Me again, purple dolphin
I dashed off my first reply in a hurry whilst the bath was running. I need to explain in more detail.
There are 3 things you need to consider:
1) Plagiarism
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This means using someone else's work and passing it off as your own. Examiners are dead against it. They will disqualify you when they discover it if you submit your composition for an exam.
So:
"Study in Bb, composed by Mad Clarinettist Purple Dolphin" would get you disqualified.
"Study in Bb by Minor 19th Century Composer Heinrich Baermann, with Superb Piano Accompaniment composed by Rising Star of the Decade and Mad Clarinettist, Purple Dolphin" would be accepted because you are attributing the original work by Baemann.
2) The syllabus
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This is the bit you need to check with your teacher. I suggest you do it soon, pd, so you avoid spending weeks working at something you end up not being able to submit.
If the syllabus demands an 'original composition' then you need to be sure that adding to an existing work counts as 'original'.
If the syllabus demands an arrangement, then you need to know that adding an original piano accompaniment to an existing work counts as an arrangement.
If in doubt, your teacher will contact the examiner for a ruling.
3) Copyright
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You are definitely
not infringing the copyright of the composer or his descendents. I don't even know if early 19th century compsers had copyright. Any such has definitely expired nearly 200 years later!
There might be a copyright issue with copying the clarinet part from a volume of music that itself is subject to copyright laws. This is the bit I am going to check out for you, unless someone comes up with a definitive answer in the meantime. I will get back to you as soon as I can.
Steve