Each octave rise halves how many hearing-range harmonics a note carries

Evidence

Thus an instrument playing the A above middle C, which has an f0 of 440 Hz, could theoretically contain 36 (= 16,000/440) harmonics within the human hearing range. If this instrument played a note an octave higher, f0 is doubled to 880 Hz, and the output could now theoretically contain 18 (= 16,000/880) harmonics. This is an increasingly important consideration, since although there is often an upper frequency limit to an acoustic instrument that is well within the practical upper frequency range of human hearing, it is quite possible with electronic synthesizers to produce sounds with harmonics that extend beyond this upper frequency limit. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 798

Categorization

• SHARE: A good fact for someone interested in synthesis or sound design—synthesizers can exceed the audible harmonic ceiling acoustic instruments hit.
• XREF: connects to: The number of harmonics audible halves with each octave rise in pitch; The audible harmonic count of a note depends on hearing’s 16 kHz upper limit

Broader Connections

• The number of harmonics audible halves with each octave rise in pitch #corroborates (0.97)
• The audible harmonic count of a note depends on hearing’s 16 kHz upper limit #expands (0.90)