So we all know the blues scale, and how it’s sometimes referred to as the “minor pentatonic” scale, referring to the fact that it is typically composed of 5 of the 7 notes of the minor scale. That means you can think of it as a minor scale. So if we think of the A blues scale as A,C,D,E,G. This means of we want to turn that into the A minor scale, we would simple need to add the two remaining notes: F,B.
You might recognize that this is all the letters of musical scales with no sharps or flats; all the white keys on the piano. You may also know that all the white keys make up the C major scale. This means that A minor and C major are composed of the same notes. That is, A minor is the “relative minor” of C major. This means that if we start with the A blues scale, then add the two notes to make it the A minor scale, that is an easy way to arrive at the C major scale.
One way to remember what major key is the relative of what minor key is to just know that it is the third note of the minor scale, second note of the blues scale: C/A-, D/B-, E/C#-, F/D-, G/E-, A/F#-, B/G#-.
So then, if we are playing a blues song in the key of A, we may stick to the 5 notes when composing a lick or idea and emphasize A as the dominant note; starting or ending phrases with A. For a minor song we’d simply add F,B, and emphasize A as the dominant note; starting or ending phrases with A. If the song is in C major, it would be the same 7 notes as A minor, but emphasize C as the dominant note; starting or ending phrases with C.
When I realize a song is in the key of C, I can either look for the C major scale patterns, or the A minor scale patterns on the fretboard. Then, I find the C notes in the pattern and begin there.