Temperament of the Musical Scale. “In the modern system, called tempered,” says a German writer on music, “all the intervals are not employed in their original perfection, as the nature of the harmonic scale presents them, but lose, sometimes in this interval, sometimes in that other, something of their acuteness or gravity. In fact, experience shows that, in tuning the major and minor thirds, the fifths, and the fourths, in their original perfection, when we reach a certain term, we meet with a fault of too great excess or too great deficiency; and from this faultiness arises the necessity of tempering this or that sound, in order to combine reciprocally the intervals of one mode with those of another, the result of which is called temperament." The nature and the principle of temperament, as applied to musical instruments of fixed sounds, may be understood by perusing pp. 610, 611, of vol. xv., article Music , and p. 533 of vol. xvi., article Organ. We shall here content ourselves with giving a very few additional remarks, and with indicating some works whence further information may be derived, seeing that the subject of musical temperament is not of sufficient importance to occupy much room in a work like this. The various systems of temperament that have been proposed for such instruments as the organ, the harpsichord, the piano-forte, &c. offer only a choice in the distribution of the imperfections of false intonation. The unequal temperament is that usually adopted; but it must be observed, that tuners in general proceed more by rule of routine and an indifferent ear, than according to any scientific principle of temperament. Hence the great differences found among instruments tuned by different tuners. It is a common error to suppose that “a person who sings in tune, tempers without lmowing it.” Even Chladni, following the lead, has asserted this; while the truth is, that there is no temperament in the voice of a singer whose intonation is perfect, unless his voice and ear happen to be misguided by the accompaniment of a tempered instrument, that is, an instrument out of tune. When left to itself, the voice of such a singer, in executing the most intricate modulations, forms the sounds in their true ratios to the different tonics or key-notes that occur, and, in the wonderful subtlety of the intonations of that only perfect musical instrument, the human voice, possesses all the intonations that are necessary to form these sounds exactly. Nearly the same thing occurs in the case of such a violin-player as a Viotti or a Paganini when he plays alone, and undisturbed by the false intonations of any accompanying instrument. This was actually proved in Paris about thirty years ago, by the experiments made by M. Charles and the celebrated violinist Viotti. We may here remark, that it [7:21:174]is of great detriment to the just intonation of a singer, to learn to sing by the guidance of an instrument such as the piano-forte, as is the common practice; for a habit of malintonation is then inevitably acquired. The same remark applies to singers taught with the accompaniment of those instruments with fretted finger-boards, such as the guitar, of which the intonation is also imperfect. As to the imperfections of the common guitar, the reader may consult the lively and ingenious work entitled Instructions to my Daughter, for playing on the Enharmonic Guitar, London, 1829. The celebrated singer Madame Mara used to say that every singer ought to learn to play the violin, in order to acquire a knowledge of just intonation. Certainly that instrument, and others of the violin kind, are the only ones we have that are capable of the nearest approach to perfect intonation, making allowances for the mechanical imperfections of their strings, as we have already hinted in the article Music . But still the human voice is the only perfect musical instrument. It has been a prevalent opinion among musicians and writers upon music, that the ancient Greeks were ignorant of many of our musical intervals, and possessed no instruments capable of executing our modern musical scales. But it is more than probable that the knowledge of the ratios of musical intervals, and of perfect intonation in a variety of scales, was much more exact among the ancient Indians, Arabians, and Greeks, than is generally supposed, or than the scanty, imperfect, and corrupted Greek relics of works on music, and the very limited examination of Indian and Arabian manuscripts, have hitherto been able to show. The reader may consult, on the subject of musical temperament, the following works. Among these, one of the best is Professor Robison’s, for clearness, as well as useful suggestions. Chapter 13, et seg, of the third book of Salinas de Musica, Salamanca, 1577. Dr Smith’s Harmonics, second edition, 1759. Dr Thomas Young’s Papers in the Philosophical Transactions, and in Nicholson’s Journal; also vol. ii. of his Lectures on Natural Philosophy. Cavallo’s Paper in the 78th vol. of Philosoph. Trans. Vol. iv. of Professor Robison’s System of Mechanical Philosophy, edited by Dr Brewster in 1822, pp. 376-451. Instructions for Playing on the Enharmonic-Guitar, London, 1829. (g. f. g. )