I'd have to look this up to give a better informed answer - but I'll throw out what comes to mind right now.

At some point one runs into the limits of digital. It's not analog - so there is a limit to frequency which is based on how fast a clock is running and when/where a signal is changed. At some ceiling - you may fall into an area where the frequencies would repeat if you kept going up ("wrap around" ) due to limitations in the minimum frequency a digital device can produce. As you "increase" frequency - since the space is so small between frequencies - you may get to the point where the phase inverts as you go up. Just like our eyes can only see at a certain frame-rate and a wheel looks like its spinning backwards at certain rotational speeds. This is the phase of the frequency setting in the digital domain vs. the "wrap around" effect - so every digital step actually gets you lower down the frequency spectrum considering the "wrap around at the top" effect. This is easier to explain with a chart (picture). Still, not sure if it's the thing happening here.

The other theory I have is more about physical acoustic stuff - and I'm less studied in this area. There may be a reason based on harmonics what happens at a certain point and how we perceive the sound. Although at some point we just all stop hearing the frequency. Some folks sooner than others - certainly the older we are - the less we hear (vs. our younger selves). Not sure if this is at all involved.

Hi Jason,
thanks for that incredible answer.
I think the first one seems to me the right one. But I'm not sure.
I hope my ears are good enough to hear al the frequencys that a human can hear. 🙂
Rainer

Vibrato is the musical term for Modulator influencing the Carrier at a ‘human’ speed... i.e., a few times per second. On the typical synth this rate is assigned to a Low Frequency Oscillator — called that because it concentrates on very low (‘human’) speed rates, a few times per second.

We know that the human ear can hear pitches between 20 cycles per second and 20 thousand cycles per second. That is the frequency response of the human ear. The lowest ‘A’ on the acoustic piano is A27.5 — hard to believe we can’t hear 7 and 1/2 cycles below the lowest ‘A’.

Low frequency behavior is not like high pitches, they seem to get softer and softer and finally fade out of our range. The low end is quite a bit different. Yes it is getting softer as you go lower, but what happens at the low end of the scale can be quite different.

It’s not that you cannot hear something that happens at less than 20 times per second... you certainly can! It is just that we don’t recognize it as a separate pitch.

Here’s an example, say I snap my fingers two times per second (2 cycles per second) you can certainly hear that. But if I were to speed up my finger snaps to (an inhuman) 20 times per second, the ear/brain would no longer hear the separate snaps, the snaps would be close enough together to sound like a low pitched buzzer. The faster the snaps are repeated the higher the pitch. Like a motor revving up, the faster the events the higher the pitch... at 440 times a second it would give off the pitch ‘A’.

The finger snap itself has a frequency of approximately 1,200 cycles per second, when I snap it 2 times a second, I can clearly hear each snap event occurring at 2 cycles per second. Let’s speed up the number of snaps per second...
By the time the events are happen 20 times a second, the ear/brain no longer recognizes the snaps as separate events, they take on a second audible pitch.

This fundamentally (pun intended) explains how when we hear musical tones we are actually hearing a complex array of musical pitches and noise components ... different harmonics both above and below the predominant pitch.

In FM, (interaction of Modulator and Carrier) harmonic sidebands occur both above and below the fundamental tone. If you think of sound waves like the ripples caused by dropping a pebble in water... the waves that occur reach the edge and fold back creating different nodes, creating peaks and troughs, at different intensities. Much of this is mathematically predictable. Change the intensity of the Modulator and a different array of results occur. Phantom tones occur as we hear additions and subtractions of the harmonics in motion.

This is where FM Synthesis let’s higher mathematics creep into the discussion (Bessel functions, etc.). But you will hear these harmonic and inharmonic sidebands on either side of the Fundamental. As you go higher and higher you will naturally hear different harmonics and sub harmonics. Sub harmonics of pitches that exceed our range manifest themselves in the audible range. You can get into that and go far down that rabbit hole, (but you don’t have to) like tuning an instrument you can know it’s right by how it sounds. Once you recognize that sonic result you get can change radically with different Output Level (Modulation Index) settings.

One could study the mathematics to predict a specific tone, say you wanted to mathematically recreate a specific bell tone, but you might have more fun and just as much success experimenting and doing it by ear.