in singing involving jumps of near-octave interval
In the standard Western 8-tone scale, singers are generally trained to be able to sing intervals of up to an octave independently (that is, without any external cues). A trained singer should be able to hear intervals up to at least a sixth (two tones, or three half-tones, short of an octave) mentally without difficulty. However, once intervals get to a seventh (one half-tone short of an octave) or a ninth (one tone greater than an octave) or higher, mentally figuring the sound is difficult without an intermediate step of transposing the target pitch into the current octave, hearing that pitch, then singing down or up the octave from that intermediate pitch to put it in its proper place.
A drill used to teach this involves singing a simple song (the Meistersingers' director used Mary Had A Little Lamb), but adding octave jumps at random points as directed; singers will jump between higher and lower registers the whole exercise.