The Alphabet

Notice the symmetries. Seconds are Sevenths reversed. Thirds vs Sixths & Fourths vs Fifths. Learn all the alphabets. The thirds will give you access to all chord theory. The fourths and fifths to progressions. The others to extensions.

A B C D E F G A B C D E F G A (Seconds)
A C E G B D F A C E G B D F A (Thirds)
A D G C F B E A D G C F B E A (Fourths
A E B F C G D A E B F C G A E (Fifths)
A F D B G E C A F D B G E C A (Sixths)
A G F E D C B A G F E D C B A (Sevenths)

(A small fix to the fifths row: after G it should continue D A E, giving A E B F C G D A E B F C G D A.)

The plain idea

Music uses only seven letters, A B C D E F G, and then starts again. Sharps and flats fill the gaps in between, but the letters themselves loop forever, like the days of the week. The “alphabets” above are that loop read with different step sizes: every letter (seconds), every other letter (thirds), every third letter (fourths), and so on. Practising them until you can recite each one forwards and backwards, quickly, is one of the most useful bits of mental groundwork a musician can do.

Why it matters

Most of music theory is counting along this loop:

Thirds build chords. Take any three consecutive letters from the thirds row: A C E is A minor, C E G is C major, G B D is G major. Four letters give seventh chords (C E G B), more give extensions (C E G B D = Cmaj9). See Triads.
Fourths and fifths drive chord progressions and the circle of fifths. Chords most often move by a fourth up (a fifth down): Dm to G to C is the ii–V–I of jazz, and it is three consecutive letters of the fourths row, D G C.
Seconds are scales and melodies, mostly stepwise.

The symmetries, explained

Each row is the reverse of another because the letters form a circle of seven. Going up a third (two steps) lands on the same letter as going down a sixth (five steps), since 2 + 5 = 7. Likewise seconds and sevenths (1 + 6 = 7), fourths and fifths (3 + 4 = 7). In the language of the groups page, the letters are the clock group $\mathbb{Z}_7$ , and stepping by $k$ forward is the same as stepping by $7 - k$ backward.

An everyday analogy: days of the week

If today is Monday, “three days later” and “four days earlier” are both Thursday. That’s exactly why the fourths row is the fifths row backwards. You already do this arithmetic every time you plan a week.

A worked example: building chords from the thirds row

Recite the thirds row from C: C E G B D F A C.

C E G → C major triad
C E G B → Cmaj7
D F A → Dm; D F A C → Dm7
G B D F → G7 (the dominant seventh)
B D F → B diminished

All seven diatonic chords of C major come straight out of one line of letters. Change the key and the letters gain sharps or flats, but the letter pattern stays the same. If you know G7 is G B D F, then G♭7 must be G♭ B♭ D♭ F♭ (spelled with F♭, not E), because the letters are fixed even when the accidentals change.

Common misconceptions

“There are twelve letter names.” Seven letters; the other five notes are sharps or flats of those letters.
“B♯ and E♯ don’t exist.” They do, as spellings (B♯ sounds like C), and correct spelling sometimes needs them.
“This is only for jazz players.” Anyone who wants to work out chords without a chart benefits.

How it connects

The truth revealed: seven letters on a circle, read with different strides, hold most of harmony in your head.