[452] 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).
[453] As, of course, in the scale, notes independent of each other.
[454] Schärfe.
[455] The reader of Browning will recall how the poet in his "Abt Vogler" exclaims "Why rushed the discords in, but that harmony should be prized?" or speaks of blunting the minor into the ninth where the musician "stands on alien ground, surveying awhile the heights."
[456] This extreme emphasis on melody must be read as further explained lower down of melody in the wider sense. Even as thus qualified it is rather an overstatement. It may be questioned whether in the mind of a musician of genius the freedom of harmonic progression is of a different quality to that of melodic. It may appear no doubt less spontaneous. But it is the task of the great artist to overcome that appearance in one case as much as in the other.
[457] It may be doubted how far such a statement is true of many chord progressions in modern music. It seems to me that this notion of harmony as für sich having no musical significance is, to say the least, very misleading.
[458] This really is the point. Inspired harmony in its progression unfolds what is really a tissue of melodic threads. The complex musical structure of a Brahms symphony is a good example.
[459] Lit., "the free self-subsistency (Beisichseyn) of subjective life."
[460] Hegel puts it the other way. What he means is that in the medium of music we neither apprehend objects of sense nor ideas as we receive them in imagination or thought.
[461] Hegel throughout uses the term Innerlichkeit. That which is the Inmost is, in fact, the ideal. It is the raison d'être and the notion itself.