The name gives it away: seventh chords must have some kind of seventh in them. Indeed, they are triads bringing their plus-one. Here are some examples with root $G$:
X:1 L:1/4 K: C "GΔ"[GBd^f] | "Gm7"[G_Bdf] | "G7"[GBdf] | "Go7"[G_B_d_f] | "Gø"[G_B_df] ||
The first of these examples, the $G^\triangle$ is a G major 7. In this
chord symbol, $G$ signifies that the base triad is G major, and the
$\triangle$ specifies the character of the seventh -- this one is a
major seventh, as opposed to a minor seventh. Read
1-intervals{.interpreted-text role="doc"} first if you don't know
what this means. Here are three examples of major seventh chords:
$$\begin{aligned} G^\triangle &= \left\{ \underbrace{g, b, d}_{G \text{ major triad}} +\quad \underbrace{f\sharp}_{\text{major seventh}} \right\}\\ D^\triangle &= \left\{ \underbrace{d, f\sharp, a}_{D \text{ major triad}} +\quad \underbrace{c\sharp}_{\text{major seventh}} \right\}\\ B\flat^\triangle &= \left\{ \underbrace{b\flat, d, f}_{B\flat \text{ major triad}} +\quad \underbrace{a}_{\text{major seventh}} \right\}\\ \end{aligned}$$
The same principle applies to the other seventh chords. A $\minor7$-chord is made up out of a minor triad and a minor seventh.
$$\begin{aligned} G\minor7 &= \left\{ \underbrace{g, b\flat, d}_{G \text{ minor triad}} +\quad \underbrace{f}_{\text{minor seventh}}\right\}\\ D\minor7 &= \left\{ \underbrace{d, f, a}_{D \text{ minor triad}} +\quad \underbrace{c}_{\text{minor seventh}}\right\}\\ B\flat\minor7 &= \left\{ \underbrace{b\flat, d\flat, f}_{B\flat\text{ minor triad}} +\quad \underbrace{a\flat}_{\text{minor seventh}}\right\} \end{aligned}$$
Here are some examples of $7$-chords, known as dominant chords for reasons that will become clear in the next post about chord progressions.
$$\begin{aligned} G7 &= \left\{ \underbrace{g, b, d}_{G \text{ major triad}} +\quad \underbrace{f}_{\text{minor seventh}}\right\}\\ D7 &= \left\{ \underbrace{d, f\sharp, a}_{D \text{ major triad}} +\quad \underbrace{c}_{\text{minor seventh}}\right\}\\ B\flat7 &= \left\{ \underbrace{b\flat, d, f}_{B\flat\text{ major triad}} +\quad \underbrace{a\flat}_{\text{minor seventh}}\right\} \end{aligned}$$
You should be able to assemble the other seventh chords yourself, based on the information in this table:
| Name | Notation example | Base triad type | Seventh type |
|---|---|---|---|
| Major seventh | $C^\triangle$ | Major | Major |
| Dominant | $C7$ | Major | Minor |
| Minor seventh | $C\minor7$ | Minor | Minor |
| Minor major | $C_\minor^\triangle$ | Minor | Major |
| Diminished | $C^o$ | Diminished | Diminished (enharmonically equivalent to $M6$) |
| Half-diminished | $C\text{\o}$ | Diminished | Minor |
And this decision tree may help you structure the various types of seventh chords into categories in your mind. You start at the top and observe every interval in the chord to decide which chord you're looking at.
Of course, all these chords don't exist in a vacuum. There are ways in which some chords create expectations for other chords to come after. This is what the next part about chord progressions will be about.