There should be a date stamp inside, too. It'll be in the form of F-XX or S-XX with XX being the year, and F or S meaning First or Second half of the year. The 3664 is the Harmony serialized number.
The logo on yours one dates it earlier, as the last 1352 models had the 'thick script' logo as well as the tortoise pickup ring.Some examples of the 'deco logo' variation also have the tortoise pickup ring. Probably transitional as they moved from one logo style to another.
Here are some catalog listings, the first is the first appearance in late 1952:

And the last in Spring/Summer 1959:

The logo style illustration changed over in Fall/Winter '58 catalog.
Hope this helps,
Randy