18. A _sharp_ is a character which causes the degree of the staff with
which it is associated to represent a pitch one half-step higher than it
otherwise would.

Thus in Fig. 10 (_a_) the fifth line and first space represent
the pitch F, but in Fig. 10 (_b_) these same staff degrees
represent an entirely different tone--F[sharp]. The student
should note that the sharp does not then _raise_ anything; it
merely causes a staff degree to represent a higher tone than
it otherwise would. There is just as much difference between F
and F[sharp] as between B and C, and yet one would never think
of referring to C as "B raised"!

[Illustration: Fig. 10.]

19. A _flat_ is a character that causes the degree of the staff with
which it is associated to represent a tone one half-step lower than it
otherwise would. (See note under Sec. 18 and apply the same discussion
here.)

20. A _double-sharp_ causes the staff degree on which it is placed to
represent a pitch one whole-step higher than it would without any sharp.
Similarly, a double-flat causes the staff degree on which it is placed
to represent a pitch one whole-step lower than it would without any
flat.

Double-sharps and double-flats are generally used on staff
degrees that have already been sharped or flatted, therefore
their practical effect is to cause staff degrees to represent
pitches respectively a half-step higher and a half-step lower
than would be represented by those same degrees in their
diatonic condition. Thus in Fig. 10 (_b_) the first space in
its diatonic condition[7] represents F-sharp, and the
double-sharp on this degree would cause it to represent a
pitch one-half step higher than F-sharp, _i.e._,
F-double-sharp.

[Footnote 7: The expression "diatonic condition" as here used refers to
the staff after the signature has been placed upon it, in other words
after the staff has been prepared to represent the pitches of the
diatonic scale.]

CHAPTER III

SYMBOLS OF MUSIC DEFINED (_Continued_)

21. The _natural_[8] (sometimes called _cancel_) annuls the effect of
previous sharps, flats, double-sharps, and double-flats, within the
measure in which it occurs. After a double-sharp or double-flat the
combination of a natural with a sharp, or a natural with a flat is often
found: in this case only one sharp or flat is annulled. (Sometimes also
the single sharp o