Keep only the odd harmonics with 1/(2k-1) amplitudes and the stack becomes a hollow square wave, the clarinet-like timbre behind chiptune leads.
In the world
A clarinet is a stopped pipe: physics allows only odd harmonics to resonate inside its bore, which is why it sounds hollow and woody instead of bright and brassy.
A square wave contains only odd harmonics (1, 3, 5, 7, 9...) with amplitudes falling as 1/(2k-1). Remove every even harmonic from your saw rig and the tone hollows out into something harsh and wooden, like striking a hollow log. The square makes for a powerful bass note but stands out even more when you play it high - those odd harmonics give it presence across the register.
A triangle is also odd-only, but with amplitudes falling as 1/(2k-1)², which is much steeper. Notice how the triangle sounds like the square but far more restrained? Same odd-harmonic family, much steeper rolloff - that is why triangles sound softer and more flute-like even though they are built from the same odd ladder.
Did you know?
The clarinet is nature's square wave generator. Because it acts as a stopped pipe (closed at the mouthpiece end), only odd-numbered modes can resonate inside its bore. This is why a clarinet can sound an octave lower than a flute of the same length - it skips every other harmonic.
Explore
Eight columns stand in a row - one per harmonic. The odd columns (1, 3, 5, 7) glow warm; even ones are dark. Click any column to toggle it. Drag up or down to set its amplitude. Try the SQUARE and TRIANGLE presets at the bottom to see how the same odd harmonics create two very different timbres just by changing their rolloff.
Compare the square to the saw you built in the previous step. It sounds hollower, woodier. That is the even harmonics you removed.