The major scale, and the formula that defines it

The major scale is not a list of notes to memorise twelve times. It is one formula applied twelve times.

The formula

From the first degree to the eighth, the sequence of distances is always this:

tone — tone — semitone — tone — tone — tone — semitone

Apply it from C and the black keys do not even appear:

C major is the only major scale with no accidentals. That makes it convenient to explain and misleading to generalise from: the scale is not "the white keys", it is the formula. C is merely lucky that the white keys fit it.

The same formula in G

Start on G and follow: tone (G→A), tone (A→B), semitone (B→C), tone (C→D), tone (D→E), tone (E→F♯), semitone (F♯→G).

The F sharp was not an aesthetic choice. The formula demands a whole tone between the sixth and seventh degrees, and F natural would give only a semitone. Without that sharp, it is not a major scale.

Why F sharp and not G flat

G flat is the same key. And it would be the wrong spelling, for a mechanical reason: the scale already uses the letter G as its first degree. Repeating it would leave the scale with two Gs and no F, and the staff, which has exactly one line or space per letter, could not represent it.

The degrees have names

Each degree has a function, and a name that describes it:

| Degree | Name | What it does | | --- | --- | --- | | 1 | Tonic | The centre; where the music rests | | 2 | Supertonic | One step above the tonic | | 3 | Mediant | Halfway between 1 and 5; decides major or minor | | 4 | Subdominant | Pulls away from the centre | | 5 | Dominant | The greatest tension; pulls back | | 6 | Submediant | One step above the dominant | | 7 | Leading tone | A semitone from the tonic, and cannot stay still |

The leading tone is the most expressive degree of the scale, and the name explains why: it sits only a semitone from the tonic. Play B4 and the ear already knows that C5 comes next.

That semitone is the reason Western tonal music sounds the way it does. It is what makes a cadence sound like a conclusion rather than a stop.

What the scale determines

Given the scale, almost everything else is a consequence:

• the key signature of the key: which accidentals hold for the whole piece
• the diatonic field: the chords born from stacking thirds on each degree
• the spelling of any melody written in that key

CITonicDmiiSubdominantEmiiiTonicFIVSubdominantGVDominantAmviTonicBdimvii°Dominant

What to take from this

Tone, tone, semitone, tone, tone, tone, semitone, applied to any of the twelve notes. The formula generates the scale; the scale generates the spelling; the spelling generates the key signature. None of it is arbitrary convention: each step is deduced from the one before.