The phrase "a note of despair" is correct and usable in written English.
It can be used to convey a feeling or sentiment of hopelessness or sadness in a particular context.
Example: "Her voice carried a note of despair as she recounted the events of that tragic day."
Alternatives: "a hint of hopelessness" or "a touch of sadness."
I detect a note of despair in his second sentence.
He concluded on a note of despair: "Advice for beginning journalists: pick a new profession".
Again and again, there is evident in his writings a note of despair.
Stoppard ends his monumental play in 1868, on a note of despair and futility and impending disaster.
Chace, the author of a previous novel, "Capture the Flag," and a memoir, "Chautauqua Summer," opens "Leaving Rock Harbor" on a note of despair.
David Baltimore, a Nobel-winning biologist, sounded a note of despair in an address to the American Association for the Advancement of Science in February.
After the show, which concludes on a note of nihilistic despair, groups of banker-ish young men were pausing to take grinning selfies in front of the theatre's marquee.
While it's an open question to what degree his words echo the filmmaker's concerns about the Zionist project, they end this dour little film on a note of howling despair.
From the first, valedictory line: "Today is my last day at Goldman Sachs", to the touchingly clumsy language – "The culture was the secret sauce" – to the faintly bizarre references to our hero's youthful sporting and academic triumphs (including a bronze medal in a table tennis tournament), the letter carries a note of authentic despair.
Whatever his source of value in Regine's eyes, the jilted nineteen-year-old, in the words of the jilter, "fought like a lioness" to keep him, breaching decorum by invading his rooms upon receipt of his letter and, in his absence, leaving a "note of utter despair" that pleaded with him, for the sake of Jesus and the memory of his father, not to leave her.
My friend the climate blogger Joe Romm, a great optimist, leaked a similar note of despair when he testified to Congress about climate change in July.
