72 On Perfect Musical Intonation. 
. The writer would remark as the conclusion of his introduc- 
sin, that no one, in the present unsettled state of the musical sci- 
ence, can expect to become thoroughly acquainted with its funda- 
mental principles, unless he will experiment and think for himself. 
He will constantly meet with the errors of the theorists, and if Z 
he cannot detect these for himself, he will find himself in per- j 
petual darkness. Reasoning on musical science is not different 
from reasoning on any other science. We must interrogate na- 
ture, and follow where she leads us, notwithstanding the time- 
honored opinions of the theorists. As an illustration of this w 
may refer to the “chord of the seventh,” which consists of a 
common chord with a certain seventh added. If we inquire 
what this seventh is, we are informed by all the theorists that it 
is a fourth above the fourth, and that its ratio is 9:16. Upon 
trial, this combination we find very discordant and disagreeable. 
If we ask a good natural singer to give the note, he gives it most 
readily and naturally 4:7, a little lower than the note laid down 
in the books, and this note (4:7) we find most natural and har- 
monious in the chord. <A theory should be made from the music 
and not the music from the theory. 
7. We find by experiment that if two or more sounds heard 
together, are in the rapidity of their vibrations in a sufficiently ¢ 
simple ratio, their relations are perceived by the ear, producing 4 
an agreeable sensation, and this effect we call HARMONY. 
8. If we take a series of sounds, the ratios of whose vibrations | 
are as the following numbers 2:3:4: : 10, &c., | 
we have the notes which will produce a series of chords, which 
commencing with the most simple, will gradually become more 
and more complicated, until the ear can no longer perceive their _. 
relations: when this point is reached they will cease to produce 
chords and harmony. Any ratio, neither of whose terms, (when 
reduced, ) is larger than 10, will ‘produce a chord appreciable by 
the ear. The extent to which the relations of chords can 
perceived, will vary of course in different persons according to 
the delicacy of the ear, aud hence it may not strictly be said that 
there is any absolute point where chords cease and discords com- | 
mence, yet as our written music contains no chord whose ratio 1s 
expressed in higher terms than ¢en, and as this last ratio 9: 10 is 7 
certainly near the farthest limits of our perception, we may prop- pa 
erly consider that all chords must have the terms of their ratios 
within this limit. It may be added, that though one or both of 
the terms be larger than 10, yet if by dividing either*or both by 
2, the quotient is brought within the limit above mentioned, they 
will still produce harmony: e.g. the chord 5:12 is 5:6 ora 
minor third, the highest note of which is raised an oc ie 
. We shall then consider any combination of sounds which 
are, each to > every sian 4 of the combination, as the ratios eX- 
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