[sdiy] saw vs ramp, audible?

[Donald Tillman]

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."

"But it doesn't look the same as my drawing."

"Oh good grief, you just scribbled that in a drunken haze.  Do you even own a saw?  Were you holding it upside down or in your left hand or something?  Sheeshe."

  -- Don
--
Donald Tillman, Palo Alto, California
https://till.com