The received text of the fourth problem of the nineteenth book of the pseudo-Aristotelian Problêmata (917b35–918a2) begins:

This is a continuation of the previous problem, which concerns the difficulty of singing parhypatê (the second-lowest note of the Greek scalar system, which stands a small interval [δίϵσις]Footnote ¹ above hypatê.) Consequently, one could translate it as:

Scholars tend to agree that the quotation’s final clause requires emendation, but there has emerged no consensus as to how. Ruelle emends σύστασιν to σύντασιν: ‘ascending is easy after tension’.Footnote ² The resulting meaning seems to be that singing hypatê is easy because it is relaxed, and singing parhypatê is difficult because it is accompanied by tension; consequently, it is relatively easier to follow parhypatê with any higher note. By associating hypatê with the voice’s relaxing and parhypatê with its tension, this interpretation explains the discrepancy in ease of singing the two notes. Yet it also reduces to irrelevance the text’s assertion that ‘ascending is easier’: the mere association of parhypatê with tension answers the question sufficiently.

Jan’s approach addresses that shortcoming: accepting Ruelle’s σύντασιν, he goes further, emending ἄνω βάλλϵιν to ἀναχαλᾶν: ‘Is it because hypatê [is sung] with relaxation [of the voice], and, at the same time, relaxing is easy after tension?’Footnote ³ The result likewise suggests a correlation of relaxation with hypatê and tension with parhypatê, but it implicitly reduces the scope of discussion to just those two notes: rather than it being easy to ascend after tension, instead it is easy to return to a state of relaxation, viz. hypatê.

Jan credits this interpretation to the eminent physicist Hermann von Helmholtz, who discussed this passage in his widely read Lehre von den Tonempfindungen. Helmholtz’s concern is whether Ancient Greek scales had a referential pitch, like the tonic of modern tonality, and he plumbs the Problêmata for pertinent details. After surmising that Greek melodies concluded on hypatê, Helmholtz loosely paraphrases our passage and then interprets it thusly:

Evidently Helmholtz approached the passage wanting to find a proto-tonal descending motion from parhypatê to hypatê, and Jan devised an emendation to support Helmholtz’s desideratum.Footnote ⁵

Jan’s emendation need not entail such a questionable universalizing impulse, however. Forster adopts Jan’s version of the text, but interprets it as asking ‘Why is it easier to sing the same interval downwards than upwards?’Footnote ⁶ Forster is fully aware, however, that this interpretation makes little sense in the context of the diatonic genus, in which parhypatê lies a semitone above hypatê:

It is certainly possible that the pseudo-Aristotelian author had the enharmonic genus in mind when composing this problem, but nothing in the surrounding context confirms that possibility.Footnote ⁸ Furthermore, an interpretation that requires restricting the passage’s range of validity to the enharmonic genus is undesirable, particularly given that the enharmonic genus appears to have become largely obsolete by the late fourth century.Footnote ⁹ Why would authors concern themselves with the relative ease of singing an interval that no one sings?Footnote ¹⁰ In short, Forster has not satisfactorily addressed the troubling objection to his interpretation of why it should be harder to ascend from hypatê to parhypatê than to descend.

Instead of the aforementioned alterations to the text, I propose emending σύστασιν to ἀπόστασιν. This results in the following:

The question no longer benefits from being reinterpreted, like Jan does, as asking why descending from parhypatê to hypatê is easier than the reciprocal ascent; rather, it simply is why singing hypatê is easier than the note just a small interval above, viz. parhypatê. In my interpretation the proposed answer seeks to explain the ease of singing a note via the ease of departing from that note to another. (Since hypatê is the scalar system’s lowest note, moving to any other note necessarily entails ascending, τὸ ἄνω βάλλϵιν.) Furthermore, not only is hypatê relaxed, but since it is also one of the fixed notes in the scalar system (regardless of genus), many of the system’s other notes are separated from hypatê by concordant intervals that are easy to sing. Parhypatê, by contrast, is a movable note, and leaping from it to most other notes requires more unusual intervals that would be more difficult to sing.

My emendation also results in a different construal of the passage’s final clause. The start of the sentence, ἢ ὅτι μϵτ’ ἀνέσϵως ἡ ὑπάτη, clearly pertains to the opening question of why singing hypatê is easy. Ruelle evidently understood the sentence’s continuation, ἅμα μϵτὰ τὴν σύντασιν ἐλαϕρὸν τὸ ἄνω βάλλϵιν, as proffering the complementary explanation for parhypatê, which is why he emended σύστασιν in order to indicate a sense of tension that contrasts with hypatê’s relaxation. Yet the crucial adjective in the last clause is ἐλαϕρόν, which strongly suggests that the clause continues the preceding explanation of why singing hypatê is easy. True, emending σύστασιν to ἀπόστασιν adds no new meaningful content (since departing from a note is necessarily entailed by ascending from it), but the emendation makes more sense than σύστασιν does and does not steer the final clause towards pertaining to parhypatê, which would sit poorly with its characterization as ἐλαϕρόν. The resulting interpretation of passage does leave implicit why it is harder to ascend from parhypatê; considering, however, that the continuation of problem four devolves into an extremely corrupted state, it is entirely possible that the original explanation pertaining to parhypatê has been lost.

Emending σύστασιν to ἀπόστασιν obviates the temptation to follow Jan and edit an ascent (τὸ ἄνω βάλλϵιν) into a descent (τὸ ἀναχαλᾶν). It also better accounts for τὸ ἄνω βάλλϵιν than Ruelle’s emendation does. Furthermore, my emendation is supported by the Latin tradition. It seems likely that Bartholomew of Messina consulted a Greek manuscript that read ἀπόστασιν when he prepared his Latin translation, the oldest extant translation of the text:

Of the fifty-two extant manuscripts of Bartholomew’s translation, eighteen, including all those from what Coucke calls the ‘Independent Tradition’ (which he identifies as ‘a superior branch of the tradition’) read dimissionem.Footnote ¹² In sum, not only does my newly proposed emendation lead to a stronger interpretation of the text, it also is supported by the evidence of the Latin manuscript tradition.