This work introduces a new music generation system, called AffectMachine-Classical, that is capable of generating affective Classic music in real-time. AffectMachine was designed to be incorporated into biofeedback systems (such as brain-computer-interfaces) to help users become aware of, and ultimately mediate, their own dynamic affective states. That is, this system was developed for music-based MedTech to support real-time emotion self-regulation in users. We provide an overview of the rule-based, probabilistic system architecture, describing the main aspects of the system and how they are novel. We then present the results of a listener study that was conducted to validate the ability of the system to reliably convey target emotions to listeners. The findings indicate that AffectMachine-Classical is very effective in communicating various levels of Arousal ($R^2 = .96$) to listeners, and is also quite convincing in terms of Valence (R^2 = .90). Future work will embed AffectMachine-Classical into biofeedback systems, to leverage the efficacy of the affective music for emotional well-being in listeners.