Apparently each of us carries within him a fundamental note which picks out all the notes struck upon us by nature and mankind and ranges them in a series. And it is this which gives to each one his values. The fundamental note which any individual carries may not be the fundamental note of mankind, or of the Universe, but it must have a more or less simple relationship with them. Thus the values of one individual are true for all others, within their limits. They are real values though not necessarily ultimate values; they can and will be related to all other values but can only be so related through a more fundamental note--hence the importance of such a note. It is my belief that the profoundest, most fundamental note in music, so far, has been struck by Beethoven. There is nothing in the music of any other composer which his does not comprehend. But his, on the other hand, has a new foundation to which no other music reaches. [Illustration] But this analogy of the fundamental note must be understood merely as an analogy, suggestive rather than explanatory. Of all the simpler musical intervals I find that of the seventeenth the most satisfying to my ear. I may wonder what is the secret of the purity of its concord--so much greater than that of the perfect fifth or the perfect fourth, which at first sight seem to be more intimate relationships. Then I discover that the ratio of the vibrations of the two notes of the seventeenth is 1:5, whereas that of the perfect fifth is 2:3, of the perfect fourth 3:4. Stated thus this may not mean much to the non-mathematically minded reader but it denotes that the seventeenth is a perfect and not a syncopated interval. That is to say there is no syncopation of the vibrations of the two notes, but they beat together in a closer more united rhythm than that of a perfect fifth or perfect fourth. But the twelfth [Illustration] (I use the tenor or C clef partly because it is more obscure and will annoy those who are only accustomed to the treble and bass clefs) has a ratio of 1:3 which also is not a syncopated interval but has the same kind of perfection as that of the octave (1:2) and the seventeenth (1:5). Yet the twelfth is not so pleasing an interval as the seventeenth, and the octave is inferior to them both. Nevertheless the twelfth and octave are mathematically closer relationships than the seventeenth. Evidently there is another principle to be discovered, and I will call it the principle of affinity in unlikeness and illustrate it by an analogy which may seem far-fetched but which I believe to be illuminating and significant.