Phase Offtset Bandlimited Saw Wave I'm able to make a standard band limited saw wave, but at some point in the past, I remember reading that if you phase offset the sinusoids, you get a different looking wave form that sounds the same.

Trying to implement this by offsetting the phase 270 degrees, I'm seeing a different looking wave form but it doesn't quite sound the same.  It has less volume and sounds a little less bright.

Am I remembering correctly / implementing correctly?  Here's the saw and "other" wave below:



Thanks!
Have you normalized the waveforms differently? The lowest point of the phase-shifted saw should be at amplitude -2 ln(2) / pi = -0.44 if the amplitude of the saw is normalized to -1 .. 1. The positive peak of the phase-shifted saw approaches infinity as you increase the bandwidth. So you could also have a clipping problem. Nonlinearities of the physical world affect the phase-shifted saw more strongly. The two waveforms have the same power spectrum and "complex envelope", but human hearing is more complex and may be able to detect some difference.