place of our use of the term vibration signature
. For indeed a collection of relative frequencies or pitches is a chord
of discrete tones or aliquot parts making up a compound sound
or complex waveform.
Chord - Two, three or more tones sounded together.
Signature or Vibration Signature - Term usually applied to the vibration frequency spectrum of a complex waveform.
In the graphic below are shown these two terms. The squiggly lines at the top are the vibration signatures. (The term signature comes from the concept these lines look like a doctor's scrolling signature.) The musical notes below the signatures are the relative and quantitative discrete frequencies making up the complex waveform as recorded in tracings or signatures.
Partials - Harmonics, so called because they are the parts of a sound. [Scientific Basis and Build of Music, page 63]
Chord of Mass
Chord of the Mass
Figure 1.1 - Chord Signatures of Brain Convolutions
Laws of Vibration
Part 12 - Russells Locked Potentials
Universal Energy Unit