H.. W. Poole on the Musical Ratios. - 293 
if so, the fifth must have at least three times its number of 
vibrations, the third five times, and the seventh seven times. 
At all events these different chords will always keep these rel- 
ative positions, or a fifth can always be sounded lower than a 
third, and both lower than a seventh; which accords with the 
practice of musicians. For certain melodic movements, it 
would seem as if all these intervals can be taken about an oc- 
tave lower than the limiting note of 33 vibrations would per- 
mit. Can not the vibrations of the octave below, or 164, be felt 
in union with the octave and other harmonics above, and in 
this way be considered as audible ? For the musical ear hears 
only what is plain enough to be understood, and relations too 
remote are often made clear and agreeable by the addition of 
other sounds. So a note in combination may be audible, which 
alone is not so. 
distributions; but it is certain that the harmonic series shows 
the best order and the proportion of each element admissible. 
Thus, before the seventh is sounded, we have the fundamental 
note in three octaves, the fifth in two, and the major third o 
in one, 
- Professor Tyndall says much about the harmonics, which he 
"calls “overtones.” He says: 
And be it remarked, that the overtones are indispensable to the 
character of musical sounds. Pure sounds, without overtones, 
would be like pure water, flat and dull. — 
I believe that pure water is good, either to use in its purity, 
or to mingle with other elements at pleasure, and that pu 
