One approach that occurs to me is the division of melody into chord and non-chord tones, and investigating the affect of accent on non-chord tones. NCTs are divided by approach/departure (step or leap) and whether they occur on an accented or unaccented beat of the bar. NCTs that occur on an accented beat such as accented passing tones and accented incomplete neighbours are less common than unaccented (eg passing tones and neighbour tones). You could also consider the way a melody starts and ends, which tend to be on strong metrical beats. You could also possibly consider harmonic rhythm vs. melodic rhythm.

I understand your question as follows: How can the pitch and rhythmic structure of a tonal melody be related? How could such melody be generated automatically?

* How can the pitch and rhythmic structure of a tonal melody be related?

There are many ways the pitch and rhythmic structure can agree and disagree with each other. For example, an important higher-level rhythmic concept are accents. Accents can be formed by certain rhythmic constellations (e.g., longer notes following short notes), by pitch constellations (e.g., a local pitch peak), but also many other factors (e.g., harmonic changes carry accents). These different "dimensions" of the music can agree but also disagree. Here are a few books discussing specifically the rhythm of tonal music, and how that is affected by different factors, including the pitches and the note values.

Berry, W. (1976) Dover reprint 1987. Structural Functions in Music. Eaglewood Cliffs, N.J.: Prentice-Hall.

Lester, J. (1986) The rhythms of tonal music. Carbondale: Southern Illinois University Press.

Petersen, P. (2013) Music and rhythm: fundamentals, history, analysis.

* How could such melody be generated automatically?

Obviously, there are again many approaches to computationally model such details. I understand from your publications that you are using neural networks, which is one approach. I am modelling music theories with constraint programming (see my publications). Currently I am writing on an article how to model rhythmic accents with constraints. In general, I try to first understand the related music theory (or formulate my own theory) and then I try to model that. Of course, using machine learning methods you could leave at least some of that understanding to the computational method itself.

Your questions is very broad, I find it difficult to be more specific :)

> You could also consider the way a melody starts and ends, which tend to be on strong metrical beats.

I am not sure I fully agree with that. In fact, it seems that very many melodies start with an upbeat, so that the first metric accent is made clear.

Thank you, deliberately asked a question in a general way to trigger discussions and to get the most variety of approaches. In addition to neural networks, in different systems, I also thought about the methods of using grammars, in particular HPSG.

However, I focus on neural networks with the help of some random solutions that have decision-making support for network or to connect a networks operating each other in cascade.

Thank you Silvio, but i;ve asked about problem of linking in general not only in clasical music. In fact, I'm talking about mechanism, because depending on the type of music can be a way to implement such restrictions relevant or tables of passes.

Anyway, thanks

Great question and great answers.

In music with text the answer becomes much simpler, since the rhythmic strength of textual accents helps envision a motor rhythm. Perhaps the brain works in a similar way with a melody without text.

You are  right that it is very important to consider the relation between rythme and text but only when your composition has text. What about rhytm in music composiotion is strictly musical.

Yes, for now only european music, but very interesting is mathematical model for tonal harmony and jazz, i have this somewhere on my computer. If someone likes mathematic very big equation it is very nice:)

Melody works well through recurrence, the same can be said of rhythm.

If recurrence is the mother of novelty in music. Then the question is,"What aspects of music should be repeated?" For instance it is quite challenging to decipher rhythm from plain chants, where the rhythm of the piece is latent, Also there are challenges for monadic melody, where the melody line is overshadowed by something else (harmonic structures/rhythm).

I think that a nice marriage between melody and rhythm/harmony is found in the piece "One Note Samba" written by Antonio Carlos Jobim. Even though some would still choose to classify it as a work of monadic melody.

http://tagg.org/articles/xpdfs/melodaccUS.pdf

http://en.wikipedia.org/wiki/One_Note_Samba

https://www.youtube.com/watch?v=0rzNLXxo01Q

 When one is active, let the other rest and vice versa. Use imitation to make the parts coherent, take a recognisable rhythmic gesture from the melody and use this as a propelling cell / motif  in the accompaniment. Alternatively, do away with the rhythm all together and present the melody in a sectional style.