"compose a note" is correct and usable in written English.
You can use it when you want to direct someone to write a brief message. For example, "Please compose a note saying that you will be arriving late to the meeting."
I've known novelists for whom the prospect of composing a note asking that a son or daughter be excused from gym that day can bring on a serious case of writer's block.
But without Saint-Saëns Saint-Saënsment, Fauré might never have composed a note; nor might he have won the post in which he taught Ravel, who in turn never failed to credit the vital nature of his influence and support.
If you find yourself wishing for a little more room to move when in the middle of composing a note, click the small arrow icon in the header area of a newly created message to open it in its own, smaller window.
On 28 September, Edvard Beneš composed a note to the Polish administration offering to reopen the debate surrounding the territorial demarcation in Těšínsko in the interest of mutual relations, but he delayed in sending it in hopes of good news from London and Paris, which came only in a limited form.
Barenboim likes to say that Wagner did not compose a single note that is anti-Semitic.
He got a pencil and tried to compose a suicide note, but he didn't know what he should say.
You boot up the app, compose a brief note, and select a recipient, and then a nearby stranger will be recruited to deliver it.
"If Beethoven were alive today, he wouldn't compose a single note, because the people would give him so many sponsorships, corporate gifts, and honorary doctorates".
Today I sat down to compose a "thank you" note to the couple who hosted the event.
