The whale is a large sea-creature, known today as a cetacean mammal, but regarded in period as a fish; it was hunted from ships for its meat, oil and baleen.  It is found in period heraldic tracts (e.g., de Bara’s Blason des Armoiries, 1581 [88]), but Your Author has not found an unarguable example from period armory.

The medieval depiction of the whale was somewhat fanciful; the illustration is taken from Gesner’s De Avibus et Piscibus, 1560.  If a naturalistic depiction is desired, it must be specified as a “natural whale”, or more explicitly, e.g., a “sperm whale”.  The whale is naiant by default.

In Society armory, there is also the “narwhal” or “narwhale”, a cetacean with a long unicorn-like “horn” (actually its tooth).  It’s generally depicted as found in nature.  The illustration shows a narwhal haurient.  For related charges, see dolphin.

The Baron of Smoking Rocks bears:  Argent, a whale haurient embowed sable within a laurel wreath vert.

André of Stormhold bears:  Argent, a whale naiant azure.

Arinbjorn Talverri bears:  Or, a narwhal haurient bendwise purpure.