Hi, I'm currently building a synthesizer with pd and I have a question.

As I play notes, I found that lower pitches sounds quieter than higher ones.

I think that's why most synthesizers have a feature called "key follow" in order to correct this issue. right?

I wonder if there's any proper method or equation to correct this.

Any suggestions?

Thank you in advance!

Key follow refers to things like a filter cutoff adjusting to the key being pressed. Without key follow, if anything lower notes would actually sound louder, depending on what the cut-off of the low-pass filter is. To be honest, most, if not all, the synths I've used suffer from this same problem, and things like key follow can be used to fix it, if needed. Key follow is typically used to make the instrument sound more natural or continuous across pitches, though.

There are few explanations for why this is occurring that I can think of off the top of my head, and they the may not all apply but can be helpful for dealing with it. The first one is simply speakers. Cheap speakers are terrible at reproducing low end. So if you're relying on consumer computer speakers instead of pro audio monitors, you can expect this to be an issue.

Another thing to consider is we actually don't hear lower frequencies as well as higher frequencies anyway, though the discrepancy is flattened out more at higher volumes, as illustrated in the Equal-Loudness Contour. This is likely the main reason why you're noticing it, and it's why it is common to all synths. If you were to attempt to "correct" it, this would probably be a starting point.

Also, if you're using oscillators that aren't band-limited, then higher pitches are going to have louder harmonics that are aliasing, and they may fall in that sensitive range on the Equal-Loudness Contour.

Thank you for your detailed answer Maelstorm!

I think my problem mostly comes under your first explanation.

Previously, I was only testing out my synth with earphones came with my iPhone.

I just tried monitoring it again with my 'DT770', and lower pitches certainly sounded louder than before.

But still, when I played lower notes and higher notes(e.g 2octaves higher) together, It seemed that higher notes sound clearer and louder than lower ones.

Maybe it could be because of the 'Equal-Loudness Contour' you've mentioned?

I wonder how most commercial synths I've used (including hardware/software) seemed sounding so natural in all pitch ranges even when I used cheap earphones.