Octaves.
Octave passages are usually played across two strings, with the thumb and third finger, the thumb stopping the lower note on the lower string, and the third finger stopping its octave on the higher string.
The most difficult progressions in octaves are those which are played in unison, that is, the higher and lower notes being sounded simultaneously—the slightest faults in intonation are here most painfully evident. Where the octaves are sounded separately, one part moving independently to the other, the difficulty of intonation is nothing near so great.
Occasionally one comes across octave passages which are either impossible to be played in the usual manner of thumb and third finger—or else sound better to be played with different fingering. An example of the former is met with in Popper's well-known "Elfentanz." This is an extremely brilliant descending passage in octaves, with the ninth used as a passing note. Here the octaves are played with thumb and second finger, thus leaving the third finger free for the added ninth. An example of the latter exception is the final octave passage in the Rondo of the favourite Beethoven Sonata for 'cello (No. 2). This passage, which remains in the lower range of the instrument, sounds much more brilliant if taken as an ordinary passage across the strings, than if attempted with the usual octave fingering.
[CHAPTER XIII.]
The Scientific Basis of Harmonics—Some Peculiar Laws which Govern a Vibrating String—"Natural" and "Artificial" Harmonics—The Manner of Bowing Harmonics.