Note 452 — Chapter II · (continued 2)

The mediant lies about midway between the tonic and dominant as the third of the scale. The researches of Helmholtz prove that the distinction between consonant or semi-consonant and dissonant intervals is not arbitrary, but the result of the nature of the intervals themselves. A musical tone is mostly a compound one, containing, besides its principal tone, other tones with fixed relations to the lowest note, called harmonics, or "upper partials." Helmholtz has shown that when two of the earlier-produced and stronger of these upper partial tones coincide in two notes sounded together, the resulting tone is pure, free, that is, from the inequalities known as "beats" (Prout, "Harmony," 10th ed., pp. 21, 22).