[1][2] "Giddy Stratospheres" is a fast-tempo song, at 136 beats per minute (bpm), and in the key of B major for the verses.

For the chorus, it switches to a slightly faster tempo (142 bmp) and changes to a key of E-flat major.

The song features indie rock instrumentation, using a call-and-answer motif between the bass and guitar, described by Drowned in Sound as "the oldest trick in the book".

"[4] These sentiments were echoed by Fraser McAlpine from BBC Radio 1 who gave the song a 4-stars review describing "shards of guitar and shrieks so sharp they could have someone's eye out.

"[5] A review by Yahoo was mixed, saying that the song stretched Jackson's voice "to its grating limits" but praised lyricist Dorian, describe his narrative-led song writing "as compelling as anything on (Arctic Monkeys') Whatever People Say I Am That's What I'm Not".