Stobaeus, Volume I

Name: Stobaeus, Volume I
Author: John Stobaeus

Greek with an independent English translation.

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Stobaeus, Volume IBook I Chapter 21 · I.21.7d.3–I.21.8

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English Page · Branch 259 of 879

Book I Chapter 21 · I.21.7d.3–I.21.8

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Ancient Greek

p. 514

7d ⟨Τοῦ αὐτοῦ⟩ · 3

I.21.7d.3

Ἁρμονίας δὲ μέγεθός ἐντι συλλαβὰ καὶ δι᾽ ὀξειᾶν· τὸ δὲ δι᾽ ὀξειᾶν μεῖζον τᾶς συλλαβᾶς ἐπογδόῳ· ἐντὶ γὰρ ἀπὸ ὑπάτας ἐπὶ μέσαν συλλαβά, ἀπὸ δὲ μέσας ἐπὶ νεάταν δι᾽ ὀξειᾶν, ἀπὸ δὲ νεάτας ἐς τρίταν συλλαβά, ἀπὸ δὲ τρίτας ἐς ὑπάταν δι᾽ ὀξειᾶν· τὸ δ᾽ ἐν μέσῳ μέσας καὶ τρίτας ἐπόγδοον· ἁ δὲ συλλαβὰ ἐπίτριτον, τὸ δὲ δι᾽ ὀξειᾶν ἡμιόλιον, ⟨τὸ⟩ διὰ πασᾶν δὲ διπλόον.

7d ⟨Τοῦ αὐτοῦ⟩ · 4

I.21.7d.4

Οὕτως ἁρμονία πέντε ἐπόγδοα καὶ ⟨δύο⟩ διέσιες, δι᾽ ὀξειᾶν δὲ τρία ἐπόγδοα καὶ δίεσις.

8 ⟨Τοῦ αὐτοῦ⟩

I.21.8

Τὸ πρᾶτον ἁρμοσθέν, τὸ ἕν, ἐν τῷ μέσῳ τᾶς σφαίρας ἑστία καλεῖται.

Stobaeus, Volume I: Book I Chapter 21

p. 515

7d ⟨The same author⟩: The musical intervals

I.21.7d.3

The extent of the octave is a fourth and a fifth; the fifth exceeds the fourth by a tone of nine to eight. For from hypatē to mesē is a fourth, from mesē to neatē a fifth, from neatē to tritē a fourth, and from tritē to hypatē a fifth. The interval between mesē and tritē is nine to eight. The fourth is four to three, the fifth three to two, and the octave two to one.⁶⁴⁷

7d ⟨The same author⟩: Tones and remainders

I.21.7d.4

Thus the octave comprises five tones of nine to eight and ⟨two⟩ dieses; the fifth comprises three tones of nine to eight and one diesis.⁶⁴⁸

8 ⟨The same author⟩: The hearth

I.21.8

The first thing fitted together, the one at the center of the sphere, is called the hearth.⁶⁴⁹

647.The traditional terms syllaba and di’ oxeian mean the fourth and fifth here; harmonia and dia pasān both designate the octave. Hypatē and neatē are its lower and upper notes, with mesē and tritē between them. The ratios combine by multiplication: (4/3) × (3/2) = 2. The supplied Greek article before dia pasān has no separate English equivalent.

648.Here a diesis is the small remainder needed to complete these intervals, with ratio 256:243, not half of an equal-tempered modern tone. “Two” is supplied from the parallel in Nicomachus. Wachsmuth does not add the further sentence about the fourth that some editions include. Compare Huffman, “Philolaus,” §2.2, on fragment 6a.

649.Philolaus fragment 7. The hearth is the central fire, not the earth or sun. The wording links its formation with the fitting together discussed above. “The one” is retained without turning it into an explicitly named abstract first principle.

About This Reading Edition

Stobaeus gathered Greek philosophy and poetry for his son Septimius. Volume I presents the dedication testimony, On Arithmetic, Book I through chapter 60, and the ancient contents of all four books. This complete bilingual edition includes an introduction and 2,117 explanatory notes.

Historical Text and Translation

The Greek follows Curt Wachsmuth’s 1884 Volume I, checked against the supplied scan. Gaps, lost-chapter headings, and uncertain attributions remain visible. Chapter 2 includes a labeled proposed reconstruction. The appendix outlines Books I–IV; the full texts of Books II–IV are outside this volume. Reader pages preserve the companion PDF’s numbering.

About Diotimos Editions

Diotimos Editions prepared this independent English translation directly from the Greek. Prose and verse retain their distinct forms, with mixed passages preserving their quoted verse. Every passage is paired with its Greek and identified by the edition’s reference number. All 2,117 notes remain linked to their passages, with continuous numbering across the introduction and text.

Rights

Stobaeus’s ancient Greek work and Wachsmuth’s 1884 printing are in the public domain. The independent English translation, introduction, and explanatory notes are © 2026 Diotimos Editions. The complete supplied edition is available as PDF, EPUB, Word, and Markdown. The PDF retains the fixed page locations used by the companion lexicon.