You can easily get an effect similar to this diagram from 3:18 in the video.
To accomplish the cross fading, you'd use a design similar to this:
In your code, you'd configure those sample players or waveform objects to create the short sounds you want.
Set all the mixer channels to 1.0 gain, since you'll be using the faders to attenuate the signals so the add up to at most 1.0 before mixing.
Then when you want to cross fade between them with a 40 millisecond transition time, you'd use code like this:
Code:
AudioNoInterrupts();
fade1.fadeOut(40);
fade3.fadeIn(40);
AudioInterrupts();
The important step here is AudioNoInterrupts() surrounding the setting of both fade objects, so they will be certain to begin their transitions at the same instant.
If you want the waveform to start at a precise point within its cycle, you'd also put that include the code protected by AudioNoInterrupts(), so the fading in waveform synthesis begins at exactly the designed phase angle (0 to 359.999 degrees) as the fading in begins.
Code:
AudioNoInterrupts();
fade1.fadeOut(40);
waveform1.phase(180.0);
fade3.fadeIn(40);
AudioInterrupts();
Of course, you can also configure for any of the 9 waveforms and their various settings. If using a modulated waveform, you can configure it and the waveform that's modulating its frequency, phase or shape (if pulse or variable triangle) so you have exact control over exactly how the waveform begins at the exact moment the 40 ms (or whatever time you configure) cross fade begins.