Idea

The Matrix is good and all, but if I want my notes to follow a sequence that follows a more complex mathematical graph than sawtooth (modes Up, Down, and Zig-Zack+), triangle (modes Up-And-Down and Zig-Zack), and random (mode Random), I'd have to manually put it in the timeline. However a mathematical arpeggiator that's designed to take a math equation and send out beautiful patterns of notes would fix this.

Parameters

Equation (String)

An equation relating a variable y as a function of x. Values of infinity and undefined are replaced with 0, negative values are wrapped around to the top, values above the max are wrapped around to the bottom, and values are rounded. Piecewise functions are supported. Trig functions, logarithms, roots, exponentiation, pi, tau, Euler's number, and other possibly-useful functions and constants would be available.

Rounding (Select)

How values are rounded. Floor, ceiling, or round.

X-step (Float)

The increment of x for every note played.

Repeat (Integer)

How many times a note is played before x is incremented.

Length (Integer)

How many times x is incremented before resetting.

Chord mode (Boolean)

Whether y represents the yth note in an incoming chord, or if it maps to a very specific note.

Step length (Duration)

How long each note is played for before moving on. Optionally, it could have a sync button.

Notes (Note Input)

The notes to be arpeggiated.

Output shift (Note Input)

Used to raise or lower the note values of the resulting notes by a second note pattern. C4 and undefined are neutral (doesn't affect the output notes), while notes above C4 bump the output notes up by a difference and notes below C4 bump them down by a difference.

Variables (Float)

Four knobs, labeled A, B, C, and D, which control the values of correspondingly-named variables for use in the equation. This enables timeline automation options.

Velocity (Float)

The velocity of outputted notes. Multiplied by the velocity of output shift notes, if any.

Concerns

This seems like a rather large project. I doubt this'll even so much as be considered. Of course, I'd understand. I'm a programmer myself and a lot of stuff I want to do gets rather large and in my experience I've been looking for solutions to problems only to learn that the problems exist because there is literally no solution. Although if this does get added, I'd be really happy, because I like math and I believe that math belongs in music.