The study of maqamat is the study of at-taghanni bi’l Quran, or the study of beautifying the voice in recitation of the Quran. Beautifying the voice in recitation is something that our beloved Messenger sallallahu alaihi wa sallam commanded us to do, when he said “Beautify the Quran with your voices”, and when he said “He is not from us, who does not ‘yataghanna‘ (chant melodiously) the Quran”.
The maqamat describe the various patterns of melody (or tunes) that reciters use in their recitation. This adds to (and shouldn’t take away from) the beauty of proper articulation and proper rhythm that one learns from studying the science of tajweed.