whereby相当于by which、by what,即“凭什么”.主干部分是逗号前边的部分,逗号的后边进一步补充说明.而本句的主干部分是逗号后边的部分,逗号前边的部分是逗号的后边原因.以此本句更正为：Though best known as a jazz vocalist,he also enjoyed gospel music,so he told his manager that he wanted to make a recording of his favorite gospel songs.或Becaus though best known as a jazz vocalist,he also enjoyed gospel music,he told his manager that he wanted to make a recording of his favorite gospel songs.再举个例子：Straitford's briefs don't sound like the usual Washington back-and-forthing,whereby agencies avoid dramatic declarations on the chance they might be wrong.
此处的whereby相当于by which、by what,即“凭什么”.所以本句的主干部分是逗号前边的部分,逗号的后边进一步补充说明.on the chance的意思是也许能够（做到某事）、希望能够（做到某事）,后边经常接that引导的从句.
本句应该重点体会whereby以及on the chance的用法.back-and-forthing在此处应译为“往来公文”.