---
title: "Hagiopolitan Octoechos"
chunk: 6/11
source: "https://en.wikipedia.org/wiki/Hagiopolitan_Octoechos"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:11:13.278479+00:00"
instance: "kb-cron"
---

== Question of intervals and their transposition ==
The exact proportions which divided a tetrachord, had never been a subject of Greek medieval treatises concerned about Byzantine chant. The separation between the mathematical science harmonikai ("harmonics") and chant theory gave space to various speculations, even to the assumption that the same division was used as described in Latin music theory, operating with two diatonic intervals like tonus (9:8) and semitonium (256:243).  Nevertheless, some treatises referred the tetrachord division into three intervals called the "major tone" (ὁ μείζων τόνος) which often corresponded to the prominent position of the whole tone (9:8), the "middle tone" (ὁ ἐλάσσων τόνος) between α and β, and the "small tone" (ὁ ἐλάχιστος τόνος) between β and γ which was usually a much larger interval than the half tone, and this division was common among most divisions by different ancient Greek theorists that were mentioned by Ptolemy in his Harmonics. Before Chrysanthos' Theoretika (the Eisagoge was simply an extract, while the Theoretikon mega was published by his student Panagiotes Pelopides), exact proportions were never mentioned in Greek chant theory. His system of 68 commata which is based on a corrupt use of arithmetics, can be traced back to the division of 12:11 x 88:81 x 9:8 = 4:3 between α and δ.