In The Free Dictionary you usually see definitions extracted from several sources.
Usually the first one uses a phonetic notation which is unknown to me.
What's the name of that phonetic notation system?
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Apparently it's called the "American Heritage Dictionary representation" (AHD), essentially identical to the one used on Wiktionary, called the "English Phonemic Representation"(enPR). It has a Wikipedia page, which shows the AHD/enPR symbols matched up with words containing that sound, and with the equivalent IPA characters: https://en.wikipedia.org/wiki/Wikipedia:American_Heritage_Dictionary_representation
Transcription systems in English-language dictionaries are generally similar, but each one seems to have its own variant! This Wikipedia page provides comparison of several such systems with each other and with the IPA: https://en.wikipedia.org/wiki/Pronunciation_respelling_for_English
The American Heritage Dictionary's website (https://www.ahdictionary.com/word/howtouse.html) links to this pdf chart of the comparison between AHD and IPA: https://www.ahdictionary.com/application/resources/misc/pronkey.pdf