Are there any theories that model how to measure the pleasantness of transitions between notes in a melody?
I'm imagining some kind of "distance" measurement of some sort in a similarity space whereby we gravitate toward certain melodies and the less similar a melody is to a pleasing one, the more displeasing we find it.
I would say no, there is none, but not because it is absolutely theoretically impossible to model pleasantness of a sequence of notes, but because the search space and variables of this model are unimaginably huge that makes it impossible to come up with a decent model, even if one exists. For example, pleasantness is judged differently by people of different counties, people of different ages, people of different music backgrounds, ..... and even for the same person in different moods, different ages, ....).
In fact, in the late eighties, the topic of Generative Music started to get some attention from computer scientists who worked in the fields of artificial intelligence and machine learning. Generative Music is used to describe music pieces generated automatically or semi-automatically by computers.
In order to do that, the machine must have a model based on which, tries to form a sequence of notes which have a high chance of being pleasant to a specific audience. Back then, it turned out that like painting, poetry or any form of art, it is impossible to model pleasantness of a work of art.
Today, only a few research groups are still working on the topic of generative music around the world.
Yes, Treatises and papers on what makes a melody good vs. bad have been written since antiquity. For example Gradus Ad Parnassum by Johann Joseph Fux, 1725.
Pitch Structure of Melodic Lines: An Interface between Physics and Perception by Rafael G. Hurtado. http://mindmodeling.org/cogsci2011/papers/0843/paper0843.pdf may be what you're looking for. The author specifically references "the existence of preferences for certain elements in a given melodic line" and "pleasant sensations in the listener" in the abstract.
In the realms of computer science and music theory there are plenty of examples of melodic analysis based on more objective criteria than "pleasantness", for example, Melodic analysis with segment classes by Darrell Conklin is an example of a paper about using machine learning to sort melodies into style categories http://link.springer.com/article/10.1007/s10994-006-8712-x#page-1
No, there is not. "Pleasantness" is subjective. There is only dissonance and consonance, and even that is relative.
