I am wondering if we can listen to sad music during the 3 weeks? because it doesnt make us feel happy or joyous.

ב"ה Shalom In principle, the inference you have made is a correct one. According to Rav Shlomo Zalman Oirbach zt"l the type of singing which is forbidden to be heard is singing that induces dancing. (Halichot Shlomo pg. 412) Therefore, we can infer that sad songs or music, for example, should be permitted since they don't induce dancing. This should also allow Chazanut, since ut also does not induce dancing. Nevertheless, the conclusion as brought in Halichot Shlomo is that one should still refrain from hearing such music. There are poskim, though, who would allow such singing when not accompanied with musical instruments. (שבט הקהתי חלק א' סי' קסט.) On the other hand, Rav Eliezer Melamed who writes in the Hebrew counterpart of this website, feels there is room leniency to listen to sad music , since there are poskim who in any case are of the opinion, that music heard from a radio and the like may be listened to during the 9 days, since electronically sounded music does not have the same joyous effect as real musical instruments. In addition, there are poskim, who allow people to listen to music from a radio and the like to relieve people from loneliness. (Halichot Shlomo pg. 412) All the best