How to build a chord

Chords can be built with three notes called the triads or with four notes called a tetrachord. Normally the chords are built in stacks of intervals of a third, either major or minor (there are of course chords built with other intervals but for now lets simplify).

Starting on the C note if we go up a major third to the note E we get a dyad of a major third (it's debatable if dyads are chords or not), if we go another third from that note E we get a G and this new dyad is a minor third, so now we have a chord with the notes C E G, because the first interval is made up of a major third this chord is a major chord and because the first note is a C we call this chord a C major. If we follow the same procedure but starting on the note D we will get the first interval a minor third, from D to the note F, then we do another interval of a third from that last note F and we get an A from the note F to the note A we get a major third interval, so because the first interval of a third is minor this chord will be minor, and because the first note is a D this chord is called a D minor chord.

Just follow this line of thought for the all the notes in the C major scale and you will get all the chords one can use in that tonality. In terms of triads the only chord that will be different from all the others will be the B chord, because from B to D is a minor third and from D to F is also a minor third, so this chord besides having a minor dyad on the first interval it also has a minor interval on the second dyad making it's fifth a diminished one, so this chord is then called a diminished chord and because the first note is a B we call it a B dim chord.

The Triadic chords go then as such:

C Dm Em F G Am Bo

A lower case m for the minors, a circle for the diminished and simply the name of the chord for the major ones.

Now adding the seventh of each chord we get on the C major chord another major third interval, from G which was the top note on C E G to the note B, making it a major seventh chord, note that the B is a half step from the next C on the next octave. So we'll get C E G B. And in this case besides calling it a C and calling it major we have to add the information that it has a major seventh. We have three possible notation to convey this information, by putting a delta symbol ∆ plus the number seven C∆7, we can put a upper case M with a seven next to it CM7 or finally just write maj with the seven next to it Cmaj7.

If we do has such for the Dm chord we will get an extra minor seventh since the upper third interval is a minor one from A to the note C. So the chord goes has such D F A C and we can notate it like Dm7 or Dmin7 or we can simply put a minus sign with a seven next to it D-7.

There are two chord that get a different structure from the other chords on the C major scale, the G chord and the B chord. The G chord gets an extra minor third interval on the top, from D to the F note, we then get a major third plus a minor third plus another minor third, or has a formula 3M+3m+3m, this formula is different from all the other chords, the major chords formula is 3M+3m+3M or has I like to call it a "3m sandwich" and the minor chords formula is 3m+3M+3m, so the inverse of the major one and so a "3M sandwich", note that the G chord with a seventh gets a 3M+3m+3m formula. This G chord is called a seventh chord or dominant chord and the notation is simply adding a seven next to the name of the chord, so G7.

The B chord triad has we have seen is notated as Bdim or Bo, called a B diminished triad, has we add the seventh we get a minor triad has the last dyad, from the F to the A note, B D F A, so the formula will be 3m+3m+3M, the inverse of the G7 formula, this B chord is then called the half-diminished chord and the notation can be written has a B minor triad with the number seven next to it and a flatted fifth Bm7b5 this way all the information is conveyed on the notation, or we can notate it with the greek symbol for emptyset Ø, so we get BØ7.

The whole of the seventh chords on the C major scale are:

Cmaj7 Dm7 Em7 Fmaj7 G7 Am7 Bm7b5

Cmaj7 - 1 3 5 7 or 3M+3m+3M

Dm7 - 1 b3 5 b7 or 3m+3M+3m

Em7 - 1 b3 5 b7 or 3m+3M+3m

Fmaj7 - 1 3 5 7 or 3M+3m+3M

G7 - 1 3 5 b7 or 3M+3m+3m

Am7 - 1 b3 5 b7 or 3m+3M+3m

BØ7 - 1 b3 b5 b7 or 3m+3m+3M