Circular Waveform

Here’s my circular waveform, a pleasant sounding compromise between triangle and square.

file: w13_circularMM.ws6
url: Upload files for free - w13_circularMM.ws6 -
md5sum: 0b3444a915cc454ca773970401251f5d



I’ll have to check this out when I get my synth. I have been constructing single cycle waveforms based on the squircle formula discussed here:

Basically can programatically give you waveform shapes between circular and square and all points in between.

The Super Ellipse formula also yields some interesting waveform shapes

For example


BTW, how did you go about bandlimiting your waveform (i.e. getting rid of frequency content above 512Hz)?

Thanks, that looks interesting.

To be honest, I didn’t do any bandlimiting, as the waveform is so regular.

But I found this post from UDO Support and indeed they recommend to band limit custom waveforms at Nyquist/4 (which is 512Hz only when your sampling rate is 1sample/s).

Just for fun, then, I applied band limiting in Audacity. Here’s how I did it:

  1. Load the waveform file at sample rate 100Hz (for some reason, the minimal rate in my ver. of the software). The audio is now 40.96s long.
  2. We want to remove any content above 512/40.96 Hz = 12.5Hz (I applied a 36dB/octave LPF at 12Hz)

Here’s a screenshot from Audacity. The first track is the original waveform, the second is the band limited one and the third is the difference between the two (the scale is in dB!):

As you can see, the difference is tiny, and when I loaded the modified waveform onto Super 6, and compared it with the previous one, I couldn’t hear any difference – I mean, it still sounds absolutely awesome! My oscilloscope and spectrum analyser didn’t show anything significant either.

Here’s the new version:
filename: w13_circularMM_bl.ws6
md5sum: 49d070651de5a6061a432d154744ea4c


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any chance you could re-up this? I’m curious how it sounds and the link has expired.


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Thank you very much for sharing your progress and essays.
I have tried the wave and I like it, it has the sound of a square wave with a shine that makes it special.
With your permission I keep it in my UDO !!

Of course. Enjoy it!

Mmm, download expired. Could you reup it again?

Sorry, haven’t checked the forum for some time. Here’s the waveform:


very interesting and geeky (I’m a geek, I admit)
Just listened to the raw wave and it sounds indeed bit like halfway between a square and a triangle.
beyond simply looking good on a oscilloscope, what is your typical use of such wave ?
any synthesic target in mind ?

Hi Miller, Otison, Could you reup it ? Thanks !

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lol this expired so many times? Can’t you just upload it the this forum and not a 3rd party?


Sorry but I feel a bit dumb. I cannot understand the math behind it. I mean, it the sample is 44100 hz shouldn’t I cut above 5512,5 hz? And I agree with you (only with irregular waveform) because you’d introduce latency, so zero crossing points might shift.