This paper we report on an interdisciplinary project for modelingGreek chant with real-time vocal synthesis. Building on previousresearch, we employ a hybrid musical instrument: Phonodeon(Georgaki et al. 2005), consisting of a MIDI-accordeon coupled toa real-time algorithmic interaction and vocal synthesis engine.The synthesis is based on data provided by the AOIDOS programdeveloped in the Department of the Computer science of theUniversity of Athens, investigating Greek liturgical chantcompared to bel canto singing. Phonodeon controls expressivevocal synthesis models based on formant synthesis andconcatenated filtered samples. Its bellows serve as hardwarecontrol device that is physically analogous to the human breathingmechanism [georgaki, 1998a], while the buttons of the right handcan serve multiple functions. This paper focuses on a particularaspect of control, namely that of playing in the traditional nontemperedand flexible interval structure of Greek modes (ήχοι:echoi) while using the 12-semitone piano-type keyboard of theleft hand. This enables the musical exploration of the relationshipbetween the spectral structure of the vocal timbre of Greek chantand characteristic intervals occuring in the modal structure of thechant. To implement that, we developed techniques forsuperimposing interval patterns of the modes on the keyboard ofthe phonodeon. The work is the first comprehensive interactivemodel of antique, medieval and modern near-eastern tunings. Thetechniques developed can be combined with techniques for othercontrol aspects, such as timbre and vocal expression control,phoneme or (expressive/ornamental/melodic pattern, inflection)sequence recall and combination, data record on/off, or others,which form part of the phonodeon project. This research can findapplications in many computer music fields such asalgorithmically controlled improvisation, microtonal music, musictheory and notation of (algorithmic/computerized) real-timeperformance, and computer modeling of experimental or nonwesternmusical styles.