"用某种调子说" can be translated into English as "say in a certain tone" or "speak with a particular tone".
Here are a few example sentences to illustrate its usage:
1、 He always says things in a sarcastic tone. （他总是用一种讽刺的调子说话。）
2、 She spoke with a gentle and soothing tone. （她用一种温和且安抚的调子说话。）
3、 Can you say that again, but in a more enthusiastic tone? （你能再用更热情的调子说一遍吗？）