Today when we want to look up anything 'factual', we go to Wikipedia. It's touted as a "Free Encyclopedia" where anyone is meant to be able to contribute, but the reality is totally different. It's really a castle full of gate-keepers, where the only information that ever gets out is the information that they deem worthy. It's a one-world view.
Sure, if you want to know about the size of an emperor butterfly's wings or the type of soil encountered in the rainforests of Brasil, you can get pretty much the right info. But go to the Wikipedia page on the 13th chord and all you will find is a mish-mash of gobbledygook. Go to the 'Talk' page and read the thwarted attempts by musicians to get some sense into this article.
The particular individual responsible for this particular instance of gate-keeping our musical information is called "Hyacinth":
This is the person responsible for providing information that is meant to be for the benefit of humankind in general. Did you read the 'talk' page? It might take a few readings to understand what's going on. But this page sums up Wickedpedia, because like our whole society, it's a total sham. And they've got the gall to ask for donations every year, as if they're some struggling operation.
It's got a lot to do with 'academics'. These 'contributors' are often doing their wiki-editing in their spare time for free, most probably connected in some way with a tertiary institution. That means they think they're smart. They most probably either studied, or maybe taught (OMG) at some university. But if you've happened to come across any 'degree holders' in your life, or, God forbid, had to deal face-to-face with these people, you'll know that academic qualifications don't mean shit nowadays. Have you noticed the way they rely on 'peer review' so much? Your peers are your competition - in everyday terms. So to say something has been 'peer-reviewed' just means it's been OK'd by the gang, the club. How cosy.
Well, after having bagged the Wiki gatekeepers, I'd better come up with the goods myself.
So, what is a good description of a 13th chord?
In a previous post, I outlined the basics:
https://classicjazzarranging.blogspot.com.au/2016/10/jazz-chords-9ths-and-13ths.html
So many songs, from the most basic to the most sophisticated, end with their final melodic resolution going from the 3rd to the tonic (e.g., E to C in the key of C). That melody note E is on a G7 chord, which makes it a 13th, heading for the C on the tonic C major chord, a V-I progression:
As I mentioned in my previous linked post, the 13th can be considered originally a suspension, an appoggiatura for the 5th (of G7, that is the D), which over time gradually became incorporated into the chord itself. It replaces the 5th. This to me is the most natural interpretation of the 13th in general practice.
But the important thing to realize, as I said previously, is that the 13th is the quintessential jazz chord. Not only in its most natural setting, but with different bass notes, the chord quality changes:
You will recognize this sound everywhere in jazz. Its characteristics are the minor 2nd (maj 7th) and the tritone (b5th).
Next up: Tatum fingerings for 13th chords