Doppelkreuz), which being placed before a note raise it respectively a semitone or a tone; the flat (♭) (Fr. bémol, Ger. Be) and double-flat (𝄫) (Fr. double-bémol, Ger. Doppelbe), which cause the note to be lowered to the same extent; and the natural (♮) (Fr. bécarre, Ger. Quadrat), which is applied to an already chromatically altered note in order to restore it to its original position.
In modern music the signs are placed at the beginning of the composition, immediately after the clef, when they affect every note of the same name throughout the piece; and they are also employed singly in the course of the piece, in which case they only affect the note to which they are applied and any succeeding note on the same line or space within the same bar. Strictly speaking, only those which occur in the course of a composition are accidentals, the sharps or flats placed after the clef being known as the Signature, but as their action is the same wherever placed it will not be necessary to make any distinction here.
The invention of accidentals dates from the division of the scale into hexachords, an arrangement usually attributed to Guido d'Arezzo (A.D. 1025) but probably in reality of later date.[1] These hexachords, of which there were seven, were short scales of six notes each, formed out of a complete scale extending from G, the first line of the bass stave, to E, the fourth space of the treble, and commencing on each successive G, C, and F, excepting of course the highest C of all, which being the last note but two, could not begin a hexachord. The chief characteristic of the hexachord was that the semitone fell between the third and fourth notes; with the hexachords of G and C this was the case naturally, but in singing the hexachord of F it was found necessary to introduce a new B, half a tone lower than the original, in order that the semitone might fall in the right place. This new note, the invention of which laid the foundation of all modern chromatic alterations, was called B molle (Fr. Bémol, Ital. Bemolle, still in use), and the hexachord to which it belonged and the plainsong in which it occurred were termed respectively hexachordum molle and cantus mollis, while the hexachord of G, which retained the original B, was known as hexachordum durum, and the melody employing it as cantus durus.
For the sake of distinction in writing (for modern notation was not yet invented, and musical sounds were generally expressed by letters), the unaltered higher B was written of a square form, after the fashion of a black letter b, from which circumstance it received the name B quadratum (Fr. Bé quarre, Bé carré, Ital. Be quadro, Ger. Quadrat, still in use), while the new lower B was written as a Roman b and called B rotundum (Fr. B rond, Ital. B rotondo). The square B, slightly altered in shape, has become the ♮ and the round B the ♭ of modern music, and they have in course of time come to be applied to all the other notes. The inconvenience, is it at that time appeared, of having two different kinds of B's led the German musicians to introduce a new letter, H, which however, probably on account of its similarity of shape, was given to the square B, while the original designation of B was made over to the newly-invented round B. This distinction, anomalous as it is, remains in force in Germany at the present day.
The sign for chromatically raising a note, the sharp, is of later date, and is said to have been invented by Josquin de Pres (1450–1521). It was originally written as a square B crossed out or cancelled, to show that the note to which it was applied was to be raised instead of lowered,[2] and was called B cancellatum (latticed or cancelled B).
Modern music requires double transposition signs, which raise or lower the note a whole tone. These are the double flat, written 𝄫, (or sometimes in old music a large ♭ or a Greek β), and the double sharp, written ※, 
, 
, or more commonly 𝄪. The double sharp and double flat are never employed in the signature, and the only case in which the natural is so placed occurs when in the course of the composition it becomes necessary to change the signature to one with fewer flats or sharps, in order to avoid the use of too many accidentals. In this case the omitted sharps or flats are indicated in the new signature by naturals. The proper use of the natural is to annul the effect of an already used sharp or flat, and it has thus a double nature, since it can either raise or lower a note according as it is used to cancel a flat or a sharp. Some of the earlier composers appear to have objected to this ambiguity, and to obviate it they employed the natural to counteract a flat only, using the flat to express in all cases the lowering of a note, even when it had previously been sharpened: thus
would be written
This method of writing merely substitutes a greater equivocalness for a less, and is only mentioned here as a fact, the knowledge of which is necessary for the correct interpretation of some of the older compositions.
After a double sharp or flat the cancelling signs are ♮♯ and ♮♭, which reduce the note to a single sharp or flat (for it very rarely happens that a double sharp or double flat is followed at once by a natural); for example—
- ↑ Guido himself never speaks of hexachords in his writings, but on the contrary says that there are seven sounds in the scale. (See Fétis, 'Biographie Universelle des Musiciens,' art. Guido.)
- ↑ Some writers contend that the four cross lines of the sharp were intended to represent the four commas of the chromatic semitone, but this appears to be a fanciful derivation, unsupported by proof.
