Who are the 'sweet Saterian dames'?

Question

I came across a beautiful (and subtly extremely rude!) poem called 'A Present to a Lady' the other day, penned by that most prolific of poets, Anonymous. I think I understand all the references - except one:

Colossus-like, between two rocks,
I have seen him stand and shake his locks,
And when I have heard the names
Of the sweet Saterian dames,
O he's a champion for a queen;
'Tis pity but he should be seen.

Who are these 'sweet Saterian dames'?

Neither 'Saterian' or 'Sateria' appears in any dictionaries or encyclopedias I have to hand. Google coughed up a reference to a Livre Saterian, a medieval French treatise on the philosophy of law, which includes the quotation:

just as the law addresses multiple and diverse affairs, so too does this book, and for this reason, it is called Saterian.

But this, to my mind, is not much of an explanation of the term, and, this whole lead feels like a red herring. My modern French is poor, and my Middle French is non-existent, but the online dictionary I consulted put forward the 'hypothèse' that 'Saterian' was an alternative spelling of 'satirien', i.e. satirical. But 'satirical' is a poor fit for this poem, and more so for the medieval legal tract.

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I would not normally do this, but, since the poem is difficult to find online, I will post the whole text below:

A Present to a Lady

Ladies, I do here present you
With a token love hath sent you;
'Tis a thing to sport and play with,
Such another pretty thing
For to pass the time away with;
Prettier sport was never seen.

Name I will not, nor define it,
Sure I am you may divine it:
By those modest looks I guess it,
And those eyes so full of fire,
That I need no more express it,
But leave your fancies to admire.

Yet as much of it be spoken
In the praise of this love token:
'Tis a wash that far supasseth
For the cleansing of your blood;
All the saints may bless your faces,
Yet not do you so much good.

Were you ne'er so melancholy,
It will make you blithe and jolly;
Go no more, no more admiring,
When you feel your spleen's amiss,
For all the drinks of steel and iron
Never did such cures as this.

It was born in th'Isle of Man;
Venus nursed it with her hand,
She puffed it up with milk and pap,
And lulled it in her wanton lap,
So ever since this monster can
In no place else with pleasure stand.

Colossus-like, between two rocks,
I have seen him stand and shake his locks,
And when I have heard the names
Of the sweet Saterian dames,
O he's a champion for a queen;
'Tis pity but he should be seen.

Nature, that made him, was so wise
As to give him neither tongue nor eyes,
Supposing he was born to be
The instrument of jealousy,
Yet here he can, as poets feign,
Cure a lady's lovesick brain.

He was the first that did betray
To mortal eyes the milky way;
He is the Proteus cunning ape
That will beget you any shape;
Give him but leave to act his part,
And he'll revive your saddest heart.

Though he want legs, yet he can stand,
With the least touch of your soft hand;
And though, like Cupid, he be blind,
There's never a hole but he can find;
If by all this you do not know it,
Pray, ladies, give me leave to show it.

Answer 1

“Sater” seems to be a rare spelling of “satyr”, a masculine spirit of nature in Greek mythology. This spelling is not given by the OED, but it is a known spelling in Dutch, which makes it plausible that someone might also adopt it in English. For example, consider this translation of Ovid’s Heroides:

Dan rinkink ik weer als de dolle Wijnpapinnen, en Cybeles Priestressen, die op Ida’s kruin keteltrommen, of’t volk dat door kragt der bos-maagden en gehoornde Saters doldriftig aan’t hollen raakt.

Now again I am borne on, like daughters of the Bacchic cry driven by the frenzy of their god, and those who shake the timbrel at the foot of Ida's ridge, or those whom Dryad creatures half-divine and Fauns two-horned have touched with their own spirit and driven distraught.

_{Abraham Valenyn (1700). De Heldinnen Brieven van Publ. Ovidius Naso, pp. 15–16. Amsteldam: Pieter Mortier. Grant Showerman (1931). Ovid: Heroides and Amores, pp. 47–49. London: William Heinemann.}

Under this interpretation, the “Saterian Dames” are the feminine nature spirits associated with satyrs in mythology, that is, nymphs, dryads, naiads and so on. The relations of nymphs and satyrs were popular subjects for art in the seventeenth century when ‘A Present to a Lady’ was written.

_{Diana and her nymphs asleep, spied upon by satyrs (1620) by Hendrick van Balen the Elder and Jan Brueghel the Elder.}