I was thinking of picking up the tenor sax as my second instrument, has anyone got any advice or tips?

I'm not too sure about it but as I'm highly influenced in Jazz, Blues, Funk and Soul I thought it may be a good idea.

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Classical instruments like the sax, trumpet, clarinet, etc., are very expensive. I would rent one for a while to see if you do like it, or take lessons for it. I would recommend not just getting one and learning to play it on your own like many people do with guitar.

Paying saxophone, and other like instruments, is much more fun when playing in a band setting. With guitar you have 6 strings so you can play off of yourself, but with sax you only have 1 string, metaphorically.

Also, you are going to sound like shite when you first start playing for the first few months. Playing reed instruments is a task in itself; there isn't a kinda right, or kind of wrong, you either make sound or you don't. I played trumpet in school band for 5 years, and jazz for 2, so I would like to think I know what I'm talking about.

Regardless, good luck!
This post may contain my opinion and/or inaccurate information.

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A tenor sax in the right hands is awesome. But there is no way that without a good teacher it'll be that great.
My advice get a slightly better than the cheapest Sax, though as the above poster said they are expensive, and find a really good teacher specifically for JAZZ. A classical teacher will make you almost incapable of being able to play jazz properly, even some of the basics are different accord in to my friend who is a saxophonist of 9 years.
And they are perfectly possible to play by yourself, just get a real book and some backing tracks and your set, in terms of playing around by yourself.
I would recommend looking into a copy of westphal's guide to teaching woodiwnds, the section on Saxophone is really good. There's another book I own that is great for sax, but the name is escaping me at the moment, I'll edit it in when I remember.

Start by renting an alto saxophone. It's lighter, can be cheaper, and is a better instrument to learn on. If you start on a tenor saxophone you'll get used to having less flexibility in your intonation, and that's not a great habit to build up from the start. If you have the freedom to, I would recommend lessons, at least a few to get you started. I'm assuming that you come from no background in fixed reed instruments, so a teacher to get you comfortable in the playing techniques, embouchure, and air column that are necessary on sax would not be a bad choice.
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Would agree with what everyone here says regarding alto, renting and lessons. Would also say not to get too downhearted when you start off learning Three Blind Mice and the like. Once you start learning what you want to learn it's hella fun!