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We present a dynamical model of the avian respiratory system and report measurements of its variables in normally breathing canaries (Serinus canaria). By fitting the model to the dynamics observed during normal respiration, we show that birds breathe in a parameter region where their respiratory system operates at a resonance. This implies that the tidal volume is maximized at the observed respiratory rate. During song, we show that our model accurately synthesizes air sac pressure dynamics using recorded expiratory muscle activity as input. We discuss how the interaction between neural instructions, the biomechanics, and the environment constraint behavior. Overall, these results support an emerging view in which several life supporting systems are strikingly fine-tuned to the sources of energy that powers them.