The definition, and the origin of this sign notation "x"

Question

Here is an example of the double sharp (within the red mark) from Liszt Les Preludes, see below.

I suppose this notation "x" is called double sharp.

Questions:

• What are (1) the definition, and (2) the origin of this notation x?

• This is a common notation in the violin sheet music. Does this notation occur often in other instruments, too?

I suppose to raise a semitone higher than the designed sharp ♯ tone. But I would like to know a precise definition, because within the bar, other than the chosen key, there could be other preceding notations sharp (♯ or #), the flat (♭ or b), or the natural sign ♮.

Answer 1

(1) Meaning

The double-sharp symbol indicates to raise the adjacent pitch two half steps (semitones) from its "natural" position (i.e., without regard to the key signature or other accidentals).

(2) Origin

The symbol was introduced around 1700, and became standard by 1758.

Next we must consider the introduction of the double flat and the double sharp.... [Johann] Mattheson tells us in the second edition of his "Great Thorough-Bass School" [ca. 1700] [that] he placed two sharps before the notes in question. He does this because he has not the necessary type for the special sign which he had already proposed for this purpose — namely, a single St. Andrew's cross.... Leopold Mozart gives in 1756 two forms of the double sharp: + and x. In 1758 we learn that its convenience had already made the latter the most fashionable form, and thus it has remained. (Niecks 1889, 94–95)

Niecks, Frederick. “The Flat, Sharp, and Natural. A Historical Sketch.” Proceedings of the Musical Association 16 (1889): 79–100. http://www.jstor.org/stable/765359.