Overtone Intervals (Click image for larger version).
Just Intonation (JI) represents the pure harmonic nature of sound.
Notes cannot be defined in isolation except by artificial pitch standardization.
The Harmonic 'Series' is really a set of overlapping, simultaneous, resonate intervals.
The Harmonic 'Series' is truly the vibrational lengths of harmonics:
naturally occurring in a length of string or column of air.
A note sounded in isolation does not define any tonal relationship (or scale).
Music is based upon intervals, the relationship between notes.
For example a G represents a Fifth to a C below it, but a forth to the C above it.
Equal temperament approximates some of the true intervals in the nature of sound.
However some very fine intervals are missing,
These natural intervals provide rich ability to express musically.