And which is utilized when turning this...
The monkey is fat.
...into a question:
The monkey is fat?
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Intonation would be the most fitting:
Not to be confused with inflection [...]
In linguistics, intonation is variation of pitch while speaking which is not used to distinguish words. It contrasts with tone, in which pitch variation does distinguish words.
So when your voice rises at the end of a question, that is technically called intonation.
Inflection has two meanings: it can sometimes mean intonation, as Dictionary.com shows:
modulation of the voice; change in pitch or tone of voice.
However, Wikipedia defines it exclusively as the form of a word, and not the sound:
[I]nflection ... is the modification of a word to express different grammatical categories such as tense, grammatical mood, grammatical voice, aspect, person, number, gender and case. Conjugation is the inflection of verbs; declension is the inflection of nouns, adjectives and pronouns.
Since inflection is ambiguous and not the correct technical linguistics term, it would be better to use intonation, so everyone can understand what you're talking about.
Inflection can mean ‘modulation of the voice; in speaking or singing: a change in the pitch or tone of the voice’ (OED). However, linguistically an inflection is a word ending that indicates the role of the word in a sentence, so it’s best to avoid using it in the other sense when talking about language. Intonation is the contrastive use of pitch in speech. The word used to describe the linguistic use of pitch, loudness, tempo and rhythm is prosody.