Starting with an Intuitive Problem When processing audio, speech, or other time series data, we will almost certainly encounter this problem: if two signal segments are similar in “content,” but not consistent in the speed of time progression, can we still judge that they are similar? This problem is very common in real scenarios. For example, two people sing the same melody, but one sings faster and the other slower; students may slow down due to hesitation during sight-singing, retreat and re-sing after making mistakes, or suddenly accelerate at certain positions; the same sentence is spoken by different people with different speaking speeds and different pause patterns....

Preface During my university studies, sight-singing and ear training was a course that gave me quite a headache. While the course itself is very fundamental, it is not easy for many music majors, and I was one of them (laughs). As I progressed through my studies, I gradually discovered a significant problem with sight-singing and ear training when practicing independently: students often find it difficult to notice their own mistakes in a timely manner....