There are 12 notes in an octave, but most musical pieces doesn't use all the notes. It tends not to sound very musical, there is too much discord and randomness. That isn't to say that you can never do that, if that is the effect you wish to achieve. But most music relies on a balance between predictability and surprise - it obeys certain rules so the listener can follow what is going on, but occasionally bends the rules to keep it interesting.
Many pieces of music use a scale, which basically defines a subset of the notes that normally appear in the music.
The scale of C major is the first scale most people learn. It holds a special place because it consists of the white notes on a piano, or put another way all the non-sharp notes.
When a piece is played using the C major scale, we say it is in the key of C.
A major scale consists of 7 notes:
C D E F G A B
The important thing about this set of notes is the intervals between them. The interval between C and D is a whole tone (T), because there is another note (C#) between them (there is a black key between them on the piano). Whereas the interval between E and F is a a semitone (S) because there is not another note between them (the white keys are next to each other).
The sequence of tones and semitones in a major scale is:
T T S T T T S
This pattern is the essence of a major scale.
There are 3 important notes in a major scale:
These chords are important is conventional western music, where chords based on the tonic and dominant, and to a lesser extent the subdominant, are found very frequently.
The G major scale will has the same intervals as the C major scale, but it starts from the base note G. For example the G major scale has the following notes:
This sequence has the same pattern of intervals as C major, but starting at G:
T T S T T T S
As you can see, the scale of G major has almost the same notes as C major, it just has one sharp, F#. This makes G a relatively easy scale to learn on the piano, as it only requires one black key. It is often the second scale people learn after C.
G A B C D E F#
In the scale of G major, the tonic is G, the dominant is D and the subdominant is C
You can base a major scale on any note. That chosen note would be the tonic, and the scale would include the notes that are 2, 4, 5, 7, 9 and 11 semitones above the tonic.
We can convert a piece of music from one scale to another by shifting every note by the same number of semitones. This will result in the same music just at a lower or higher overall pitch. We call this conversion a transposition.
For example, suppose we have a simple melody in C major, of 4 notes C, E, F, D. If we wanted to transpose this to G major, we would need to add 7 semitones to each note. This would give us G, B, C, A.
Alternatively we could subtract 5 semitones from each note - this would still give us G, B, C, A, but an octave lower.
Why would we want to do this, and indeed why do we have different scales at all? Couldn't we just play everything in C major? There are several reasons why we use different scales.
The first is, of course, playing the same piece in different key sounds different. Although the melodies and chord sequences are obviously related, the overall pitch is different and that affects the mood of the piece. A tune like Happy Birthday gets rendered millions of times every day in all keys and none, but if you heard your national anthem played in the wrong key it would sound quite wrong.
Also, different instruments have different ranges, so it might sometimes be convenient to shift the key of a piece to fit the instruments being used. This is particularly true of the human voice, and singers will often change the key of a song to match their vocal range.
Finally, some keys are easier to play on certain instruments. It is easier for beginners to play in C on a piano, using just the white keys, than playing the same song in a key that uses multiple black keys, so often pieces for beginners are transposed.
Fortunately we have few of those problems in electronic music, and it is even possible to transpose automatically if you wish.
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