The major scale is the most important and fundamental scale in all of Western music. To derive these scales we will use a technique involving major tetrachords.
A major tetrachord is a set of four notes arranged in sequence by pitch. From the starting note, a major tetrachord consists of the following ascending intervals: whole-step, whole-step, half-step.
Our first example is building the C major tetrachord. We start with the root note, C, and follow the interval pattern above to derive the other notes in the tetrachord. A whole-step up from C is D, our second note. Going another whole step gives us E. The final half-step brings us up to F. So, the C major tetrachord is C-D-E-F.
Now, to finish the major scale, we go up one more whole-step and then append the major tetrachord of that note onto the first tetrachord.
Continuing our example: the note which is a whole-step above F is G. From the technique above, we derive the G major tetrachord as G-A-B-C. Putting the two tetrachords together, we get the C major scale: C-D-E-F-G-A-B-C
This technique can be used as an easy way to derive any major scale.
Constructing the Circle of Fifths ⟩⟩