You see those little symbols at the beginning of the sheet music, whether a sharp, flat or natural symbol, those are what identifies the scale that a piece of music is played in. To you, the player, that also indicates the kind of chords that will be contained within that music.
Key signatures are a kind of musical shorthand that cut down the amount of accidental symbols required in a piece of music. In the key of C, that has no sharps or flats, there would be no need for additional symbols, but in all other keys this could create a messy manuscript. For example, in the key of F major (also known as D minor), there is one flat (a note that is played half a pitch lower) occurring on the B note which becomes B flat. Without a key signature each B in the manuscript would appear with the flat sign following it. The key signature places the flat at the beginning of the line so that you know to play each B as B flat. This produces a much clearer line of music to follow - especially when the amount of sharps or flats rises and could affect most notes in the music!
The placement of the sharp or flat after the clef always keeps the same order and each one is placed on the relevant line of music so that you know which notes are affected. The flats follow the following sequence, B, E, A, D, G, C, F - easily remembered because the first four notes spell out the word BEAD, and then you just need to learn the GCF.
Flats always occur in this order in any key signature:
Bb Eb Ab Db Gb Cb Fb
The sharp sequence follows a reverse sequence - F, C, G, D, A, E, B. If there is only one sharp at the beginning of the music, you will learn that this has been composed in the key of G major (also known as E minor), and the one sharp is F sharp. All F notes should be played as F sharp.
Order of the sharps: F#
C# G# D# A#
Each music key has both a major and minor name. From the key signature you will usually identify the major key, but it's by listening to the music itself that you can identify if the music you originally thought of as being in the key of D major is actually B minor. This point doesn't really matter as much for the practicalities of playing because no matter what name you give the key, the same notes (F and C) are sharpened by half a tone.
Accidentals occur in the music when the composer wishes to create a sound where the half note change implied by the key signature doesn't apply. In this instance a neutral symbol will appear next to the note that is covered by the key signature but isn't to be raised or lowered. For example, if your key signature is G but the composer wants to create a specific sound and so doesn't want some of the F notes to be sharp, then a neutral symbol will be placed on the staff beside the affected notes. This neutral symbol is known as an accidental and is only good for the note that it is placed beside; the other F notes should be played sharp as per the key signature. Sharps and flats can be used in the same way as neutrals in order for the composer to have greater control over the melody and harmony they create.
At first key signatures seem like a secret code, but once you learn then, you'll find that that it's quite logical and makes a lot more sense than having individual flats and sharps next to each note as required. Watch this short video on key signatures:
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