[sdiy] saw vs ramp, audible?

[Tom Wiltshire]

> On 9 Dec 2024, at 18:02, Donald Tillman <don at till.com> wrote:
> 
> On Dec 9, 2024, at 8:47 AM, Tom Wiltshire <tom at electricdruid.net> wrote:
>> 
>> On 8 Dec 2024, at 22:43, Donald Tillman <don at till.com> wrote:
>>> 
>>> Note that a sawtooth ramping down has all the harmonics in phase with the fundamental.
>>> 
>>> And a sawtooth ramping up has its harmonics alternating in phase (+1, -1/2, +1/3, -1/4,...) from the fundamental.
>> 
>> That's an odd way to look at it, since it produces a waveform which is half-a-cycle out of phase. In my view, it's the half-cycle-out-of-phase that leads to the harmonics being alternately flipped, not the changed slope.
> 
> (Hey, "an odd way to look at it" is exactly why I'm here.)
> 
> Out-of-phase with respect to what?
> 
> What should the phase of a sawtooth wave be?  The ramp-down-sawtooth says, "Oh sure, the phase reference is the point where all my constituent sine waves are crossing zero, flying from negative to positive, all at the same time, slamming the wave up.  Nothing else makes sense.  And this happens to be exactly the same as summing sinx + 1/2 sin2x + 1/3 sin3x +...  So it's a big win-win."

Out of phase with respect to the sawtooth that we started with, surely!

If you have an ramp-down that starts at the vertical point in the waveform, then your ramp-down should start at the same point, right? Otherwise you're introducing another element which might account for the difference.

That's why I don't like the formulation with the inverted-alternate harmonics. Yes, it's a ramp-up instead of a ramp-down, but it starts at the zero crossing halfway up the ramp, not on the vertical edge. Sure we could use that for the experiment instead, but in that case, we could make a ramp-down version to match by flipping all *those* harmonics instead (so negatives become positives and vice versa). That'd still be fair!

So many ways to make sawtooth waveforms...