TEMPERA31ENT AND TUNING. Temperament is the name given to the discussion of the subject of which tuning is the appli cation; and tuning is the art of adjusting the several sounds of a musical instrument so as to make its scale approach to correctness ; also that of putting two instruments, each of which has the parte of its scale in proper relative adjustment, into agreement with each other.
Some musical instruments have a permanent relative scale, all the parts of which, if changed at all, change together. Thus a horn or a flute may change its pitch from the heat of a room, but all the parts change together, and the whole effect of temperature is corrected at once by lengthening the pipe of which the instrument consists. Other instruments require to have the parts of their scales compared with each other from time to time, owing to their several parts being unconnected and subject to unequal wear or to separate accident, such as the organ and piano-forte. Others again are so liable to these derangements as to require tuning on every occasion of use, as the violin class, the harp, the drums, &c. It is not our intention to enter into the mode of tuning instrtunents in detail, but, as promised in the article SCALE, to give some account of the difficulties which are met with in the actual construction of any scale, and the ordinary modes of meeting them.
In the article just referred to we have pointed out the mathematical commencement of this subject, and have made it evident, from first principles, that a perfect * scale is impossible ; that is to say, one in which all the intervals, or even all the principal intervals, in every key, shall be perfect. Let additional notes be introduced to make existing keys perfect, and those additional notes would themselves become the key-notes of new keys, requiring additional notes to make them. perfect. Again, the conditions of the ordinary musical instruments require that the octave shall consist of only twelve semitones ; and though some organs have been constructed with more, it is not worth while to embarrass the subject by treating of any other scale than that of the twelve amitotic& We shall use the same notation as before, namely, expressing the following note of the treble scale, by c, we shall denote the successive es in ascent by ci, &c., and
those in descent by c„ &o. : thus, c, is three octaves below c, and is four octaves above it The first point is to fix upon some one note, by the pitch of which all others may be determined. The only way of retaining a permanent pitch for use is by having an instrument which time will not alter. It is true that the pitch of a note depends only upon the number of vibrations in a second, and can, by the description of this number, always be recovered by acoustical experiments. But we might as well expect a carpenter to ascertain his own foot rule for himself by the pendulum as an ordinary musician to appeal to the theory of musical vibrations. A standard pitch is usually obtained, or professed to be obtained, by the tuning-fork, an instrument consisting of two steel prongs growing out of a steel handle. When these prongs are sharply struck they vibrato ; and if the instrument be then held to the ear, or placed upon the flap of a table or any other sound-board, a low and very pure sound is heard, if the prongs be perfectly equal. These tuning-forks are usually made to sound either or A, and they would answer their purpose exceedingly well if there really were in existence any standard from which they were made. But this there is not ; and the consequence is, that not only do the tuning-forks of different makers frequently vary a little from each other, but the new forks are sensibly higher than the old ones. We have already seen how much the pitch used in different places varies [Acousnce], and also how very much what is now called concert-pitch is higher than it was a century ago. [Ptee.] This rise, it appears, is still going on, and, unless measures be taken to stop it, will not finish until all the com positions of the old masters are played and sung two or three notes higher than they were really written.