和らぐ and 和らげる: a state easing and something easing it
Compare tension easing after music, evening heat, and the effects of a window or joke, identifying the changing state and what influences it.
Tension or heat easing
和らぐ (やわらぐ) means to ease or subside. “音楽を聞いて緊張が和らいだ。” says that listening to music eased the speaker's tension.
“夕方には暑さが和らぐ。” describes heat subsiding in the evening. 緊張 and 暑さ are the changing states. The music example has a stated circumstance, so 和らぐ does not mean a change without a cause.
The effect of a window or joke
和らげる (やわらげる) means to ease or soften something. “窓を開けて部屋の暑さを和らげる。” describes opening a window to ease the heat in the room.
“彼の冗談が張り詰めた空気を少し和らげた。” says that his joke softened the tense atmosphere slightly. 冗談 is the influencing subject, and 張り詰めた空気 is the affected object.
Identify the changing state and the influencing subject
緊張が和らいだ focuses on tension easing; 冗談が空気を和らげた focuses on a joke's effect on the atmosphere. The subject of 和らげる does not have to be a person acting intentionally.
Preserve the degree 少し: the atmosphere softened slightly. Do not expand that into tension disappearing completely or heat being eliminated.
Does 少し和らげた mean that the joke made all tension disappear?
Show the answer and why
No. It says that the joke softened the tense atmosphere slightly. 和らぐ focuses on a state easing, while 和らげる focuses on something influencing that state.