Page:Philosophical Review Volume 1.djvu/85

Rh fourths in the theoretic scale only about a third give, in the estimated scales, intervals varying noticeably from just intonation; while of the combinations of notes which in the theoretic scale give approximate thirds and sixths only a very small fraction in the estimated scales give perceptibly worse intervals, and nearly half give intervals perceptibly better than the diatonic approximations. Taking all the combinations of notes together, which in the theoretical scale give either just or approximate harmonious intervals, in the estimated scales the aberration from perfection is not over that of the theoretical thirds and sixths in four-fifths of the cases, while in half of them it is not over half this error. In a word, cases of aberration in the practical scales from the perfection of the theoretical fourths and fifths are balanced by cases where the approximate thirds and sixths of theory have been improved upon in practice; the intervals in general showing a tendency to come closer to just intonation than do the thirds and sixths of the theoretical order. Apart from the abnormal intonation of pien-Koung the deviation of these scales from that of Chinese prescription may be regarded on the whole as an improvement upon it.

Although according to the indications of these Samien melodies, Chinese performance is not always as barbarous as is commonly asserted, it must be admitted that one, at least, of the horn-player's songs goes far to maintain the ancient reputation of the Chinese for inaccuracy of intonation. In the song Man-nen-fōn, although the groups of attempts at the same note of the scale have a wider compass than in the Samien melodies, they are still distinguishable, and taking their centres of gravity yield the following scale:

Here f', by its infrequency, announces itself as a pien. Koung has accordingly the customary pitch g', and the scale is of nearly the customary form.