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COMBINATION TONES.                          131
The one condition necessary for the production of differential tones, is, that the same mass of air be simultaneously and power­fully agitated by two tones; that is, the tones must be sufficiently loud. As the intensity of the generators increases, so does that of the differential, but in a greater ratio. The condition just referred to, is best satisfied on the Double Syren of Helmholtz (fig. 22), two circles of holes in the same chamber being open. The differentials produced by this instrument are exceedingly powerful.
Two flageolet fifes, blown simultaneously by two persons, also give very powerful differentials. The latter may be approximately ascertained from the table given above, but allowance must be made for the tempered intervals. Thus, if the tones G3 and F3 be loudly blown, the differential produced will be very nearly that given in the table, viz., F, three octaves below.
Differential Tones are very conspicuous on the English Concertina: in fact, so prominent are they, that their occurrence f orms a serious drawback to the instrument. They may be plainly heard also on the Harmonium and American organ: especially when playing in thirds on the higher notes. Two soprano voices singing loudly, will produce very audible differentials. Owing to the evanescent character of its tones, it is difficult to hear differ­entials on the pianoforte, but they can be detected even on this instrument by a practised ear. Differential tones may be easily obtained also from two large tuning-forks, which should be struck sharply. Two singing flames are also well adapted for producing these tones.
Not only do two generating tones give rise to a differential, but this differential may itself act as a generating tone, together with either of its generators, to produce a second differential tone ; and this again may in its turn act as a generator in combination with one of the original generators, or with a differential, to produce a third; and so on.
The differential tone Z\ which is generated by two simple or compound tones x and y, is termed a differential of the first order. If x and Z| or y and Z\ generate a differential z2, this is said to be of the second order; and so on, Differential tones of the second order are usually very faint, and it requires exceedingly powerful tones to make differential tones of the third order audible: in fact, the latter are only heard under very exceptional circumstances.
To determine what differentials of the second and third order can be present, when two tones at any definite interval are loudly