The major scale · Music theory
Whole and half steps, tetrachords, the names of the degrees and how to write the major scale on any note.
Scale, degree and diatonic scale
A scale is a stepwise succession of notes, from a note to its octave. Each note is a degree, numbered in Roman numerals from the first one, the tonic: I, II, III… VII.
The major scale is diatonic: it has seven notes, one of each letter name, separated by whole and half steps. Its structure is always the same: whole, whole, half, whole, whole, whole, half. The half steps fall between degrees III and IV and between VII and I.
The two half steps give it its character: the one at III–IV gives its color and the one at VII–I makes the melody want to reach the tonic. If they move, it stops being a major scale.
A scale is not the same as a key
A scale is the ordered material, the notes from low to high. A key is also a hierarchy: a central note, the tonic, toward which everything tends, and chords with different roles. A melody in C major rarely runs up and down the whole scale, but its notes and resting points revolve around C.
In proportions, the octave is shared out as 5 whole steps and 2 half steps: 12 half steps, from which the scale uses 7 notes. The unequal distance is what lets you find your way: on hearing the half steps, the ear knows where the tonic is.