I did see this posted before but it was not the answer for me. My price set has a "select" field type and all options have a membership type populated. Yet, using the contribution page with this price set only generates a contribution record and not a membership record.
That is, when I go to a contact record, I see the contribution under the contribution tab but I don't see the membership under the membership tab.
Civi 4.7.27 on WP 4.9.4