Such as generating a spoken sentence or series of sentences in a particular person's voice?
[RPG] Can Minor Illusion be used to simulate speech
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The fun way to do this, as well as the obvious interpretation of the rules, would be to have them imitate phrases perfectly, sounding like the original speaker, but using them in approximately the sense they originally heard them. So their voices can change completely from sentence to sentence - one being a dwarf they heard speaking yesterday, the next sentence being a small elf child they heard ten years ago, and the third being something you said to them three months ago.
They understand what phrases and sentences mean, but if they can't break down phrases into words and use the words individually, they're still fairly limited by their curse. They would sound a bit like Dilbert's pointy-haired boss, who tends to come out with phrases and clichés that belong in a subtly different conversation.
This would be an interesting challenge for a player who was usually verbally adroit. Precedents for even more extreme versions exist in the Librarian from Terry Pratchett's Discworld series who manages to get by with just one word, "Oook", and Mr Punch in the classic Punch & Judy show, most of whose lines are "That's the way to do it!"
The main problem with playing a Kenku this way would be avoiding humour in serious moments of the game.
You are not restricted to an origin point.
Compare the wording of the Minor Illusion cantrip to the Thaumaturgy cantrip:
Minor Illusion: You create a sound or an image of an object within range that lasts for the duration.
Thaumaturgy: You create an instantaneous sound that originates from a point of your choice within range, such as a rumble of thunder, the cry of a raven, or ominous whispers.
While minor illusion goes into great detail specifying that a visual illusion cannot permeate the full 30ft radius, there is no RAW limitations on the sound's location or lack thereof while in the range.
You cannot, however, have multiple sources of sound. An illusion is limited to a single object unless otherwise specified. You may create a complex chain of discrete sounds as part of the illusion, but it's still one audio illusion.
Lastly, minor illusion's source cannot be moved. Jeremy Crawford has repeatedly confirmed that minor illusion cannot move. He states that illusion spells that were meant to move (mislead, major image) will specify that you can move the spell.
Of course, this is all limitations on the spell. You can manipulate the actual sounds produced by the spell, incorporating echoes and changing the volume of discrete sounds. The DM can decide if your character is a skilled-enough sound engineer to craft a believable illusion, or if these tweaks will have any effect. As Crawford himself says,
There are no D&D rules police, thank goodness. Customize the game in the ways that give your group the most enjoyment.
Best Answer
Yes!
Since this is still the top answer, I'm going to update it in light of more recent information from WotC. As Derek Stucki points out below, Jeremy Crawford was asked on Twitter:
and he responded with a simple "Yes".
As far as how much can be said, Josh Clark points out that in the Out of the Abyss official adventure module, an NPC uses minor illusion to simulate two senteces (p. 171).