1. Introduction. Sources of difficulty in the investigation.–II. Dr. Monro′s pitch theory. The passage in Heraclides. Supplementary evidence from the Problems.–III. Prof. Macran′s theory. Evidence against this theory. Prof. Macran′s answer to this evidence. Further objections. Criticism of the evidence in favour of Prof. Macran′s theory.–IV. Prof. Cook-Wilson′s theory. Platonic and Aristotelian evidence against Dr. Monro. Objections to this theory.–V. Recapitulation. Statement of the antinomies in the evidence.–VI. Conclusion. The nucleus of certainty. The Greek, as contrasted with the modern, musical sense.