The kanji 慨 (gai) primarily conveys the feeling of "grief," "sorrow," "regret," or "resentment." It expresses a deep emotional response to a loss, mistake, or unfortunate situation. It implies a sense of sadness or dissatisfaction that is often accompanied by a sigh or a feeling of helplessness. The emotion is often directed toward a situation or a past event that cannot be changed.

・On-yomi (音読み): ガイ (gai) ・Kun-yomi (訓読み): なげ（く） (nage(ku)) - to lament, to grieve; this is an intransitive verb

⚫︎ 痛（いた）ましい事件（じけん）を慨嘆（がい）する。 Translation: To lament the tragic incident. ⚫︎ 慨然（がいぜん）として語（かた）る。 Translation: To speak with a feeling of regret. ⚫︎ 過去（かこ）の過（あやま）ちを慨（がい）する。 Translation: To feel regret over past mistakes.

The kanji 慨 is a 形声文字 (keisei moji), which means it's a character formed by combining a semantic component (a part that indicates the meaning) and a phonetic component (a part that indicates the pronunciation). In the case of 慨, the semantic component is 忄 (りっしんべん), which represents the "heart" or "emotion." The phonetic component is 既 (ki), which provides the sound of the character. Therefore, the kanji's meaning is related to the heart, specifically expressing the emotional states like sorrow, regret, and resentment.