Octave Illusion is the first example in Diana Deutsch's book "Musical Illusions and Phantom Words". It is recommended to listen with headphones.
The left and right channels are composed of intermittent high tones and low tones. The signals of both channels are the same, but with the time of the high tones and the low tones are staggered when playing back.  (The black boxes indicate high tones and the white boxes indicate low tones.)
If you haven't done the interesting hearing experiment, please go here:
Some people perceive the same sound as it actually is, but many people perceive it like the followings: (The black boxes indicate high tones and the white boxes indicate low tones)
They feel the high tones are all on the right and low tones are all on the left; or vice versa, the high tones on the left and low tones on the right.
There are a few people perceive the high tones on the right and intermittent high and low tones on the left like the following:
Please listen to it again. Try listening only to the right or left channel and compare the result with listening to both channels.
The signals used in this experiment are pure sine tones. There is only a narrow lobe in the frequency domain.
When the signal contains only a pure sine tone, the illusion of separating the high and low tones into the left and right ears happens easily. When the waveform is modified into a sawtooth wave or other waveforms containing harmonics, the effect becomes insignificant. In this condition, most people can perceive the high and low tones running in both ears, becoming more like two parallel lines of high and low sounds, or at least one of the ears can perceive the same sound as the actual signal.
The above figure shows there are double, triple and other integer multiples of the fundamental frequency in the spectrum. These are the so-called harmonics.
In addition to the fundamental frequency, musical instruments have components of the harmonics as shown in the figure above, which are often called overtones in music. They form the unique timbre of each musical instrument with specific proportions. All musical instruments sound different, that is, the waveforms are different, because the waveform of each musical instrument is composed of these harmonics with different proportions.
From this experiment, we can know that such an illusion cannot be detected in daily life or in general music, because we usually don’t hear such a pure sine wave. Since harmonics form the unique timbre of each sound, our auditory perception has other mechanisms to avoid this illusion, which will be discussed in another article.
In addition, people who have received musical training, such as composers, conductors, instrumentalists, sound engineers, etc., are more likely to have the ability to use more delicate listening skills to crack this illusion and discover what the sound signal really is. This proves that hearing ability can be trained. Trained people can freely choose to disassemble the sounds they hear, or regroup them together. In fact, it is not the ears that are trained, but the brain.
 Deutsch, Diana. Musical Illusions and Phantom Words (p. 25). Oxford University Press. (2019)