[442] Gezwungene. I presume the meaning is that the oscillations are effected by a curved form of musical instrument.
[443] I am not sure there is not a certain confusion here. Our text, at any rate, when speaking of wind instruments, refers to the column of air as the medium of sound, but in the case of stringed instruments draws attention rather to the thing which creates the waves of vibration, the string itself. The nature of the timbre of an instrument is no doubt an important one, but it may be questioned whether this distinction between line or column and surface is very satisfactory or sufficient.
[444] Jenem linearen Tönen. The expression appears to me not very easy to interpret even from Hegel's own point of view. In what sense can you call a musical tone linear? The theory here stated, though ingenious enough, appears to me to miss the fundamental question, what actually constitutes the timbre of an instrument, in its assertion, for instance, of distantly related harmonies or non-assertion of such. Even assuming that the form of the instrument, or the part of it set into vibration, may partially explain this, it is obvious, I think, that Hegel's manner of stating it is open to considerable criticism.
[445] Die näher abgeschlossene Bestimmtheit. The meaning seems to be that definition of them in which they stand out with most distinctness from others.
[446] The comparison is unfortunate—in two respects. Violet is a cardinal colour, and the theory of Goethe to which it refers is, of course, untenable.
[447] The true scientific reason why octaves resemble each other so much more closely than two notes at any other interval is that the upper of two notes at an octave's distance is the first "upper-partial" tone of the lower, and all its harmonies are also harmonies of the lower note; the compound tone, for there is no entirely simple tone, of the higher note contains no new sound, which is not in the compound tone of the lower. This is not the case with two notes at any other interval.
[448] Ihre besonderen Seiten. I presume this means what is immediately called below the several intervals between note and note.
[449] There is really a distinction between the consonance of the dominant and a major or minor third.
[450] That is, the third is only third in relation to the key-note, or the leading-note only as the note previous to the octave.
[451] Three notes are really essential to any true chord.