The Sun reveals itself in the 386–2.439-nHz (1-mo–13-yr) band of polar (φsun>|70°|) fast (>700 km s^−1) solar wind’s decade-scale dynamics as a globally completely vibrating/resonating magnetoalternator and not just a proverbial engine anymore. Thus North–South separation of hourly-averaged, 1994–2008 Ulysses samplings of the <10 nT polar winds in ~1.6·10^7 –2.5·10^9-erg energies revealed spectral signatures of a ≥99%-significant Sun-borne global differential resonant activity, verified across disparate data. Confirming the Alfvén’s view on a Sun globally resonating under its Ps=~11-yr Schwabe mode, this Alfvén (a-mode) resonance (AR) comprising Rossby-like r-modes and cavity-confined R-modes, is governed by Ps at a remarkable ~25% field variance northside, a ~9-yr degeneration of Ps at ~20% southside, and a ~10-yr degeneration of Ps under equatorial mixing. While composing the PG∈~(88–100-yr) Gleissberg cycle, the 9–10–11-yr sector coupling also co-triggers AR, Pi=Ps/i, i=2…n, n ∈ א, imprinted in the fast winds at least to the order n=100. The overwhelming (anisotropy moderating) and deterministic (with Φ>>12 fidelity) AR is accompanied by a most useful symmetrical antiresonance, P(-), whose both N/S tailing harmonics P(-)17 are the well-known 154-day Rieger period, from which the couplings-freed Rieger resonance sprouts as wind’s own. Thus the Sun is a typical, ~3-dB-attenuated ring system of differentially rotating and contrarily vibrating conveyor belts and layers, with a continuous spectrum of modes, patterns complete in both parities, and resolution better than 81.3 nHz (S) and 55.6 nHz (N) in lowermost frequencies (≲2μHz in most modes). Unlike a resonating car engine that tries but fails to separate its fixed casing, the resonating free Sun exhausts the wind in a shake-off alongside the rotational axis. AR advances standard stellar models, agrees with laboratory experiments for enhanced studies of the Sun interior and heliosphere, and can explain the million-degree corona and solar abundance.