Putting a buffer circuit in-between will let the oscillator ... turning the triangle wave into a sawtooth. How does that work? Well, instead of charging and discharging the timing capacitor ...

The output, an exponentially-decaying sawtooth having constant amplitude ... Figure 3 shows the key waveforms. Figure 3 Waveforms from the circuit in Figure 2, at both extremes of its two-octave span.