## 3 Results
### Expert Evaluation and Ratings
Erroneous note harmonization was performed not only in overall bad harmonization results, e.g., in the \"Solar-Giant Steps\" cross-harmonization shown Figure 3a, but also in segments of good overall harmonizations, where one or two chords were not producing satisfactory matching with the underlying melody, e.g., in the \"Solar-Time Remembered\" cross-harmonization. In the latter case, the harmonization was overall satisfactory and the broader harmonic concept of Song B (Time Remembered) was indeed passed in the cross-harmonization: no dominant chords were employed, except for the last chord, which is a constraint chord of Song A. Regarding the ratings, they were based, as much as possible, on an \"academic\" point of view, which was pursued by instructing the music expert to rate as if they were rating re-harmonizations of students. The ratings (on a scale of 0-10) show that the algorithms are, in general, capable of generating re-harmonizations that are rated high, i.e., above 8 (5/13), while all except three harmonizations are rated above 7 (10/13). There are three cases with poor rating, namely 6, 5.5 and 3.5. The ratings of each re-harmonization are examined in terms of their correlation with some features obtained from the log files. Specifically, the correlation is studied between the rating and the accumulated number of constraints per transition, supported transitions per transition, new chords per transition, transition probabilities and melody matching in each re-harmonization. The results are shown in Table 5. Even though the re-harmonizations are very few (13) and, additionally, there are no high-enough values to show clear correlations, the indicated weak relations provide interesting insight that can be valuable for future studies that focus more on the qualitative, subjective evaluation of the methods. \begin{table}
\begin{tabular}{c c c c c} \hline
**Song A** & **Song B** & **Melody** & **Chords** & **Average** \\ \hline Afro Blue & Giant Steps & 9.5 & 9 & 9.25 \\ All Of Me & Giant Steps & 7.5 & 6.5 & 7 \\ All The Things You Are & Darn That Dream & 8 & 8 & 8 \\ Anthropology & Darn That Dream & 9 & 8.5 & 8.75 \\ Beautiful Love & Darn That Dream & 9.5 & 8 & 8.75 \\ Blue Bossa & Giant Steps & 6.5 & 8.5 & 7.5 \\ Blue Bossa & St. Thomas & 6.5 & 8.5 & 7.5 \\ C-Jam Blues & Time Remembered & 8 & 4 & 6 \\ Relaxin’ At Camarillo & Time Remembered & 7.5 & 7.5 & 7.5 \\ St. Thomas & Blue Bossa & 10 & 5.5 & 7.75 \\ So What & Giant Steps & 3 & 8 & 5.5 \\ Solar & Giant Steps & 1 & 6 & 3.5 \\ Solar & Time Remembered & 9.5 & 9.5 & 9.5 \\ \hline \end{tabular}
\end{table} 
Table 4: Re-harmonization sessions and their ratings according to melody matching, selected chords and the average of the two. Table 5 indicates that the average rating is correlated negatively with the number of supported transitions, while it is positively correlated with the appearance of new chords, i.e., better rates correspond to less supported transitions but more new chords. However, in the entire set of all 196,249 re-harmonizations, the number of supported transitions is correlated with the number of new chords. It happens that the 13 re-harmonization tasks that are examined exhibit no correlation between these two features (i.e., correlation between number of supported chords per transition and new chords per transition is 0.08). The negative correlation component, regarding the supported transitions, is related with melody rating, i.e., the fewer  
Figure 3: Two example cross-harmonizations with “Solar” as Song A and (**a**) Giant Steps and (**b**) Time Remembered as Song B. Melody mismatches are indicated. In (**a**), melody mismatches are very often, in contrast to (**b**).