Question: As far as I know, it is valid to say "they can produce music ***on*** their own terms" when you want to say that a group can produce music without having to answer to anybody but themselves. 

Is it also valid to say "they can produce music ***in*** their own terms"? Does this convey the same thing? If not, what does it really mean?

Answer: 
The "standard" idiomatic meaning of [on one's own terms](http://www.merriam-webster.com/dictionary/term) is *in accordance with one's wishes : in one's own way*. In that link, Merriam-Webster's example is *he prefers to live on his own terms*.

*"In one's own terms"* isn't such an established idiom, but it's [certainly not uncommon](https://www.google.co.uk/search?q=%22in%20their%20own%20terms%22&btnG=Search%20Books&tbm=bks&tbo=1#q=%22in%20their%20own%20terms%22&hl=en&tbo=1&tbm=bks&ei=XrmRUJf_HfS20QWG0YHgDQ&start=10&sa=N&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=1301a46b09d10054&bpcl=36601534&biw=1302&bih=870). There's a degree of semantic overlap anyway, but it seems to me about half the instances linked to there basically have the above meaning. The rest have the more literal sense we normally see rendered as *"In one's own **words**"* (using the words and phrasings one is most familiar with).

My advice would be to stick to *"**on** your own **terms**"* when you mean something akin to ***done in line with** the terms and conditions you have decided upon*, and use *"**in** your own **words**"* for the sense of ***described using** your own natural language*.

---

In short, *"they can produce music **on** their own terms"* would normally mean they make music the way they want, but *"they can produce music **in** their own terms"* could easily be taken to mean *they make what **they** call music, but other people might just call it noise.*
They indeed seem to have (re-)created music ***in*** their own terms as Bruce Eder writes in the Bee Gees [biography](http://www.allmusic.com/artist/bee-gees-mn0000043714). 

> 
> *Saturday Night Fever*, as an album and a film, supercharged the phenomenon and broadened its audience by tens of millions, with the Bee Gees at the forefront of the music.
> 
> 
> It was a profound moment although, ironically, there wasn't that much difference in their sound. Amid the dance numbers, the Bee Gees still did a healthy portion of romantic ballads that each offered memorable hooks. They'd simply decided, at Arif Mardin's urging, to forget the fact that they were white Englishmen and **plunged into soul music, emulating, in their own terms, the funkier Philadelphia soul sounds** that all three brothers knew and loved. In one fell swoop, the group had managed to meld every influence they'd ever embraced, from the Mills Brothers and the Beatles to early-'70s soul, into something of their own that was virtually irresistible. Spirits Having Flown was their crowning commercial triumph, topping 30 million in sales and yielding three more number one singles. 
> 
> 
> 

[emphasis mine] 

*Terms* here seems to refer not to 'conditions', but literary terms, such as characteristic words and phrases, as the Bee Gees generally used. Did they create music using soul sounds and their usual kind of lyrics? It seems so.