Per my understanding, when playing a certain pitch, say 440 Hz (middle C), the VCOs will produce their corresponding waveforms (say sawtooth) at that frequency. Because of the characteristics of the waveform, some harmonics will be present, e.g sawtooth includes all integer harmonics of the fundamental frequency. These are then passed through a VCF and filtered according to the filter's parameters.
Now say the VCF is a low-pass one with a cutoff of 1000 Hz, then won't it produce the same sound regardless of the fundamental frequency? e.g what is filtered should be the same regardless of the input signal. If we go up on octave to 880 Hz, the only difference is that the odd harmonics of 440 Hz frequency are no longer present (but the even ones are all there because 880 = 2 x 440) but still anything below 1000 Hz should be equally filtered for both pitches, meaning these notes should sound more or less the same. But this is clearly not the case, otherwise the presence of the filter would defeat the purpose of having a full-size keyboard.
What am I missing?