The proportions expressed as an arithmetic series beginning with 1 and increasing incrementally, theoretically, into infinity.
Most sounds with definite pitches (for example, those other than drums) have a timbre which is based on the presence of harmonic overtones. The are also known as partials, as they are higher pitches which have wavelengths which are integer partial lengths of the wavelength of the "1", and thus with integer multiple frequencies of the frequency of "1".
For example, a typical musical sound will have an overtone series in which the 1st (fundamental), 2nd, 3rd, 4th, 5th, and 6th partials can be discerned. Many sounds have higher partials, or lack some of these, or indeed have inharmonic overtone series and thus timbres (such as the piano).
Because standard Euro-centric harmonic practice has tended to emphasize or follow the types of intervallic structures embedded in the lower parts of the harmonic series, it has often been assumed as a paradigm or template for harmony. Many modern composers are using tunings which refute this idea.