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The phrase "another set of variations" is correct and usable in written English.
It can be used when referring to an additional group or collection of different forms or versions of something.
Example: "In this study, we will explore another set of variations on the original theme to see how they impact the overall outcome."
Alternatives: "an additional group of variations" or "a different collection of variations".
Exact(2)
The Arietta, yet another set of variations, goes from gentle lyricism to delirious premonitions of ragtime: visionary music, handled by Mr. Schiff with exquisite sensitivity.
The idea was evidently to avoid illustrating the Rzewski work's similarities to another set of variations — that ground has been well trod — and instead to use the juxtaposition with Bach to tease out other musical aspects.
Similar(58)
Among them were the piano cycles Papillons and Carnaval (composed 1833 35) and the Études symphoniques (1834 37; Symphonic Studies), another work consisting of a set of variations.
But the real glory of the book, for me, are the pieces that miraculously seem to have it both ways: Donald Antrim's manic (in every sense) four-way romantic farce, "Another Manhattan"; Denis Johnson's laconic set of variations on the idea of confusions and mistakes, "The Largesse of the Sea Maiden"; perhaps a half-dozen others.
The endless tea party is like a set of variations on another childhood drawing, this one showing a man staring fixedly at a clock – the joke being that a clock in a picture always looks as if it has stopped.
These stories feel as though they had been written fast, one after another, expressing with some urgency a closely related set of variations on a given theme.
A half-dozen skillfully interwoven subplots create a set of variations on the theme of divided sensibilities tugging one another into states of perpetual unrest and possible happiness.
If somebody would write a set of variations that had ten variations in it, he would write a set of variations with twenty variations in it.
And they gave a vital account of the playful set of variations that end the work.
Unhappy families have their dominant themes, but each member has a particular set of variations.
"Beethoven did an incredible set of variations on that dumb Diabelli waltz.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com