Sit at a piano, play the white keys from C up to the next C, and the run ends like a door clicking shut. Play the very same white keys from A to A and the mood turns wistful and unsettled. Same seven notes, different home. That difference is the whole story of the C major scale: it is the bright, resolved version of those keys, the sound that has taught generations of musicians what "home" feels like.
The notes of C major are C, D, E, F, G, A, B. On a keyboard they are all white keys. Its key signature (the set of sharps or flats written at the start of a piece of sheet music to tell you which notes to change) is empty: no sharps, no flats. That is why so many first piano pieces, school songs and theory lessons start here.
Each letter of the musical alphabet appears exactly once, in order. That is the rule for spelling any major scale, and in C it works out without a single sharp (#) or flat (b). Other keys need accidentals to keep the right distances between notes. C just happens to fit the white keys perfectly.
There is one curiosity worth knowing about, though you will almost never meet it. B# Ionian sounds exactly the same as C major, because B# is the same piano key as C. Written that way, though, it needs 12 sharps. Nobody writes music like that. If you ever see it in a theory book, smile and move on. C major is the sensible spelling.
A half step is the smallest distance in Western music, like moving from one piano key to the very next one, black or white. A whole step is two half steps. Every major scale follows the same pattern of steps: W - W - H - W - W - W - H.
Starting on C:
Look at a keyboard and you will see the two spots where white keys touch with no black key between them: E-F and B-C. Those are exactly where the pattern calls for half steps. Musicians often call this scale Ionian, its name as a mode, and it is the yardstick every other mode gets measured against.
Two notes give C major its particular personality. Theory names notes by their number in the scale, so these are the 4th (F) and the 7th (B).
B is the leading tone, sitting a half step below C. Sing up the scale and stop on B: you will feel an almost physical need to finish on C. That pull is what makes major-key endings sound so final.
F, the natural 4th, leans the other way, wanting to slip down a half step to E. Put F and B together and you get the tension in the G7 chord, which resolves so satisfyingly to C. Swap F for F# and you have left C major for a dreamier mode. That one note is the line between them.
Build a three-note chord (a triad) on each scale note, using only notes from the scale, and you get the family of chords in C major:
Capital Roman numerals mean major chords, lowercase mean minor, and the little circle means diminished, a tense, unstable sound.
Pop leans heavily on four of these. The Beatles' "Let It Be" sits in C major and builds its verses from C, G, Am and F, the I, V, vi and IV chords. Classical composers went everywhere with the key. Bach opened The Well-Tempered Clavier with the Prelude in C major, which is little more than flowing broken chords from this family, and Mozart's Piano Sonata in C major, K. 545, is a favourite of piano students for its clean, singing scale runs.
What those pieces teach: C major does not need decoration. Its strength is clarity. Try this progression slowly: C - Am - Dm7 - G7 - C. Listen to how Dm7 and G7 keep raising the tension and how C releases it.
Melodies in C major rest on C, E and G, the notes of the home chord. They feel like solid ground. D and A are good passing notes. F and B are the restless ones, and good melodies use that restlessness on purpose: hang on a B over a G chord and the ear begs for C.
Improvisers in jazz and pop often treat the scale the same way: wander freely, then land a strong beat on C, E or G. Singers can feel this too. End a phrase on B and it sounds like a question; end on C and it sounds like an answer.
Your root notes are on the low E string at frets 8 and 20, and on the A string at frets 3 and 15. The A-string 3rd fret is the friendliest starting point: play the scale up from there and notice that the half steps (E-F, B-C) fall one fret apart. Then shift to the 8th fret on the low E string and find the same notes in a new shape.
Something to try today: play or sing C, D, E, F, G, A, B slowly, and stop on B. Hold it for four beats, then take your time before letting it fall onto C. Do the same with F resolving to E. Those two small moves are C major's whole sense of arrival.
For the bigger picture, read The Major Scale (Ionian Mode).