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Theories of spiral structure traditionally separate into tight-windingLin-Shu spiral density waves and the swing-amplified material patterns ofGoldreich & Lynden-Bell and Julian & Toomre. In this paper we consolidate thesetwo types of spirals into a unified description, treating density waves beyondthe tight-winding limit, in the regime of shearing and non-steady open spirals.This 'shearing wave' scenario novelly captures swing amplification that enablesstructure formation above conventional Q thresholds. However, it alsohighlights the fundamental role of spiral forcing on the amplification processin general, whether the wave is shearing or not. Thus it captures resonant andnon-resonant mode growth through the donkey effect described by Lynden-Bell &Kalnajs and, critically, the cessation of growth when donkey behavior is nolonger permitted. Our calculations predict growth exclusive to trailing spiralsabove the Jeans length, the prominence of spirals across a range oforientations that increases with decreasing arm multiplicity, and a criticalorientation where growth is fastest that is the same for both modes andmaterial patterns. Predicted structures are consistent with highly regular,high-multiplicity gaseous spur features and long filaments spaced close to theJeans scale in spirals and bars. Applied to stellar disks, conditions favor lowmultiplicity (m<5) open trailing spirals with pitch angles in the observedrange $10 deg$<$i_p$<$50 deg$. The results of this work serve as a basis fordescribing spirals as a unified class of transient waves, abundantly stimulatedbut narrowly selected for growth depending on local conditions.

Bottom's Dream and the amplification of filamentary gas structures and stellar spiral arms