study of the natural sciences, as we progress, we find that "hills peep o'er hills, and alps o'er alps arise." As regards keyed instruments, it appears that the effect of those notes which act two parts, such as C# and D♭, is rectified in some way so as to be perfectly attuned to the ideal of harmony within us. Again, the "Amen" sung by the choir in a cathedral may not be in accurate tune, but if nearly the correct intonation is sounded, after traveling along the aisles, the chords always return to the ear in perfect harmony, because the natural laws of music, assisted by the echoing power of the building, have attuned them to the perfect harmonical triad. If the "Amen" be too much out of tune, these laws decline to interfere, and there is no such helpful resonance.*
Here we see why music, as a science, takes the priority of painting; for if music is good, it is perfected by natural laws which cause its tones to melt into each other in the most delicate gradations, while the painter who endeavours to represent the exquisite variations of tints and lights in the living landscape is dependent entirely upon his own resources. The early writers on music were philosophers and mathematicians on the broad basis of general science, not on that of music only. Mathematicians, for the most part, have only studied the subject of musical sounds up to a certain point, and have then left it. The musician must take the chromatic scale—not as it exists in Nature, for that offered by the mathematician, without the ordinary compensations of conventional theory, is of no use to the practical musician.
Of course, true Art cannot be opposed to Nature, although all the rules of the musician are not the facts of Nature. Music, pure, natural, and harmonical, in the true and evident sense of the term, is the division of any key-note, or starting-point, into its integral and ultimate parts, and the descending divisions will always answer to the ascending, having reference to a general whole. The essence and mystery in the development of harmonies consist in the fact that every key-note, or unit, is a nucleus including the past, the present, and the future, having in itself an inherent power, with a tendency to expand and contract. In the natural system, as each series rises, its contents expand and fall back to the original limit from any point ascending or descending; we cannot perceive finality in any ultimate; every tone is related to higher and lower tones, and must be a part of an organised whole. It is well known how deeply the late Sir John Herschel studied this subject; and it was his opinion that there was some principle in the science of music which had yet to be discovered.
I think it will be seen that most of the difficulties in the rules of harmony arise from not taking the key-note, with the six tones which it developes from itself, as guiding the ear, first to the six notes of its harmony, and then to the key-note which becomes the leader of the scale. In the study of the natural gamut,
- See remarks on the wonderful power of the ear in adjusting defects of intonation in Macfarren's Lectures on Harmony, No. II.