I copied everything that is not typical words and Ariel sure makes much "noise" - here is what I found.
Right off the bat - some of the first words PROSPERO says:
The hour's now come.
The very minute bids thee ope thine ear.
Why would Shakespeare warn the audience to listen? Do you think he is saying, listen to more than what the actors say - listen to the other sounds.
OK here we go...
To run upon the sharp wind of the north,
To do me business in the veins o'th' earth
When it is baked with frost.
Suggesting the silence of frost that comes with the quiet blow of the sharp north wind.
Did make wolves howl,
Ariel encased in the Oak
howled away twelve winters.
The watch-dogs bark!
Bow-wow!
Hark, hark! I hear
The strain of strutting chanticleer
Cry cock-a-diddle-dow!
FERDINAND
Where should this music be? I'th' air or th' earth?
This music crept by me upon the waters,
With its sweet air. Thence I have followed it,
Or it hath drawn me, rather. But 'tis gone.
No, it begins again.
ARIEL Song
Full fathom five thy father lies,
Of his bones are coral made;
Those are pearls that were his eyes;
Nothing of him that doth fade,
decay, decompose, become corrupt
But doth suffer a sea-change
undergo, sustain, endure
Into something rich and strange.
Sea-nymphs hourly ring his knell:
Ding-dong.
Hark! Now I hear them – Ding-dong bell.
no sound event, happening, occurrence
That the earth owes. I hear it now above me.
He does hear me,
And that he does, I weep.
Enter Ariel, playing solemn music
SEBASTIAN
Thou dost snore distinctly.
There's meaning in thy snores.
Enter Ariel with music and song
Sings in Gonzalo's ear
While you here do snoring lie,
Talk about the sound of bulls and lions
Enter Caliban with a burden of wood.
A noise of thunder heard
another storm brewing. I hear it sing i'th' wind.
it should thunder as it did before, I know not where to hide my head.
thunderbolt.
Thunder Alas, the storm is come again.
STEPHANO
singing
He drinks and then sings
Come on, Trinculo, let us sing.
ACT III.ii.
Sings
Ariel plays the tune on a tabor and pipe
CALIBAN
the isle is full of noises,
Sounds, and sweet airs, that give delight and hurt not.
Sometimes a thousand twangling instruments
Will hum about mine ears; and sometime voices
That, if I then had waked after long sleep,
Will make me sleep again; and then, in dreaming,
The clouds me thought would open, and show riches
Solemn and strange music; and Prospero on the top,
invisible. Enter several strange shapes, bringing in a
banquet; and dance about it with gentle actions of salutations;
Marvellous sweet music!
Thunder and lightning. Enter Ariel, like a harpy
Wound the loud winds,
He vanishes in thunder. Then, to soft music, enter the
shapes again, and dance with mocks and mows, carrying
out the table(assuming that dancing makes sound)
ALONSO
The winds did sing it to me; and the thunder,
That deep and dreadful organ-pipe, pronounced
The name of Prosper: it did bass my trespass.