WOLF, THE. I. A term applied to the harsh howling sound of certain chords on keyed instruments, particularly the organ, when tuned by any form of unequal temperament.
The form of unequal temperament most widely adopted was the mean-tone system. The rule of this system is that its fifths are all a quarter of a comma flat. The thirds are perfect, and are divided into two equal whole tones, each of which is a mean between the major and minor tones of the diatonic scale; hence the name Mean-tone system.
The total error of the whole circle of twelve fifths, at quarter of a comma each, amounts to three commas. Since the circle of twelve perfect fifths fails to meet by about one comma, the circle of mean-tone fifths fails to meet by about two commas, or roughly, nearly half a semitone. In the mean-tone system on the ordinary keyboard there is always one fifth out of tune to this extent, usually the fifth G♯–E♭. There are also four false thirds, which are sharp to about the same extent, usually B–E♭, F♯–B♭, C♯–F, and G♯–C. All chords into which any of these five intervals enter are intolerable, and are 'wolves.'
The use of unequal temperaments disappeared in Germany during the latter part of the 18th century, probably under the influence of Bach. Unequal temperaments ceased to be employed in the pianoforte in England at about the termination of the first third of the present century. At the same time the transition process began here in connection with the organ; and by 1870 it was practically complete, few cases only of the unequal temperament then surviving. The Wolf has in consequence ceased to have any but historical and scientific interest. [See also Temperament, vol. iv. pp. 72, 73; and Tuning, ibid. 188, 189.]
II. In bowed instruments the Wolf occurs, owing to defective vibration of one or more notes of the scale. When it occurs, it is generally found more or less in every octave and on every string. Different instruments have it in different places: it is most common at or near the fourth above the lowest note on the instrument, in the violin at C, in the violoncello at F. The more sonorous and brilliant the general tone, the more obtrusive it becomes: if the tone be forced, a disagreeable jar is produced. Hence it is idle to attempt to play the wolf down: the player musC humour the troublesome note. It is commonly believed that there is a wolf somewhere in all fiddles, and it is certain that it exists in some of the finest, e.g. in Stradivaris. Probably however it is always due to some defect in the construction or adjustment. Violins with a soft free tone are least liable to it: and the writer's viols in all three sizes are quite free from it. The cause of the wolf is obscure, and probably not uniform: it may result from some excess or defect in the thicknesses, from unequal elasticity in the wood, from bad proportion or imperfect adjustment of the fittings, or from some defect in the proportions of the air chamber. It may be palliated by reducing some of the thicknesses so as to diminish the general vibration, and by as perfect as possible an adjustment of the bar, bridge, and sound-post: but in the opinion of violin-makers where it is once established it cannot be radically cured. Some instruments have what may be termed an anti-wolf, i.e. an excess of vibration on the very notes where the wolf ordinarily occurs. The writer has a violin which exhibits this phenomenon on the B and C above the stave. When these notes are played forte on any of the strings, the B or C an octave below is distinctly heard. This is probably a combinational tone due to the coalescence of the fundamental tone with that produced by the vibration of the string in each of its 2–3 parts. In some Forster violoncellos the wolf is so strong as to render them almost useless.
