[sdiy] saw vs ramp, audible?

[Mattias Rickardsson]

On Wed, 11 Dec 2024 at 08:26, Donald Tillman <don at till.com> wrote:

> On Dec 10, 2024, at 1:00 PM, Mattias Rickardsson <mr at analogue.org> wrote:
>
> And a sawtooth ramping up has its harmonics alternating in phase (+1,
>>> -1/2, +1/3, -1/4,...) from the fundamental.
>>>
>>
>> But are you counting from the midpoint now? Surely they must still be in
>> phase if you just flip the sawtooth backwards around its discontinuity?
>>
>>
>> (I had to think about this...)
>> Good point!  When you play it backwards the even harmonics reverse
>> polarity but the odd harmonics don't.  So yeah, it's consistent that way.
>>
>
> Not sure how you mean now, but... :-)
>
>
> Yeah, I goofed... I guess I meant to say that when you flip it backwards
> the sine components reverse polarity but the cosines don't.
>

Aha! Well, occasional goofing is allowed, normal, even recommended. Don't
stop goofing!


> So, the traditional slope-up sawtooth that steps down at t=0 is:
>
    saw = -sin(t) - (1/2)sin(2t) - (1/3)sin(3t) - (1/4)sin(4t) -...
> Which is problematic when you want to mix it with another wave because the
> fundamental is out of phase.
> You can shift it over so that it steps down halfway through, but then you
> have alternating harmonic polarities:
>     saw = sin(t) - (1/2)sin(2t) + (1/3)sin(3t) - (1/4)sin(4t) +...
> My choice, because I care about phases, is a slope-down sawtooth that
> steps up at t=0, and that's completely in phase:
>     saw = sin(t) + (1/2)sin(2t) + (1/3)sin(3t) + (1/4)sin(4t) +...
>
> That is, when you start with a description of the spectrum you want, and
> figure out the waveform from that, the result is a slope-down sawtooth.
>

This is a good thing, because slope-down sawtooth is also the one to choose
when it comes to modulation! Connecting a sawtooth to modulate amplitude,
frequency, etc - it makes more sense to use the downwards-going variant,
especially in lower frequencies, since it results in decaying amplitudes or
spectra. Similar to how real-world sounds can behave. The opposite, using a
slope-up sawtooth, results in sounds that can feel like when playing things
backwards.

I believe this modulation-polarity preference is totally unrelated to the
overtone-polarity preference that you described, so we should be thankful
that they happen to be the same. :-)

/mr
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://synth-diy.org/pipermail/synth-diy/attachments/20241219/0fbb20d1/attachment.htm>