[9] 
Art. I. Essay on Musical Temperament.* 
By Professor Fisuer, of Yale College. 
L 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. 
Tt has been demonstrated by Dr. Smith, from an investigation 
of all the positions which the major, the minor, and the half- 
tone can assume, than 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 Vith 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 tliose of the natural scale, which, of 
course, furnish it with onl y three sharps and two flats. Hence, 
* From the MS. papers of the Connecticut Academy, now published 
by permission. 
VoL....1. Ne. 1. 2 
