TL;DR - I want my angelic race to have the ability to speak in a way in which up to three sentences are communicated at the same time. (Assume English for the sake of simplicity. I want physiology answers, not conlang answers, as evidenced by the question on whole and my tags.)
In my story, angels have the ability to express 3 sentences at the same time. If I were to write this out, it'd be a matter of [Main sentence], [Supertext], and [Subtext] all being in line with one another (like furigana in Japanese in terms of writing, but I know that's not how it works when spoken). These three sentences would be restricted to the same topic, but might be along different expressed ideas with the Main Sentence being the critical information and the Supertext/Subtext adding details to the sentence. For example:
The dog has brown fur.
The dog ran away.
The dog was barking.
In English, we'd simply say "The brown dog ran away while barking."
(And because I know somebody would ask "Why not just use English then?") Alternatively, using a more "high school" example:
Did you see what she was wearing?!
Jenny is such a b-.
She's totally sleeping with Mr. Caulton.
In this example, the person would be expressing three sentences all about how much they dislike "Jenny", but the three thoughts aren't all describing Jenny directly. Aside from making a paragraph saying these things (or a LONG compound sentence), English doesn't really have a way of properly expressing this. In the angelic tongue, this would be nicely condensed, though.
Now, I know asking for details on writing the language would more be a matter for the Conlang SE (maybe), but what I am curious about is this: What would be necessary for not only an angel to say these three sentences at once, but for somebody to be capable of understanding them clearly?
MAKING IT A SINGLE QUESTION: What would be the necessary requirements for this kind of speech to be communicated effectively?
I'll accept whichever answer is the simplest, but most effective. My current process involves manipulation of polyphonic vocalization, but I feel like there has to be a better way. I want my angels to still pass for being aesthetically human. They can't be distinctly alien in appearance to make this work. It needs to be up to 3 separate sentences spoken at the same time, but needs to also allow for only one or only two sentences as well. (Meaning, just because they can speak three sentences at once, that doesn't mean they are physically required to. It should be something they can control.)
To answer questions: - I need it to be a single mouth if at all possible. If there HAVE to be multiple mouths, I could always give the angels an inherent glamour effect, but would prefer to minimize the amount of magic used to keep them looking human. - The voices can be somewhat differently pitched, but preferably not in a way where one sounds like Crocodile Dundy and the other like Mickey Mouse (and the third like it's coming straight from the depths of hell). I'd prefer if they were all "normal" voices, even if one is higher pitched and another lower.