of his personal hallmarks, such as melodies that "leap backwards and forwards in a remarkably acrobatic manner while still sounding not only smoothly lyrical, but spontaneous as well". In such up-tempo numbers as the "Galop infernal", Offenbach makes a virtue of simplicity, often keeping to the same key through most of the number, with largely unvarying instrumentation throughout. Elsewhere in the score Offenbach gives the orchestra greater prominence. In the Jupiter's part, consisting of buzzing like a fly, is accompanied by the first and second violins playing sul ponticello, to produce a similarly buzzing sound. In , Gustave Lafargue remarked that Offenbach's use of a piccolo trill punctuated by a tap on a cymbal in the finale of the first scene was a modern recreation of an effect invented by Gluck in his score of . Wilfrid Mellers also remarks on Offenbach's use of the piccolo to enhance Eurydice's couplets with "girlish giggles" on the instrument. Gervase Hughes comments on the elaborate scoring of the [Act 3, 1874 version], and calls it "a tour de force" that could have inspired Tchaikovsky. Faris comments that in Offenbach shows that he was a master of establishing mood by the use of rhythmic figures. Faris instances three numbers from the second act (1858 version), which all are in the key of A major and use identical notes in almost the same order, "but it would be hard to imagine a more extreme difference in feeling than that between the song of the King of the Boeotians and the Galop". In a 2014 study Heather Hadlock comments that for the former, Offenbach composed "a languid yet restless melody" over a static musette-style drone-bass accompaniment of alternating dominant and tonic harmonies, simultaneously evoking and mocking nostalgia for a lost place and time and "creating a perpetually unresolved tension between pathos and irony". Mellers finds that Styx's aria has "a pathos that touches the heart" – perhaps, he suggests, the only instance of true feeling in the opera. In 1999 Thomas Schipperges wrote in the International Journal of Musicology that many scholars hold that Offenbach's music defies all musicological methods. He did not agree, and analysed the "Galop infernal", finding it to be sophisticated in many details: "For all its straightforwardness, it reveals a calculated design. The overall 'economy' of the piece serves a deliberate musical dramaturgy." Hadlock observes that although the best-known music in the