We engineered an interactive music system that influences a user's breathing rate to induce a relaxation response. This system generates ambient music containing periodic shifts in loudness that are determined by the user's own breathing patterns. We evaluated the efficacy of this music intervention for participants who were engaged in an attention-demanding task, and thus explicitly not focusing on their breathing or on listening to the music. We measured breathing patterns in addition to multiple peripheral and cortical indicators of physiological arousal while users experienced three different interaction designs: (1) a "Fixed Tempo" amplitude modulation rate at six beats per minute; (2) a "Personalized Tempo" modulation rate fixed at 75\% of each individual's breathing rate baseline, and (3) a "Personalized Envelope" design in which the amplitude modulation matches each individual's breathing pattern in real-time. Our results revealed that each interactive music design slowed down breathing rates, with the "Personalized Tempo" design having the largest effect, one that was more significant than the non-personalized design. The physiological arousal indicators (electrodermal activity, heart rate, and slow cortical potentials measured in EEG) showed concomitant reductions, suggesting that slowing users' breathing rates shifted them towards a more calmed state. These results suggest that interactive music incorporating biometric data may have greater effects on physiology than traditional recorded music.