Is there a word for the 'pitter patter' of speech?
I think you are looking for cadence -
Cadence noun
the way a person's voice changes by gently rising and falling while he or she is speaking
If you are referring to a particularly low sound, then perhaps murmur is a better fit -
Murmur noun
a low indistinct but often continuous sound
I think the word you are looking for is prosody
In phonology: collectively; the patterns of stress and intonation in a language.
If you're asking for the term describing the characteristic of speech that allow you to discern its context without an understanding of the language itself, I would suggest:
Intonation
In linguistics, intonation is the variation of spoken pitch that is not used to distinguish words; instead it is used for a range of functions such as indicating the attitudes and emotions of the speaker.
I think Elliot's "cadence" is part of the sports announcer's formula, though these other definitions of "cadence" seem more fitting for what the OP describes as "pitter, patter":
Balanced, rhythmic flow, as of poetry or oratory.
The measure or beat of movement, as in dancing or marching.
Additionally, the characteristic "staccato" speech pattern, a la Howard Cosell, which has been much imitated, is unmistakable. We watch World Soccer and foreign boxing matches at home and though I don't understand the language, the combination of staccato speech pattern and cadence make it clear that you're listening to a sporting event.
Staccato:
- with each sound or note sharply detached or separated from the others.
There is susurration. A background whispering noise.