I need to update my own post! I found the books that the previous owner had – they are Buchtel method book for C recorder, Baroque system, Soprano and tenor. I ggogled Buchtel tenor recorder and it looks pretty close to what I have. After a bit of struggling trying to completely cover the bottom un-levered hole, it does play C when all the holes are covered. So I think my confusion as to what this really is was complicated by my small hands and deficient finger-pad fingers! This is why I really can’t play violin or guitar – I don’t have enough padding on my fingertips.