On Perfect Musical Intonation. 73 
pressed by the numbers above, (viz., 1:2: 3, &c., to 10,)as har- 
monious. Here is the fountain head from which an abundant 
which do not come within the class just named, we give the 
name of discordant. Whether such combinations shall be used, 
is left entirely to the taste of the composer; we only insist on 
this, that we shall not call them harmony. 
_10. To the chords produced by the above ratios have been 
given names as follows: 
1:2— Octave. By combining these numbers 
2:3— Perfect Fifth. differently we obtain different 
3:4 — Perfect Fourth. chords, e. g. : 
4:5 — Major Third. 3: 5— Major Sixth. 
5:6— Minor Third. 5: 8— Minor Sixth. 
6:7 — 2 These twochords have| 4: 9 — Major(or Perfect) Ninth. 
7:8— , not been named.* 4: 7 — Perfect Seventh. 
8:9— Major Tone. 5:7 — )Chords derived from 
9:10 — Minor Tone. 7:9 — fie Perfect Seventh, 
7:10— )and not named. 
11. All these chords are produced from four prime numbers, 
viz., 2, 3, 5, an The prime 2 produces the octave, the prime 
Jifths, can we obtain a major third, nor from either or both - 
ae chords (thirds and fifths) can we produce a perfect sev- 
— enth. Elach are original, prime chords, not resolvable one into 
the other. From the neglect of these simple mathematical hat 
it 
ciples result much of the mystery and fallacy connect 
€mperament. It is attempted in temperament to produce a 
, major third from a series of four fifths, or what is the same thing, 
“ an alternate series of ascending fifths and descending fourths, 
7 * It is remarkable that scarcely any mention has been made in musical treatises of 
: two beautiful and important chords. They are » 
found in the chord of the Seventh. In this chord ap- om _ 
: , E, G, Bb, and C, whose vibrations are as these ah a pw 
: numbers, viz. ih G bb C. Thus it will be seen eS. 
that the ratios of G to Bb is as 6:7 and the ratio of 
Bb to C is as 7 to 8. 4:7 we 
_ Perfect Seventh, and for the same reason that the perfect fifth was so named. 
, e have not called it the minor seventh, as the ratio of the minor seventh has 
always n stated so far as we have seen to be 9:16. 
Seconp Serres, Vol. IX, No. 25.—Jan., 1850. 10 
