## 4 Conclusions  
The multi-criteria experiments performed on different key-finding approaches allowed us to evaluate their strengths and weaknesses. It turned out that in the scenario implementing the aggregate durations of individual pitch-classes, based on the analysis of the shortest initial fragments of music for which the key was indicated in all the considered approaches, the key detection efficacy obtained with the method using the signature of fifths was greater than the efficacies obtained with the strictly correlational approaches utilizing key-profiles (on average by 9.27 pp). In the case of the analogous analysis carried out for the scenario implementing the multiplicities of occurrences of individual pitch-classes, the average efficacy obtained with the strictly correlational approaches utilizing key-profiles  
Figure 17: The beginning of [PERSON]’s prelude No. 7, Op. 28, in A-major, where SF is the key-finding method using the signature of fifths and K-K, T, and A-S are the strictly correlational key-finding approaches based on the Krumhansl–Kessler, Temperley, and Albrecht–Shanahan key-profiles, respectively (incorrectly detected keys are marked in red). was greater than the efficacy achieved with the method using the signature of fifths (by 2.7 pp; Figure 15). In the light of the above, representing the analyzed compositions with the aggregate durations of individual pitch-classes seems more appropriate for the method utilizing the signature of fifths. On the other hand, the use of the multiplicities of individual pitch-class seems a better choice when one utilizes the other approaches. It is evident that the method implementing the signature of fifths is a good alternative to the strictly correlational key detection approaches based on the key-profiles. There is no doubt that it is a computationally simpler technique that yields comparable results and provides greater stability of the detected keys. The conducted experiments showed that the method utilizing the signature of fifths was superior if the key detection process was performed on the initial fragments of the analyzed pieces of music. This results from the fact that the applied algorithm indicates the key only when the main directed axis of the signature of fifths is determined. In other approaches, the key is indicated based only on the values of correlation coefficients, which can be calculated for any number of notes/chords comprising a given fragment of a composition. The problem is that in the strictly correlational approaches, the keys detected based on the analysis of short fragments of music are often incorrect. Additionally, it is difficult to determine the optimal length of an analyzed fragment of music. In the case of the key detection method utilizing the signature of fifths, the number of chords/notes needed to detect the key is chosen adaptively. The key is pointed out only when there are enough notes to make a sensible decision. The method based on the signature of fifths is well suited for real-time implementations where the analyzed fragments of music need to be very short. In particular, it is suitable for hardware applications in electronic musical instruments in which the musical notation representing the piece being played is displayed on an LCD screen. It is worth emphasizing that, for the purposes of the discussed study, in order to visualize the signature of fifths, we used a normalization procedure so that the signature of fifths inscribed in the circle of fifths had a unitary radius. In hardware applications, though, this step is not needed because the main directed axis of the signature of fifths can be determined without it. This leads to further simplification, which significantly reduces the computational complexity of the method. Currently, we are focused on simplifying the presented technique further to eliminate the need for calculation of two correlation coefficients used for the final selection of one of two relative keys.