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On Perfect Musical Intonation. 71 
explain musical intervals is the key-board of a piano forte! 
An interval is the distance of one piano-key from another. He 
defines a fifth thus: ‘“a fifth is an interval of five places.” 
had defined his intervals by reference to the horn or trumpet, as 
thtis—that the interval between the lowest and the second notes 
given by the horn is an octave—that the interval between the 
second and third notes is a perfect fifth, and so on—his definitions 
could have been depended on, as the horn will always (if prop- 
erly blown) give its intervals eractly thus. But so far from attempt- 
ting to establish his theory on any scientific or mathematical basis, 
he distinctly declares, “that it is not susceptible of such an estab- 
ishment, or at least, has thus far failed of proving itself to be so.” 
5. The writer of this paper is of opinion that music is as sus- 
ceptible of a systematic and mathematical basis as chemistry, as- 
tronomy, or any other science—that what are called the “mys- 
teries” and ‘ imperfections” of the musical scale contain in them 
nothing that is mysterious or imperfect—that temperament is no 
longer necessary, and would be as useful applied to a multiplica- 
tion table as to a musical scale—that the same sound can no 
shall express. Some further reference to this instrument will 
be made in the latter part of this paper. 
