Chords

A chord (in a tertian harmonic sense; ie. harmony built on thirds) must have all of its notes a third apart (either minor or major)

this rule holds true for extended chords (e.g. 9th, 11th chords), since the 9th is a minor third above the 7th,

chords are often augmented with "tensions". A tension is an additional chord member that creates a relatively dissonant interval in relation to the bass.

Harmonization usually sounds pleasant to the ear when there is a balance between consonance and dissonance. Simply put, this occurs when there is a balance between "tense" and "relaxed" moments.
A misplayed note or any sound that is judged to detract from the whole composition can be described as disharmonious rather than dissonant.

Think of a chord as a harmonic structure that supports melody

chords are built from scales

Chords are composed across instruments. You can be standing next to two guitarists and a keyboardist who think they're playing a C major chord and if I choose to play an A, screw that, they're playing Am7.

Fifth

The fifth in the traditional triad acts more of a stabiliser to the chord, and serves less of a function when compared to the root and the third (giving identity and tonality respectively). The fifth is often the first omitted in the pursue of adding colour tones to a chord - such a voicing is known as a shell voicing. It also has implications for production, a redundant note takes up valuable bandwidth in the limited frequency. Incorporating the fifth, potentially doubling up on notes that aren't going to add colour to a chord will muddy a mix.

this is due to the face that most instruments carry a prominent fifth in their overtones

Often, another instrument will play the fifth anyway during some point during the chord's life (e.g. a passing bass note)

On the other hand, styles of rock music utilise the fifth and omit the third in the tonally ambiguous power chord (a borrowing from the modal jazz tradition). Because the fifth interval with the root is so consonant, it can be subject to mass amounts of distortion with much breakup. As rock incorporated more and more distortion in its practice, power chords became evermore useful because of these properties.

There are rare instances where omitting the fifth can make harmony ambiguous. Especially if you are establishing the key of the piece or changing keys. For example, if you are in the key of a minor, and you want to shift over to C major, you will more than likely need the fifth to establish that a c-e triad is not just the upper half of an a-minor chord.

Augmented

Augmented chords can be used as a substitute for a dominant chord.

Augmented can be used to increase the tension of the V chord, before bringing it back to the tonic, creating an even bigger resolution.

Examples:

Oh! Darling - Beatles (opening chord)

If you take a minor triad and augment the 5th you wind up with a major triad of the augmented note

ex. Gm with an augmented 5th yields an E♭ major chord.

Add chords

An add chord simply adds the scale degree to the chord

ex. a C6 chord is a Cmajor with the 6th

add chords notably don't remove the 3rd, making add2 and add4 chords distinct from sus2 / sus4

Try arpeggiated add♯4 and let the bass drive the progression.

Lydian

Try arpeggiated addb2 and let the bass drive the progression.

Phrygian

Extension chords (compound intervals)

ex. 9th, 11th, 13th They are called compound because they are greater than one octave

Compound chords are normally played with the 7th.

this is the principal difference between an add2 chord and a 9th chord

Augmented 5th (aka minor 6th)

Arpeggiated, provides a mysterious vibe

Slash chords (e.g. `C/E`)

A slash chord denotes which note should be played in the most bass register

ex. if we have a C/E chord, we should play a C major chord with notes E/G/C.

If the slash chord contains a note not found in the chord (e.g. C/B, since B is not part of C major), then we have to reconstruct the chord. In this case, a C/B chord is a Cmaj7 chord with B in the lowest register.

The Four Chords (I-V-vi-IV)

They work well together because they offer a lot of space to work with. They are fairly neutral sounding, and therefore a lot of melodies can work with them.

Children