This app plays a melody at various speeds, including very fast (8192x). You can connect a MIDI keyboard or controller to record new melodies and adjust speed, etc.
A friend sent me a link to The Coltrane fractal. Supposedly, when you play the opening bars of John Coltrane's solo in Giant Steps at 4096x speed, it sounds identical to 1x speed. I wondered if maybe it was his MIDI player cutting corners.
So I reproduced the experiment with my own program (this page) that generates the waveform explicitly, as a continuous sine wave with variable frequency [sin(Θ), where Θ = frequency*τ*t)]†. To advance theta after Δt, we add Δt(d(Θ)/d(t) = frequency*τ), using the current note's frequency.
To be exact, we should adjust the pitch [recalculate d(Θ)/d(t)] each note, no matter how short it is. Sadly, this produces no fractal effect at high speeds. Try it here with Hold... set to 0.
I wondered if the fractal effect came from taking a shortcut: suppose we only adjust the pitch after a certain number of samples have elapsed? Some Hold... settings are more fruitful. Try Hold:128, Speed:4801 (or Speed:4411, depending on your device). I think it's like when the wheels appear to move slowly or backwards in car commercials.qubtrace.js for fast waveform plots.
† τ is the true circle constant: the number of radians in one full turn (τ = 2*π).