Not all Interludes are available upon a Servant's release. The table below summarizes what Interludes are missing from current Servants, as well as estimated time of release based the Japanese Server.
Rank Up Quests are similar to Interludes but without the story sections, and they are numbered separately. These are usually released in batches.
Ascension Material Drops from Interlude / Rank Up Quests
Check out the Interludes and Rank-ups Guaranteed Mats spreadsheet maintained by Officerアルトリア, solution, and Ty2012 at the Atlas Academy!