You could use the Arcane Talent feat to learn spark, a 0-level spell with the [fire] descriptor. The wording of the feat should satisfy the necessary requirements:
Choose a 0-level spell from the sorcerer/wizard spell list. You can cast this spell three times per day as a spell-like ability.
The Paizo FAQ clarifies that spell-like abilities count as being able to cast that specific spell for prerequisites, and (right underneath the previous question) by default will count as arcane spells from the sorc/wizard list.
You should probably also consider the Pyromaniac alternate racial trait, since it augments fire spells, but sadly it doesn't grant any arcane casting that would qualify you for the Fire Music feat.
That said, I'm not really sure why the feat requires the spell be arcane, so it might be worth discussing options with your DM.