  The study of contemporaneous variations of the continuum flux and emission
lines is of great importance to understand the different astrophysical
processes at work in T Tauri stars. In this paper we present the results of a
simultaneous $BVRI$ and H$\alpha$ photometric monitoring, contemporaneous to
medium-resolution spectroscopy of six T Tauri stars in the Taurus-Auriga star
forming region. We have characterized the H$\alpha$ photometric system using
synthetic templates and the contemporaneous spectra of the targets. We show
that we can achieve a precision corresponding to 2$-$3 \AA\ in the H$\alpha$
equivalent width, in typical observing conditions. The spectral analysis has
allowed us to determine the basic stellar parameters and the values of
quantities related to the accretion. In particular, we have measured a
significant veiling only for the three targets with the strongest H$\alpha$
emission (T Tau, FM Tau, and DG Tau). The broad-band photometric variations are
found to be in the range 0.05$-$0.70 mag and are often paired to variations in
the H$\alpha$ intensity, which becomes stronger when the stellar continuum is
weaker. In addition, we have mostly observed a redder $V-I$ and a bluer $B-V$
color as the stars become fainter. For most of the targets, the timescales of
these variations seem to be longer than the rotation period. One exception is T
Tau, for which the broad-band photometry varies with the rotation period. The
most plausible interpretation of these photometric and H$\alpha$ variations is
that they are due to non-stationary mass accretion onto the stars, but
rotational modulation can play a major role in some cases.
