ESSAY ON PERFECT INTONATION. 1. This paper will treat only of one department of the science of music—the laws which fix the tune of all musical scales, and determine all musical intervals. Any one, who is at all conversant with the musical discussions of the last few centuries, will per¬ ceive that this is but partly explored and disputed territory, where eminent scientific writers have entertained different opinions—• while all have agreed in admitting the fact, that there ever have been, and still are, difficulties and imperfections in the musical scale, as executed on organs, piano-fortes, &c., which no one has yet shown how to overcome. It is with the belief that he has overcome these difficulties, and is able to throw light on this abstruse and unsettled department of the science, in a prac¬ tical point of view, that the writer proposes to discuss it. Very little on this subject reaches the eye of the theoretical and prac¬ tical musician. In our elementary musical works it is either omit¬ ted, or is treated as utopian and chimerical ; indeed the writer is not aware of a treatise in which it is fully or correctly discussed. 2. It is a singular fact, that while the human ear delights in pure harmony, (as performed by voices, violins and other instruments without fixed scales,) and while improvement has been made in every other science and mechanical art, the organ of the present day has all the imperfection of intonation which pertained to that instrument, four centuries since. For so long a period has this imperfection existed, that it has come to be considered as neces¬ sary, not only in this instrument, but by many it is believed to be inherent in all music. Instead of remedying the difficulty by introducing the sounds requisite to form the several scales (played in) perfect, and inventing such mechanism as would bring these sounds under the ready control of the organist, “ temperament” has been substituted, which allows but one sound for G# and Ab, which makes the same sound answer for A, the sixth of the key of C, and A, the key-note of three sharps; which fiats every, fifth, sharps every major third, and leaves every musical interval (with the exception of the octave) more or less out of tune. 3. Various attempts have been made during the last three cen¬ turies to remedy the above difficulty, and to reduce the apparent imperfections of the musical scale to a scientific and mathematical basis. Salinas wrote on the subject as early as 1577, and the folio volume of Father Mersenne was published in French and Latin in 1648. These plans were to be effected by multiplying finger keys, which of course would augment fearfully the difficulty of