Getting contacts (via /api/party) by member type?

So, I feel like this is a really simple question, and should be supported by the REST API, but I just can't seem to figure it out.

I've tried the following endpoints:

/api/party?memberCode=X
/api/party?memberTypeCode=X
/api/party?memberType=X
/api/party?member=X
/api/party?customerCode=X
/api/party?customerTypeCode=X
/api/party?customerType=X
/api/party?custTypeCode=X
/api/party?customer=X
/api/party?memType=X
/api/party?member_type=X

Notice how they get progressively more desperate?

All of these return 400 Validation Error with this message: "In the query, customerTypeCode is not a known property name."

What is the correct filter on the party endpoint for this? The additional values has a CustomerTypeCode property, as well as an IsMember property, but both of those are not filterable.