## 5 Conclusions  
This paper presents a new methodology for creating novel melodic harmonizations of jazz standards through cross-harmonization, i.e., harmonization of the melody and some chord constraints of Song A, with the chords and transitions of Song B. While developing the basic Hidden Markov Model in collaboration with jazz experts for achieving this task, two new methods were created, which function on top of the Viterbi algorithm: the incorporation of chord groups (rather than individual chords as states) and the introduction of a \"supporting\" chord transition space, trained on the entire dataset of jazz standards, at the exact time steps where incompatibilities between the melody or the constraints of Song A and the chord groups and transitions of Song B are encountered. Results were presented on a dataset of 444 chord-melody annotated jazz standards, providing an understanding on how often the \"supporting\" space was employed and how often that led to the introduction of new chords that were never used in other jazz standards of the dataset. Expert analysis showed that the main problem, in some cases, is that there are still significant chord-melody mismatches. Possible solutions are discussed, along with a discussion about other possibilities for improvement. From the results presented herein, it can be concluded that the presented approach has the potential to lead to new interesting applications pertaining to the field of computational creativity in music, while it opens up new research directions both for improvements of the proposed methods and for the development of other methods that facilitate cross-harmonization. Two limitations of the presented study are the small dataset that is currently available and the fact that the proposed approach has not been assessed within the context of practical applications, such as music learning. Except for the method-related issues discussed in Section 4.2, application and evaluation issues should be additionally addressed. The inclusion of more jazz standards will provide further insight into how the support space can introduce new solutions, while it will allow the examination of support \"subspaces\" that do not include the entire dataset, but a smaller subset of the dataset the Song B belongs to. Evaluation needs to address issues related to the feasibility and the usability of the presented approach in specific application scenarios. The current results aim to shed some light on how the methods behave, mainly based on some quantifiable criteria, but there exist concrete real-world scenarios for which the effectiveness of the proposed approach needs to be assessed. The presented re-harmonization methodology allows intertwining of a given harmonic structure, i.e., that of Song B, with a combined melodic-harmonic context, i.e., that of Song A. The context of Song A integrates melodic and harmonic components, both in the form of the constraint chords (beginning and ending of sections), as well as in the form of the harmony implied by the melody under consideration. The results indicate that interesting harmonic phenomena can emerge for some combinations of Song A and Song B, although there are cases in which algorithm decisions may lead to re-harmonizations that are not favorable for the idiom of jazz standards as it stands. In such cases, applications are sought in settings that can either have a higher degree of tolerance to errors, or that have exploratory settings, in which errors may be of interest for developing new musical idioms. In live performances, musicians will often start performing one piece without concluding the previous one. This is usually done by developing the melodic theme of the second piece within the duration of the first piece. The methodology presented here can offer ideas for such seamless transitions between two pieces of music, which, in an analogy to the signal processing terminology, may be considered to provide some form of 'harmonic morphing'.