Ramsay
HARMONICS ON THE VIOLIN.
At the middle of the string the stopped note and the harmonic notes are the same; but corresponding places above and below the middle give the same harmonic, although these places when stopped give different notes. [Scientific Basis and Build of Music, page 92]
Nine-tenths of a string, if stopped and acted on, gives a tone the ratio of 9:10, but if touched and acted on as a harmonic it gives a note which is three octaves and a major third above the whole string. If the remaining tenth of the string be acted on either as a stopped note or a harmonic it will give the same note which is three octaves and a major third above the whole string the ratio of 1:10, so that the stopped note of one-tenth and the harmonic of nine-tenths are the same. Indeed the bow acting on stopped note of one-tenth, on harmonic of nine-tenths, or on harmonic of one-tenth, produces the same note, as the note is the production of one-tenth in each case; for in the harmonic, whether you bow on the nine-tenths or the one-tenth, while it is true that the whole string is brought into play, yet by the law of sympathy which permeates the entire string, it vibrates in ten sections of one-tenth each, all vibrating in unison. This is what gives the harmonic note its peculiar brilliancy. [Scientific Basis and Build of Music, page 92]
See Also