What are 6/9 chords, really?

Ok, so before we start... Nice.
This week, we are going to look at the infamous 6/9 chords. You might have heard of them, maybe even joked about them, but now, let's learn about them.
The 6/9 chords are used primarily for when you don't want to go for a major 7th, from reasons ranging from pure artistic choice to avoiding the dissonance created by the major 7th against the root of the chord. In order to solve the issue, musicians have been using the 6th or the 9th (which is also the second degree of the scale an octave above) of the chord, but together they enrich your progressions even more and can even help with voice leadings.

an Eb6/9 on piano
Constituting the chord is easy, it is 1-3-5-6-9; for example in a Eb6/9, the notes are Eb-G-Bb-C-F. It's that easy! And compared to the maj7 alternative, this will generally sound more resolved and jazzy.
Another good aspect of the 6/9 chords are their usefulness in quartal harmony. You can already see the perfect fourth gap between the 6th and 9th degree (continuing with the Eb6/9 example, this would be C and F). But if you go down another perfect fourth from the 6th degree, you actually arrive at the 3th degree of the chord (which is a G)! Is this a coincidence? We think not.
You can also use minor 6/9 chords to spice things up. They sound resolved and firm while still maintaining the jazzy feel.