+“ 
9:10, and 15:16. The notes are represented by the syllables 
2 H. W. Poole on Perfect Harmony, etc. 
A 
sible and used in music, although this, so far as I have seen, 
first time 
It is clearly evident that this 
element enters into music of all kinds, and that the diatonic 
scale must contain it, or that there must be two diatonic scales: 
which latter supposition is most correct. If only fifths and 
thirds are admitted in forming a diatonic scale it will naturally 
be made of the common chords of three roots, namely, the 
tonic or key-note, the dominant or fifth above, and the subdom- 
inant or fifth below. This I have distinguished as the ¢riple 
diatonic scale, which has three intervals in the ratio of 8 
0, Re, Mi, etce., which always bear the same relation to the 
key-note and to each other. Thus, Do to Re is always as 8:9 
rule. Considering the key-note to make 48 vibrations in a given 
time, we have the 
TRIPLE Draronic Scate. Do to Do. 
Common chords on Do, Sol and Fa. 
Do Re Mr Fa Sot... haé St... 
Rel. vibrations, 48 54 60 64 72 80 90 
Firs 
t. Second. Third. Fourth. Fifth. Sixth Seventh. Octave. 
Intervals, 8:9 9:10 15:16 8:9 9:10 8:9 15:16 
8. But if the ear prefers—and it often does prefer—the sub- 
dominant harmony may be suppressed, and the fourth of the 
seale, Fa, and the sixth, La, may be replaced by the perfect 
seventh and ninth of the dominant harmony ; so that if we still 
Dovste Diarontc Scatu. Fa to Fa. 
. Common chord on Fa, chord of 7 and 9 on Do. 
ecm Ee bea we. Be Do es Mi Fa 
Rel. vibrations, 32 36 40 4 
or ta ae a 63 12 xs 2. oe 
: Second. Third. Fourth. Fifth. Sixth. Seventh. Octave. 
Intervals, 8:9 9:10 20:21 7:8 8:9 9:10 15:16 
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