This expression refers to when you're hyper, psyched, nervous, excited, revved up, buzzing, or in high gear... You can choose how to visualize it, according to the situation.
E va be', mi è successo di tutto. -No, perché sembri un po' su di giri, ecco.
Well OK, a lot happened to me. -No, because you seem a little revved up, that's it.
Captions 19-20, La Ladra EP. 10 - Un ignobile ricatto - Part 8
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In the previous example, we can see from the context (if we watch the video), that the person who is revved up is revved up in a good way. Eva (the one su di giri) had just had a romantic encounter with Dante and she was on cloud nine, but also very excited.
But in this next example, Nicola is talking about what he has to do in his job as a cop. He often has to visit homes where couples or family members are fighting. The expression is the same, but its nature is different.
Certo, entrare il quel momento dentro casa di queste persone, voi capie'... voi capite che, eh... gli umori sono abbastanza a terra, la rabbia è su di giri
Of course, entering at that moment into the home of these people, you understand... you understand that moods are way low, anger is wound up,
Captions 36-38, Nicola Agliastro Poliziotto
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In this next example, Manrico wants to seduce a woman, and thinks of "getting her going" with a drink.
Cocktailino [sic] per mandarla su di giri, eh? Cenetta, vino rosso...
Little cocktail to get her revved up, huh? Little dinner, red wine...
Captions 64-65, Sposami EP 5 - Part 16
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Now that we have seen a few practical examples of this little expression, let's unpack it.
We're including the verb essere (to be) in the expression, but often it's not included, or another verb is used, such as mandare (to send) as in one of the examples above.
Then we have su which is a preposition meaning "on" but it's also an adverb meaning "upwards" or "up" and that is how it is used here, and often refers to one's mood or state.
Di is a preposition meaning, primarily, "of."
Then we get to the important word: giri. It's the plural of giro, which is a rotation, or, in a mechanical sense, a revolution. That's where "revved up" comes from. More revolutions in less time!
On a car, the tachometer is called il contagiri (the tachometer or rev counter). To keep with the meaning of giri, we have used "revved up" as the translation. But there are so many other ways to interpret the expression, and this "motor" reference might not be appropriate in many situations!
Sometimes, su di giri describes one's heart beating fast (for whatever reason). Sometimes it's about not being able to stop talking, pacing, or tapping one's foot or pencil. It can be about not being able to calm down.
It might be a reason too skip that second cup of coffee.
No, grazie, sono un po' su di giri (no thanks, I'm already a bit wound up).
Are you old enough to remember hit singles? In other words, 45 rpms. This means 45 revolutions per minute on a turntable or record player, as we used to call it. In Italian, it's 45 giri.
Il quarantacinque giri più venduto di Italia è "In ginocchio da te" di Gianni Morandi.
The forty-five that sold the most copies in Italy is "On my Knees Before You" by Gianni Morandi.
Caption 57, L'Eredità -Quiz TV La sfida dei sei. Puntata 2 - Part 8
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The noun giro is a favorite of Italians and can mean so many things. See this lesson for some examples. If you do a search of the noun giro and its plural giri, and diminutives such as un giretto, you will get a sense of the variety of nuances connected to this word. And let's not forget the phrasal adverb in giro which has its own collection of nuances.
We'll also mention the verb girare (to turn, to go around). The verb, too, has a great many meanings and nuances, so check it out.