With ScratchPad I've been rapidly working on new melody ideas.  One particularly interesting one revolves around raising numbers to fractional powers.  It's the first truly mathematical melody method that I've experimented with, and the results are turning out better than I would have expected.

The method of generating goes as follows.  First, the user chooses a fractional power that will be used to generate the melody as well as a digit depth that will be used in determining how far into the digits of the function the program should search.  The plugin then creates a base number by multiplying a seed by certain compositional indices such as the style class of the movement or the index of the chord rotation.  It then raises the base number to the chosen fractional power, removes the decimal point, and digs into the digits of the resultant irrational number until it reaches the digit specified by the depth setting.  This digit will be used to determine the pitch offset.

Such is only a fraction (get it?) of what actually happens during the generation - since duration must also be dealt with by similar means, and several other factors weigh in to improve the quality of the results.  Nonetheless, it's cool to think about "music drawn from the very nature of the square root function."

The plugin already beats all other melody plugins, hands-down.  Fraccut and Fraccut v2 were, of course, close contestants with the root method.  In the end, though, the ease of development in ScratchPad led the new module to victory.  The module is almost ready to bud off of ScratchPad and become an independent plugin.  I think I'll call it Entropic Root, since it both sounds cool and hints at the use of the "entropy" of fractional power functions (of which roots are a convenient class).

Below is an image of four instances of the plugin loaded into mGen.  The preview shows coherent, creative, and complex melodies: