We perceive sound as a whole but even if the fundamentals of that sound are not present (1st and 2nd overtones, etc.); our brain can still reconstruct the fundamental tone.
However, if we continue to remove the following overtones, gradually we begin to lose that ability. This means that the lower we are in the harmonic series, the greater is the pull to the fundamental tone and as we go up, the looser that pull is. If you look at the overtone series, you can see that the perfect 5th is the first interval that appears (from C to G), and then the perfect 4th (from G to C).
So, it wasn’t by accident that the first steps towards harmony in Western music, started with the first intervals of the overtone series. The early polyphony of the middle ages consisted in one or more voice parts accompanying the cantus firmus, often in parallel motion using the interval of the octave, fifth or fourth (the first intervals found in the overtone series).
The intervals of the octave and the perfect fifth have ever since remained the two most important building blocks in Western music; the octave providing the framework of stability and repetition; and the fifth, generating the primary harmonic driving force, the dominant to tonic cadence.
The perfect fifth is crucial in tonal music because it is so important for defining a sense of key center. If you consider its importance in the harmonic series, it is no wonder why a circle of fifths exists. You probably heard about it for harmonization purposes and as a tool to modulate to the nearest key centers.
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