58
LIMITS OF MUSICAL SOUNDS. [II. § 20.
per second, the lowest note of the double-bass, that
we get a satisfactory musical sound. There is no
corresponding limit absolutely barring the scale of
pitch in the opposite direction, but sounds above a
certain degree of acuteness become painful to the ear,
and therefore unfit for musical purposes. The highest
note of the piccolo, the shrillest sound heard in the
orchestra, makes 4752 vibrations per second. And
this we may regard as constituting a practical
superior limit to the scale of pitch at the disposal
of musical art. The extremest range attainable by
exceptional human voices, from the deepest note of a
bass to the highest of a soprano, lies, roughly speak¬
ing, between 50 and 1500 vibrations per second.
Ordinary chorus voices range from 100 to 900, or
1000 vibrations per second. The number of sounds
within the limits of the musical scale, which can be
recognized as possessing distinct degrees of pitch,
will vary -with the acuteness of perception of in¬
dividual observers. Trained violinists are said to be
able to distinguish about seven hundred sounds in a
single octave, which would give nearly five thousand
for the whole scale. But, since the difficulty of fix¬
ing the pitch with accuracy increases very rapidly
with very low or very high sounds, this estimate
would probably much exceed the limits of what
could be achieved by the very finest ear. We shall,