# Enhancement of Conventional Beat Tracking System Using Teager-Kaiser Energy Operator
## 4 Discussion  
Generally, the newly proposed method provided some improvements to the reference database. We analyzed 30 tracks and the results are reported in Table 4. The results suggest that the TKEO can help the proposed beat tracking system to pick better onset candidates for the beat positions and to slightly improve the GT calculation. The difference was about 8 BPM on average for all tested recordings of the first database. However, many recordings reported the same estimated GT for both methods. Then, the ABD was calculated. We used the reference database with manually corrected beat positions to determine the accuracy of both systems. We did not use F-measures, but rather average differences between consecutive beats. P values show that there is a difference between both systems. This gives us an idea of how close the beat tracking was to the reference positions. The system with the TKEO generally reported lower ABD for all settings used. The results suggest that the TKEO pre-processing improved the accuracy of the beat tracking system. This does not apply for the general onset detection function. Onset detection accuracy was reduced in most cases. The only exception was the recording of the clarinet.  
As far as the string quartet database is concerned, the results were again slightly in favour of the system based on TKEO. All 33 recordings of the second database were tested. The difference between the average deviation from the EAT of the TS and the DS was only 0.17 BPM, and therefore both systems had more or less the same detection accuracy. We chose such complex music to see how the enhancement would deal with a very difficult task. The actual usefulness of the application also depends on the settings of selected parameters, not just on the TKEO pre-processing.  
The idea of using TKEO in the pre-processing stage was to help the onset detection function to find more relevant onsets and therefore enhance the beat tracking system in terms of choosing better candidates for beat positions. It reduced the number of insignificant onsets detected. Onset detection accuracy has usually been reduced, but the final beat detection output may be more stable; the algorithm chooses from less and more important onsets. This is useful for analyzing tracks where we suspect a stable and non-agogic rhythm. We tested the effect of the TKEO to see how the output detection function would behave. We did not change the parameters such as tightness of the beat tracking system for each tested track; the correct setting (set for the particular piece of music) would yield better results for complex music analysis.  
The limitation of this study is that the EAT in the string quartet database may be a reference value for the beat tracking system, but it is not the actual GT of a particular track since we cannot include any expressive elements in it. It does not provide any information about beat positions or local tempo changes. The same thing applies to the reference global tempo. In enhanced interpretation analysis, we need to track all beat positions in the segment and compare them to the real beat positions. However, in this case, we analysed relatively stable tracks with no abrupt tempo changes. In the future, we would like to use this system to create a database and its additional information about manually corrected beat positions of segmented string quartet music. The impact of the TKEO on audio recordings will be tested in more detail in our future work.  
Cooperation between researchers and musicologists is the crucial part of such interdisciplinary projects and MIR science field. Different base knowledge and tendencies can lead to mutual misunderstandings, but both sides could benefit greatly from each other. Projects like these are the important bridge for computer scientists, MIR researchers and musicologists.