Page:Philosophical Review Volume 1.djvu/72

56 probable that the absolute pitch as here expressed does not vary from that of the performances by more than a fraction of a tone. A line drawn above a note signifies that the sound is between that written and the note a semitone higher. In order to avoid the multiplication of bars and an appearance of regularity in the sequence of stronger notes which does not always characterize this music, emphasis has in all cases been denoted by accents. The sharps apply only to the notes against which they are written.

Our present knowledge of Chinese music is very largely a notes. It is found that when the difference in pitch between the components of any two pairs of notes is the same, the ratio between the numbers of vibrations per second producing the two notes of one pair is the same as that between the numbers producing the two notes of the other. To each interval, in other words, corresponds a certain ratio between the rapidities of vibration of the two sources of sound producing the notes entering into it. In our modern keyed instruments the distance in pitch or interval between any pair of adjacent notes is the same as that between any other pair, and is called a semitone. This equalization of the interval between adjacent notes is what is known as equal Temperament. Any two keys between which eleven others are included give the interval called the octave, conspicuous for the likeness in sound between the notes concerned. A tempered semitone is therefore an interval one-twelfth the size of the octave. Mr. Ellis has proposed to express difference of pitch in terms of the hundredth part of a tempered semitone; that is, the twelve-hundredth part of an octave. This unit, called by him the cent, we shall find it convenient to use in our discussion. The compass in cents of the intervals principally used in music, in their perfect form and as they are approximately given on tempered instruments, is as follows:

In the text we shall use the common symbolism of accented and unaccented letters for the sequence of notes on a keyed instrument. The letters c' c'# d' ... b' indicate the middle octave, whose notation reaches from the first ledger line below the treble stave to the third line from the top of it; the pitch here meant by c' being produced by 268 vibrations per second. The next lower octave is written without accents, and the next higher is doubly accented.