A chord, by definition, is three or more notes played at the same time, usually belonging to a common key. All the chords in a chord family will sound good together because all the notes in them belong to the same scale. Today we'll look at the chords in the C major family, just for the convinience of no sharps or flats, but you can apply this to any other key.
The C major scale consists of the notes CDEFGAB. An important concept for this is knowing the intervals between each note of the scale. I will write the intervals out, using ".5" meaning a half step away, and "1" meaning a whole step.
C 1 D 1 E .5 F 1 G 1 A 1 B .5 C.
Throughout this lesson you might want to refer to this outline.
Many guitarists even the most advanced, simply memorize the chords in a family, without really knowing why some are minor, and some major, or whatever, and I didn't really understand this, until my guitar teacher taught me about scales and modes.
Along with the chord, I tried to add its corresponding mode.
The basic chord consists of the 1, 3, and 5. There are two main types of chords/scales, major and minor. For any scale/chord to clasify as a major, it must have the major 3rd (1 whole step from the second), and to be minor it must have a minor 3rd (.5 step from the second). So for the C major scale, ionian, the notes are C, E, G. This is major because the E is C's major third. If you want to add a little more flavor to the chord, you could use some embellishments such as 7 chords. This would mean you add the 7th note of the scale which is B. C major 7 would therefore contain CEGB.
The second chord is D minor, dorian, (DFA). If you look above where it has all the notes, and start from D, you'll notice its 3rd is F (a minor third away) and A is the perfect 5th. If you were to play a D 7 chord, it would b D minor 7, because C is the 7th note in the sequence, and is a whole step bellow D.
The third chord is E minor, phrygian, (containing the notes EGB). Just like D, the embellished 7 will be a minor 7 because D is a whole step bellow E. However, in C major, the note after E is F, which is only a half step above. Therefore, if you wanted to have an add 9 chord (which is where you add the second in the scale) you would make the usual E 9, and flatten the F# making it an F.
Next is F major, lydian, (FAC). Just like C, the embellished 7 is the major 7 making it (FACE).
G major, mixolydian (GBD) is the fifth chord in the C family. However, if you notice, the 7th is F, which is a minor 7th. This makes it slightly weird that it is a major scale, but the embellished 7 is minor. The name for this is G Dominant 7.
A minor, aeolian, is the penultimate chord (ACE). The aeolian mode is also the natural minor scale. The embellished 7 is A minor 7 (ACEG).
The final chord in the C major family is B b3 b5 (BDF), witht he corresponding Locrain mode. This chord has a lot of dissonance, without having a perfect 5th in it. This chord is minor, because of the minor 3rd. The 7th embellishment is the added minor 7 (BDFA)
Before I conclude the lesson, I just want to say that these are the chord families, but that doesn't mean that a song in the key of C major has to be restricted to only these chords, and others that only contain notes of the major scale. There are many deviations in all music, especially when it comes to the Locrain chord, as its sound is a bit to cacaphonic for most generes of music. A perfect example of where the Locrain chord isn't followed exactly is Greenday's "Wake Me Up When September Ends". This is in the key of G major, so its 7th is Gb. However instead of the progression being:
C Cm G Gb
Wake me up, when september ends
The Gb major chord used at the end of the chorus contains notes outside the G major scale (Bb, C#). The progression also includes a Cm chord, which also deviates from the family, further illustrating my point. To make a long story short, knowing the chord family is very useful in music, but don't take it for some sort of mandatory musical boundry that can not be deviated from.