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Is there a definitive calculation to what is considered FM?
MUFF WIGGLER Forum Index -> Modular Synth General Discussion  
Author Is there a definitive calculation to what is considered FM?
I think in the end, I'm wondering if there is a specific ratio that defines "audio rate". A student was curious about how we separate audio and control rates. A very slow sine wave modulating the pitch of an oscillator. We can clearly here the pitch going up and down. As the speed of the modulator increases, we keep hearing the pitch going up and down faster and faster until at one point, the phenomenon that we call "audio-rate modulation" kicks in, and the modulation is now having more an impact on the timbre of your source, rather than the frequency.

Mathematically, how are we calculating the precise moment that "audio-rate modulation" happens? hmmm.....
Dave Peck
We don't "calculate it precisely", because the transition point between perceived event changes and perceived timbre changes is just a matter of the individual's PERCEPTION. But in general, that transition tends to be near 20 Hz.
So, to put it on a more sciencey kinda footing, it's when the modulator signal moves into the audible range, which varies between individuals...?

Interesting experiment springs to mind... You know those hearing tests where they play you tones at various frequencies? Use those as modulators and compare the effect. Might make a fun classroom demo. Or not... seriously, i just don't get it
That's an interesting question, as Dave said it is usually around 20Hz but there is this real grey area at around 10-20Hz. I think it was Adam Neely who made a great TED talk on this subject. The ambiguity between rhythm and tone is fun to play with.

Edit: Yep, it was Neely and at Loop:

Adam Neely Talk
Dave Peck
Yup, it varies not only from person to person, but it also depends on exactly what the signal is doing.

For example, a series of narrow pulse spikes being swept from a frequency of 1 Hz up into the audio range may be perceived as transitioning from a series of events to an audio timbre at one frequency, while a sine wave modulating the pitch or amplitude of another sine wave may be perceived as making that transition at a different frequency.
The gray area is actually quite big. One of my peeves is that FM with an upgoing saw wave (the most common) doesn't sound as good as with a downgoing wave. (obviously with both centered at 0V.) The difference is slight but still audible at frequencies well above 20Hz or even 100Hz.
"Audio rate" is a property of biology, not physics. I believe cats for instance have a lower hearing threshold of 55Hz, so audio rate to them would stop there instead of 20Hz.

The equations, Bessel functions and other crap Dr. Chowning worked out for FM synthesis should still hold no matter how low the modulator frequency is.
I would do that demonstration in some of my classes. I’d set up the patch, then sweep the modulator frequency up, having asked the students to raise their hand once they heard a steady tone. A few hands would go up at 15 Hz, then more and most would be up at 25 Hz, although a few holdouts didn’t respond below 30. I’d call it a Gaussian distribution around 22 Hz. When I repeated the exercise going down, the distribution was the same but centered lower, maybe 18 Hz. The results were the same with AM or FM or just listening to a pulse wave.
Rex Coil 7
I reckon the word "audio" pretty much defines the beginning and the end of the issue.

In fact, I think the initials "FM" don't really define anything or mean anything other than "frequency modulation" ... which could be anything that modulates the frequency ... from a single cycle produced by an envelope generator ... to a five minute long cycle ... to a manual manipulation with a pitch wheel ... to audio rate modulation sources.

If the OP is referring to Yamaha's use of the initials "FM" as branding to describe their operator based synth engines, I think it's been long determined that the technically correct term for what they do with their DX series is Phase Modulation ("PM").

I'm just providing some gratuitous and unnecessary observations.

Rex Coil 7 wrote:
I'm just providing some gratuitous and unnecessary observations.

That's a good old Muffwiggler tradition.

I think the best way to understand the original poster's question is to read in "audio-rate" before "FM." It does seem to be specific to modulation (the question isn't just "What frequencies can people hear as tones?") but it also seems to be getting at the old audio/CV distinction.
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