Essay on Perfect Intonation. 25 perfectly. We are so constituted, however, (and wisely so, of course,) that we can get accustomed, in time, to almost any amount of discord, so that it will not be, to us, disagreeable. It is said that men, whose whole lives are spent in riveting the plates of steam-” boat boilers, perceive no discord in the harsh clangor of their business. Such artists might perhaps prefer a tempered organ. It is for the natural and uncontaminated, as well as for the culti¬ vated, ear to appreciate fully the beauty and perfection of pure harmony. The best tuners, in our large manufactories are free to confess that there is but little musical satisfaction in leaving an instrument, which has been constructed carefully in all its parts, out of tune. Notwithstanding the evidence of our senses, that the perfect scale is most pleasing to the ear—notwithstanding the sure deduc- tions from the mathematics, there are those who speak and write against perfect intonation. u Why,” it is asked, “if it was in¬ tended, in nature, that music should be in perfect tune, has a tem¬ pered scale been used for so many centuries?” Admit such an objection, and there is an end of all invention and discovery, in this, and every other science. Against the greatest invention of the age—the electric telegraph—the same objection has equal force. So long as no mechanism had been invented, by which more than twelve sounds could be conveniently managed by the performer, we should naturally suppose that organ-builders would manufac¬ ture such instruments as we have, and give to them the best tune they could, even if it was somewhat imperfect ; but we might not have expected, that learned and professedly scientific writers should have attempted to prove, from this fact, that the nature of music does not permit its chords to be in perfect tunel* It has * Prof. Peirce again says, § 115. “ It is a mistake to suppose, as some have done, that temperament applies only to instruments with keys and fixed scales. Singers, violin-players and all others who can pass through every gradation of tone, must all temper, or they could never keep in tune with each other, or with themselves.” “ Any one, who should keep on ascending by perfect fifihs, and descending by oc¬ taves and thirds, would soon find his fundamental pitch grow sharper and sharper, till he could at last neither sing nor play ; and twro violin-players accompanying each other and arriving at the same note by different intervals, would find a continual want of agreement.” With regard to the statement in the first paragraph, we shall now take occasion only to say, that the reverse we believe to be true ; and it appears to us contradic¬ tory, to assert that singers, to sing in tune, must sing out of tune, (for this is pre¬ cisely the meaning of temperament.) If the learned Professor will visit our instru¬ ment in Boston, we will satisfy him that, with our instrument as an accompaniment, which does not temper in the least, singers find no difficulty in keeping in tune. The second paragraph probably refers to a case like the following, which has often been quoted by those who advocate temperament. “ If from C we ascend by four perfect fifths and descend by two octaves and a major third, we find the last note a comma higher than the C commenced with.” This is entirely true. Neither can we multiply a number by f’s, and divide the product by -§-’s and j’s, and reach at length the original number ; for this reason, nevertheless, the Professor does not advocate a temperament in the mathematics. The supposed trouble with the violin-players who