The paper presents a novel approach to analyzing and comparing melodic constructs in MIDI format. The calculated digital audio fingerprints of these constructs contain the encoded transitions between note pitches and distances between their heights. It helps identify and compare melodic constructs with their variety of possible interpretations played with different chords, in different keys, tempos, etc. This approach can be useful for searching the music in the music library or helpful for music composers to avoid unintended plagiarism. There are also many prospects when using the approach of real forensic studies and the tasks of verification and authentication of music pieces and recordings. The algorithm developed within the proposed approach includes the required steps and procedures to process music compositions, calculate their digital audio fingerprints, and conduct the search of the specific music composition using the audio fingerprint data. Performance testing is done using the arranged data set, which includes 894 MIDI files of various music compositions played with different instruments and music effects. The obtained results demonstrate the effectiveness and robustness of the developed algorithm and the proposed approach to matching audio fingerprints and identifying similar music compositions with 100% accuracy. Additionally, the concept of using the developed algorithm to locate music in online music libraries by “humming” is presented and tested in the paper.