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.]
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 or flat will be found by itself, cancelling the double-sharp or double-flat). The natural is often used when a composition changes key, as in Fig. 11, where a change from E to G is shown.
[Footnote 8: It has already been noted (p. 6, Note) that in the German scale our b-flat is called b, and our b is called H. From this difference in terminology has grown up the custom of using the H (now made [natural]) to show that _any_ staff-degree is in _natural_ condition, _i.e._, not sharped or flatted.]
22. The group of sharps or flats (or absence of them) at the beginning of a staff partially indicates the key in which the composition is written. They are called collectively the _key-signature_.