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Comment by jhedwards | Hacker News Reader

I am little confused by the article because it sounds like they are describing "pulse width" which is a common parameter on analog and digital synthesizers to change the character of the square wave. A square wave with a low pulse width will sound thinner than one with a high pulse width, and layering square waves with different pulse widths gives you a pleasant phasing effect.

Based on some cursory research, however, it seems that duty cycle is different than pulse width, so now I am unsure if they are trying to use duty cycle variation to implement pulse width modulation (PWM) or if they are doing something else entirely.

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More precisely "pulse width" would be a time, while "duty cycle" would be a percent.

And while when going from 0% to 50% duty cycle it could be said that "a square wave with a low pulse width will sound thinner than one with a high pulse width", however, once you go past 50% duty cycle the situation reverses. So a 25% duty cycle would sound almost identical to a 75% duty cycle...the amplitudes of their Fourier transform components would be identical.

> almost identical ... components would be identical

I'm having a tough time reconciling how the former could be almost identical while the latter is identical. I guess the former involves a human listening through a speaker which has asymmetric imperfections (maybe the speaker moves outward more easily than it moves inward, or a DC offset in the signal leads to compression in the high-excursion side that doesn't exist on the low-excursion side, etc.) whereas the FFT readout doesn't necessarily have a speaker in the system at all.

25% and 75% would sound identical alone, but in a mix there often are interplays where it can create a difference. An easy way to hear it is to run two synced oscillators, say a square and a saw, with sharp attack. The resulting sound should be sufficiently different, one side would dampen the attack compared to the other. Furthermore, I think in hardware synths and those that emulate them changing pulse width can cause the module to implicitly shift the signal up or down to ensure consistent average voltage, further complicating things. I am curious what you mean by compression.

Good point. If I have 2 oscillators, and no control over their phase as they mix, then an option to choose 25% vs 75% for one of them would at least offer some variation instead of none.

As for compression, this [0] is a good intro. Most commonly it is applied to a signal deliberately to achieve a desired outcome, but I'm referring to a (generally) undesired speaker nonlinearity [1] near its maximum power handling capacity.

[0] https://en.wikipedia.org/wiki/Dynamic_range_compression

[1] https://marshallforum.com/threads/what-exactly-does-speaker-...

Thanks! I’m very familiar with the first one, but never thought of the second one actually.

Different linearity properties on the positive and negative side would be pretty bad for a speaker, but possible. In the case of a square wave, non-linearity would be identical to a fixed amplitude change though, possibly with a DC bias.

Based on the gameboy wiki I looked up, the phase of the 25% duty and 75% duty are such that they are inverse of each other, seemingly eliminating the possibility of combining the two for different waveforms.

They are synonyms in this context

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