(Note: Some of the references below are copyrighted. Selected parts of publications are reproduced here at low quality for educational purposes only. I recommend buying the books as they are very valuable to have anyway).

Boudouris says that ecclesiastical pieces can be chanted both "by-beat"("kata xronon") and "by-rhythm" ("kata rhythmon"). He argues that although pieces can be chanted beat by beat (monosimos), however, the pieces are not properly executed until the experienced psalti adds the rhythmic element in the interpetation. That is to aggregate the beats ("xronous") of the piece into groups ("podes") to form rhythms (as he says elsewhere in the definition of rhythm). He went on to say that the Patriarchal psaltai are exemplary for chanting by-rhythm and not by-beat.

Along the same lines is Psaxos' essay (read to the audience of the Musical Association of Constantinople more than 100 years ago, can be found on the analogion). Psaxos admits that was taught Byzantine music using "by-beat" counting, however his whole essay is an argument about why that was wrong and presents various examples to support "by-rhythm" chanting..