Refutation of All Heresies 4.11.2
Authorship disputed: The work names no author. Book 1 was long printed among Origen's works as the Philosophumena; after books 4–10 were found in a manuscript from Mount Athos (published 1851), it was assigned to Hippolytus, the usual view today, though some scholars ascribe it to another Roman writer of the same circle. Books 2 and 3 are lost, and book 4 lacks its beginning.
Summary: Only double and triple intervals preserve harmony.
Greek text · Duncker–Schneidewin, 70
Οἱ δὲ ἐναρμόνιοι καὶ σύμφωνοι λόγοι σώζονται, καθάπερ προειρήκαμεν, τοῖς διπλασίοις καὶ τριπλασίοις διαστήμασιν.
English · Claude translation
And the harmonious and concordant ratios are preserved, as we said before, by the double and triple intervals.
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Hippolytus, Haer. 4.11.2 (trans. Sophia Scriptura, https://sophiascriptura.com/fathers/hippolytus-refutatio/4/11/2/).
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Plain text
Hippolytus, Haer. 4.11.2 (trans. Sophia Scriptura, https://sophiascriptura.com/fathers/hippolytus-refutatio/4/11/2/).
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