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Art. I. Essay on Musical Temperament.^ 



By Professor Fisher, of Yale College. 



JLt is well known to those who have attended to the subject 

 of musical ratios, that a fixed scale of eight degrees to the oc- 

 tave, which shall render all its concords perfect, is impossible. 

 It has been demonstrated by Dr. Smith, from an investigation 

 of all the positions which the major, the minor, and the half- 

 tone can assume, that the most perfect scales possible, of which 

 there are two equally so, differing only in the position of the 

 major and the minor tone above the key note, must have one 

 Vth and one 3d too flat, and consequently the supplementary 

 4th and Vlth too sharp, by a comma. In vocal music, and in 

 that of perfect instruments, this defect in the scale is not per- 

 ceived, because a small change may be made in the key, when- 

 ever the occurrence of either of those naturally imperfect in- 

 tervals renders such a change necessary to perfect harmony. 

 But in instruments with fixed scales, such as the guitar, the 

 piano-forte, and the organ, if we begin with tuning as many 

 concords as possible perfect, the resulting chords above-men- 

 tioned will be necessarily false in an offensive degree. Hence 

 it is an important problem in practical harmonics, to distribute 

 these imperfections in the scale among the different chords, in 

 such a manner as to occasion the least possible injury to har- 

 mony. 



But this is not the only nor the principal difficulty which 

 the tuner of imperfect instruments has to encounter. In order 

 that these instruments may form a proper accompaniment for 

 the voice, and be used in conjunction with perfect instruments, 

 it is necessary that music should be capable of being executed 

 on them, in all the different keys in common use ; and espe- 

 cially that they should be capable of those occasional modula- 

 tions which often occur in the course of the same piece. Now 

 only five additional sounds to the octave are usually inserted 

 for this purpose, between those of the natural scale, which, of 

 course, furnish it with only three sharps and two flats. Hence, 



^ * From the MS. papers of the Connecticut Academy, now published by per- 

 mission. 



