Only about 1,400 discriminable pitches exist across the entire audible range

Evidence

From a musical perspective, based on the pitch 50% JND, it turns out that there are around 1,400 individual pitches that are audible within the 20 Hz to 20 kHz nominal (see Section 2.3) human hearing frequency range. In terms of semitones, there are 10 octaves between 20 Hz and 20.48 kHz and therefore 120 semitones (12 semitones per octave), but note that pitch perception above 5 kHz is poor and therefore is not used by musical instruments (see Section 3.2.4). — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 872

Categorization

• CANDY: A tidy fact: the whole audible range holds only ~1,400 distinguishable pitches — great party conversation.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 872