barbarian
羯 centers on the historical concept of a barbarian, specifically a non-Chinese ethnic group from the north or west. The meaning is narrow and refers to a particular ancient people rather than a general idea of wildness.
羯 combines 羊 (sheep/goat) with 曷, which likely contributes the sound. The character was used to name a historical ethnic group, possibly associated with pastoralism or animal husbandry.
A sheep 羊 beside the phonetic 曷: imagine a barbarian tribesman from the steppes, clad in sheepskin, representing the ancient Jie people.
For カツ, picture a barbarian warrior eating a fried cutlet (カツ) made from sheep: cutlet -> カツ, tying the sound to the sheep component.
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