{6 On Musical Temperament. 
when a greater number of flats or sharps is introduced, the 
music can be executed only by striking, in the former case, 
the sharp of the note next below; and, in the latter, the flat 
of the note next above. But as the diatonic semitone is more 
than half the major, and much more than half the minor tone, 
if the additional sounds in the common artificial scale be fae 
perfect for one of the above employments, they must be ex- 
tremely harsh for the other. Hence arises the necessity of 
adjusting the position of these five inserted sounds so that they 
may make tolerable harmony, whichever way employed. A 
change in these will require corresponding. changes in the po- 
sition of the several degrees of the natural scale; so that it is 
highly probable that the best scheme of temperament will leave 
no concord, either of the natural or artificial scale, absolutely 
perfect. 
In adjusting the imperfections of the scale, the three follow- 
ing considerations have been usually taken into view. 
I. One object to be aimed at is, to make the sum of the tem- 
peraments of all the concords the least possible. Since expe- 
rience teaches us that the harshness of a given concord increas- 
es with its temperament, it is obvious that of two systems which 
agree in other respects, the best is that in which the sum of the 
temperaments is least. 
II. When other things are equal, the best adjustment of the 
imperfections of the scale is that which diminishes the har- 
moniousness of all the different concords proportionally. The 
succession of a worse toa better harmony, is justly regarded 
by several of the best writers on the subject, as one of the princi- 
pal causes of offence to the ear, in instruments imperfecly tuned. 
if. When different chords of this same kind are of unequal- 
ly frequent occurrence, there is an advantage, ceteris paribus» 
in giving the greatest temperament to that which occurs most 
seldom. This important consideration has indeed been neg- 
lected by Dr. Smith, in the systems which he recommends, 
both for his changeable and the common fixed scale; as it is, 
also, by the numerous advocates of the system of equal semi- 
tones. But many authors on temperament, and most instru- 
ment-makers, pay a vague regard to it. Their aim has been, 
Paps ger re 
a Sy RE 
fe ts 
ike sik 
pahgirie Sie r 
