An Oxyrhynchus Fragment on Harmonic Theory

The tattered remains of a few paragraphs of a work on harmonic theory were published in 1986 as P. Oxy. LIII.3706, with a careful commentary by M. W. Haslam. There are six fragments. Four of them are too small for any substantial sense to be recovered; and while fr. 2 and the second column of fr. 1 allow us to pick out significant words and phrases here and there, the remnants of these columns are very narrow, and the line of reasoning seems inaccessible. Musicological analysis must focus on the first column of fr. 1. There is little enough even of that, and in attempting a relatively detailed interpretation I shall have to be rather less cautious than Haslam quite properly was. But I think that something can be made of it without stretching speculation too far, and if I am right the piece is of some genuine interest. Here are the two versions of the text that Haslam prints. The first records what is decipherable on the papyrus itself, while the second represents a partial reconstruction, restoring word-divisions and some of the missing letters