Although Arrigo Boito devoted 56 years to the composition of his Nerone, at his death the opera was still incomplete; Arturo Toscanini bustled to refine and finish the last act for the work’s premiere at La Scala on 1 May 1924.
Since the figure of the mad psychopath Nero is best remembered in the collective imagination as he plays and sings while observing the Great Fire of Rome, for the first staging of the opera a true kithara was made by the lute maker Piero Parravicini at the Milan workshop of Antonio Monzino e Figli; today the instrument is on display at the Civico Museo degli Strumenti Musicali in Milan.
This according to “‘Or che i Numi son vinti, a me la cetra, a me l’altar!’: Kithara constructed for the premiere of Arrigo Boito’s Nerone” by Donatella Melini (Music in art XL/1–2  pp. 267–72).
Above, the instrument in question (click to enlarge); below, the scene referred to in the article’s title.
Although the notion of pitches being relatively high or low was well-established by the first century C.E., when Pliny used the terms summus, medius, and imus, there is no evidence that earlier Greek theorists espoused this metaphor. The terms νήτη (nētē, “down-located”) and ὑπάτη (hypatē, “up-located”) were used, but they referred to the physical placement of kithara strings, not to a spatial concept of pitch; in fact, the higher the pitch in our terms, the further down-located it was on the instrument.
The commonest adjectives for pitch in ancient Greek writings are ὀξύς (oxys, “sharp, piercing”) and βαρύς (barys, “heavy”). Ptolemy wrote that the former quality was a result of λεπτότης (leptotēs, “fineness”) and πυκνότης (pyknotēs, “close spacing [of notes]”, and that the latter was caused by μανότης (manotēs, “thickness”) and παχύτης ( pachytēs, “loose spacing”) . The idea of higher and lower sounds, and their eventual depiction as such in notation, was a later development.
This according to “The development of vertical direction in the spatial representation of sound” by Eleonora Rocconi, an essay included in Archäologie früher Klangerzeugung und Tonordnung: Musikarchäologie in der Ägäis und Anatolien (Rahden: Leidorf, 2002), pp. 389–392.
Many thanks to David Bloom for help with this post!
Related article: The perfect-pitch puzzle