Échelle diagrams based on the stretched periods of dipole mixed modes. The abscissae are the periods τ derived from Eq. (20), modulo the asymptotic period spacing ΔΠ₁; the ordinates are frequencies. The most prominent mixed modes, marked with filled squares, are automatically identified. In the background of the figure, the spectra are plotted twice and top to tail to make the mode identification easier, with the pressure radial orders indicated on the radial modes. From left to right we show RGB stars with different rotational splittings. Left: star seen equator-on where only m = ± 1 modes are visible and with a moderate mean core rotation; they draw two ridges from which the rotation frequency δν_rot can be derived. Middle: star seen with an inclination such that all three components of the rotational multiplets are visible and with a moderate mean core rotation. Right: star seen equator-on; as a consequence of the large mean core rotation, the ridges m = ± 1 intersect.