Synonyms for “cackle” include “giggle”, “chuckle”, and “laugh”.
“Giggle” is a light, high-pitched laugh often associated with amusement or nervousness. For example, “The girls giggled at the joke.” It shares with “cackle” the sense of spontaneous laughter, but is usually softer and more delicate.
“Chuckle” is a quiet, amused laugh. For instance, “He chuckled to himself as he read the funny story.” It is a more restrained form of laughter compared to “cackle”, but still indicates amusement.
“Laugh” is a more general term for expressing mirth. It can range from a soft chuckle to a loud guffaw. For example, “They laughed heartily at the comedian’s antics.” While not as specific as “cackle”, it can be used in many contexts where there is amusement.
All of these words convey different forms of amusement through laughter, but “cackle” stands out as a more distinct and perhaps louder, more raucous form of laughter, often associated with a certain exuberance or even a touch of madness.