sinusoid

This patch shows a simple method for mixing and viewing two sine tones generated by the cycle~ object.

To generate a series of numbers in Max that outline a sinusoidal shape, you can use the sin() function in the expr object. As the argument in the sin() function goes from 0 to 2π (6.283185), the output will be the sine of that value, going from 0 up to 1, down to -1, and back up to 0. So, by feeding a series of numbers into expr, you can generate numbers that follow that sinusoidal pattern.

You can calculate the desired acceleration/deceleration curve using expr. The smoothest acceleration/deceleration is exhibited by simple harmonic motion (like the swinging of a pendulum), which would be a sinusoidal curve rather than a sigmoid curve (and a sigmoid is theoretically asymptotic, i.e. never truly reaches its goal). You can calculate either with expr. Here’s an example comparing the two. 

This example shows interference between two sine tones that have nearly the same frequency, causing a beating effect.