ving the impression of a single tone. The most important tone of the
series is the _fundamental_, which dominates the combination and gives
the pitch, but this fundamental is practically always combined with a
greater or less number of faint and elusive attending tones called
_overtones_ or _harmonics_. The first of these overtones is the octave
above the fundamental; the second is the fifth above this octave; the
third, two octaves above the fundamental, and so on through the series
as shown in the figure below. The presence of these _overtones_ is
accounted for by the fact that the string (or other vibrating body) does
not merely vibrate in its entirety but has in addition to the principal
oscillation a number of sectional movements also. Thus it is easily
proved that a string vibrates in halves, thirds, etc., in addition to
the principal vibration of the entire string, and it is the vibration of
these halves, thirds, etc., which gives rise to the _harmonics_, or
_upper partials_ as they are often called. The figure shows _Great C_
and its first eight overtones. A similar series might be worked out from
any other fundamental.

[Illustration: (NOTE:--The B[flat] in this series is approximate only.)]

It will be recalled that in the section (10) dealing with _quality_ the
statement was made that _quality_ depends upon the shape of the
vibrations; it should now be noted that it is the form of these
vibrations that determines the nature and proportion of the overtones
and hence the quality. Thus _e.g._, a tone that has too large a
proportion of the fourth upper partial (_i.e._, the _third_ of the
chord) will be _reedy_ and somewhat unpleasant. This is the case with
many voices that are referred to as _nasal_. Too great a proportion of
overtones is what causes certain pianos to sound "tin-panny." The tone
produced by a good tuning-fork is almost entirely free from overtones:
it has therefore no distinctive quality and is said to be a _simple_
tone. The characteristic tone of the oboe on the other hand has many
overtones and is therefore highly individualistic: this enables us to
recognize the tone of the instrument even though we cannot see the
player. Such a tone is said to be _complex_.

12. The mathematical ratio referred to on page 134, if strictly carried
out in tuning a keyboard instrument would cause the half-steps to vary
slightly in size, and playing in certain keys (especially those having a
number of sharps or