This paper first discusses how the signal segmentation and tonal characteristics of music notes effect in music chord detection. Two approaches, pitch class profile approach and psycho-acoustical approach, which differently represent these tonal characteristics, are examined for chord detection. The analysis of the tonal characteristics reveals that not only the fundamental frequency of music note but also its harmonics and sub-harmonies in different octaves contribute for detecting related music chord. A hierarchical approach, which transforms the music chord tonal characteristics in each octave onto probabilistic space, is then proposed for modeling the music chord. Our experimental results show that detection of chord type, Major, Minor, Diminish, and Augmented, and individual chords, 12 chords per chord type, are improved with the proposed hierarchical chord modeling approach. Experimental results also reveal that the tempo proportional signal segmentation is more effective extracting tonal characteristics than using fixed length segmentation.