The signal needs to cross the 20 mV input hysteresis band before triggering occurs. This hysteresis prevents the input from self-oscillating and reduces its sensitivity to noise. Other names for trigger hysteresis are "trigger sensitivity" and "noise immunity". They explain the various characteristics of the hysteresis.
Fig. 3-10 and Fig. 3-12 show how spurious signals can cause the input signal to cross the trigger or hysteresis window more than once per input cycle and give erroneous counts.
Fig. 3-13 shows that less noise still affects the trigger point by advancing or delaying it, but it does not cause erroneous counts. This trigger uncertainty is of particular importance when measuring low frequency signals, since the signal slew rate (in V/s) is low for LF signals. To reduce the trigger uncertainty, it is desirable to cross the hysteresis band as fast as possible.
Fig. 3-14 shows that a high amplitude signal passes the hysteresis faster than a low amplitude signal. For low frequency measurements where the trigger uncertainty is of importance, do not attenuate the signal too much, and set the sensitivity of the counter high.
In practice however, trigger errors caused by erroneous counts (Fig. 3-10 and Fig. 3-12) are much more important and require just the opposite measures to be taken.
To avoid erroneous counting caused by spurious signals, you need to avoid excessive input signal amplitudes. This is particularly valid when measuring on high impedance circuitry and when using 1 MW input impedance. Under these conditions, the cables easily pick up noise.
External attenuation and the internal 10x attenuator reduce the signal amplitude, including the noise, while the internal sensitivity control in the counter reduces the counter's sensitivity, including sensitivity to noise. Reduce excessive signal amplitudes with the 10x attenuator, or with an external coaxial attenuator, or a 10:1 probe.