"Music Understanding" is one of the most important research topics in contemporary music esthetic field. The cognition in music can not be separated from the study of music compositions, interpretation, and appreciation. The importance of composers is unable to be denied, though we may or may not know who wrote the certain music. However, without the "interpretation" of the performers, the listeners can not "appreciate" it. Besides the research and analysis on the definitions between music and composer, interpretation and interpreter, this paper aims to propose opposing points of view, which relate to interpretation, from composers writing materials and inspiration, and the interaction between interpreters and composers under the circumstance of the evolution of music notations. Also, the clarification of the conception in music appreciation, types of audience, problems of listening to 20th-century music, are subjects of this paper. Finally, the discussions of difficulties for performing practice can assist both interpreters and listeners while appreciating early musical works.