The soprano clef determines the position of the C note on the staff (stave ):
From this reference, all others music notes will be placed before and after the C note:
What instruments use the soprano clef?
The soprano clef was used for soprano voices (high voice of women and children), but nowadays this key is used almost exclusively for the transposition for some players and for the conductors.
The soprano clef for transposition (players)
We will look at the case of the horn players of the symphony orchestra, this wonderful wind instrument from the brass sub-family. The horn players (those who play the horn) are known to be the champions of transposition, and we will understand why. The instrument on the left of this paragraph is a modern horn (a double horn more precisely) and this instrument is in F, it is a transposing instrument, that is to say that when the horn player plays a C, the note actually heard is an F (yes I know it's weird, but it's like that). But the horn was not always equipped with rotary valves (pistons), and the ancestor of this instrument was the natural horn, which was user in classic period (W.A Mozart, Haydn, Beethoven, ...)
This second image on the left is a natural horn from Gebr brand. Alexander (model 290). In the past, when it was written horn in D on the score of the horn player, it was necessary to put the D crooks between the body of the instrument and the mouthpiece for the instrument to set the horn in D, and the horn players played the score as it was written, without transposition, in a way it was the instrument which transposed and not the brain of the player. But with modern instruments in F, the brains of the horn players must transpose to play scores written for the natural horn.
To illustrate the use of the soprano clef for transposition, let's look at the very beginning of Franz Joseph Haydn's horn concerto n°1, this excerpt is written for a horn in D. At the time of this composer, the horn player had to set his instrument in D, and the instrument transposed by itself (in a way ...).
But when the horn player plays on a modern instrument, he plays with a horn in F, and it is the horn player himself who must transpose the score at sight. The principle is very simple, the horn player thinks in F (because his instrument is in F) and he must play in D, so he must transpose everything at sight a minor third lower, so it is the same as reading the score with a soprano clef.
Here is the score of this concerto (the 1st staff is the score of the horn player and the second staff is the equivalent in concert pitch (in C).
The soprano clef for transposition (orchestra conductors)
The soprano clef is very useful for conductors, let's look at the concerto in A major for clarinet by W.A. Mozart:
The first staff is the one played by the clarinet in A, and the second staff corresponds to the sounds in concert pitch (in C). If the conductor wants to know the sounds in concert pitch that the clarinet plays, then he must mentally add a soprano clef and also add 3 sharps, because the A clarinet is a transposing instrument.
Life as a conductor is not easy... But he is much better paid than the horn player, I can guarantee that ...
Key signatures in soprano clef
Evolution of the C-clef symbol
In the book A history of music by Charles Villiers Stanford and Cecil Forsyth, a representation of the evolution of the C-clef clef symbol is exposed (source):
Learn to read soprano clef
Here is a game to learn soprano clef notes: