A scale consists of all the notes of an octave that belong to that scale arranged in ascending or descending order. It is the way we include or exclude notes and the way we order the selected notes, is what gives the scale its individuality. Looking at the C major scale below, we see that the "ascending C major scale" is played as the following sequence of notes: C-D-E-F-G-A-B(-C)
Now, if a song is written out in C major scale, the notes that we expect to see in it are the ones listed out above. We also expect chords used to be those derived from these notes and conforming to this scale.
But does that mean that a major scale song cannot contain a minor chord or a note from outside the scale? The question can be generalised - If a song is in scale X (major, minor, diminished, or anything else), can it have chords that do not come directly from the scale in question? Can we have notes in the composition that do not feature in the scale with which it is labelled?
The short answer is, yes - it most certainly can. A composition is in no way restricted by the scale that is assigned to it. The notes or chords chosen are chosen at composer's pleasure, and are not restricted (as a rule) by the scale chosen. The purpose of assigning the label of scale comes from staff notation - the key signatures. In the example below, the line of staff notation below uses key signatures.
These key signatures, denoting the sharps and flats being used (or not) spell out which notes are to be played sharp or flat even when they are not explicitly marked as a sharp or a flat in the staff notation. These of notes are understood to be sharp (or flat) everywhere it occurs in the staff line without using the # or b symbol on the every time. This reduced the clutter on the actual line making the music easier to read. Now, since most songs would tend to have notes from a particular scale, the key signature can be taken to refer to the scale in the vast majority of cases.
Now, if we have to add a note that does not belong to the scale, we can still include it using the natural symbol () or # or b - as is required. Similarly, chords that are not a part of the set of chords that can be derived from the scale being used, can also be a part of the composition.
The use of scale indicating the scale of music is only relevant to staff notation, but has become such a part of tradition, that even chord-lyrics notes often cite the scale, though redundantly.
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