Function

A function describes the relationship between a chord and a tonal center, all in the context of the harmonic progression.

Tonic function

stable chords of a key.
In major: I iii vi. They are stable because their triads (ex. C E G) all contain the key's third scale degree (ex. Here, all C E and G chords contain an E.
In minor: i ♭VI⁶ ♭III Has 3rd but no 4th

The third is the most important note for defining the scale's overall sound (modality)

bridge chords between other 2 functions. These chords take you away from home rather than lead back home.
In major: ii IV. How these chords feel changes depending on if we are using triads or 7th chords. The IV triad contains the root of the key, giving it a little more stability. Meanwhile, the ii lacks the root, making it sound more adrift. The 7th of that chord happens to be the tonic, giving it more stability
Has 4th but no 7th
Chord contains the tonic note of the mode (c)

Common melodic resolutions are 5 -> 1, 2 -> 1, 7 -> 1

In minor, the 4th is usually a iv⁷

unstable chords that provide tension and point back to tonic. Main engine that drives songs forward.
- it is unstable because of the characteristic leading tone
in the major scale, if we add a 7th it adds even more instability, thus making it have more gravity in wanting to point back to the tonic (ie. it makes the dominant function of the V scale even more dominant by making it a V⁷)
In major: V vii°. They both contain the 7th (leading tone) and 2nd degree of the scale. These notes circle around the tonic and want to collapse in toward it.
Has 7th but no 3rd
Doesn't really exist in minor, because there is no leading tone in minor, which dominant needs. Harmonic minor scale includes a leading tone, which effectively brings back the leading tone (and by extension the dominant resolution).
- this is only partially true, because the V chord can still create tension to make us want to return to a i. It all depends on context really.

Playing the V keeps the music from resolving

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Tonic function