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: 
“**On** someone’s terms” means according to the “terms”—stipulations or provisions—which that person sets. “We do it on my terms” means “We do it my way.” “We bought it on his terms” means “We bought it at a price he set.”

“**In** someone’s terms” means using the “terms”—the language, the categories, the concepts—which that person uses. “In Kant’s terms, this is the ‘categorical imperative.’”

I find it difficult to imagine a natural situation in which musicians “produce in their own terms”, or anybody else’s—perhaps Beethoven, when he abandoned *allegro*, *andante*, *adagio* and other Italian words in favor of metronome markings, and started using *Hammerclavier* instead of *pianoforte*?
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*.

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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.*