# Is a frequency modulated (in an FM synth) signal perceived by our ears in the same way as two signals played at the same time?

Setup 1: oscillator with the carrier frequency and a oscillator modulating the carrier frequency.

Setup 2: two independent oscillators, one set to the carrier frequency and one with the modulation frequency.

Do we hear the same sound and/or timbre?

If so, this would mean that our ear just does what the FM synth does internally.

This was a side question in this thread and thank you for answering already @Kevin Reid, but I still would like to discuss this.

The following article shows two signals, playing together, and there are two graphs, one how they overlap and one how they are heared by our ears. Can anyone explain me, how that second graph would differ, if that previous signal would just be frequency-modulated before its played?

Background: I have the possibility to create many signals, but have only one frequency modulator parameter per signal. I have the idea, that I can just play the sounds together to "simulate" a signal going through multiple modulators. But somehow I think this is not working in practice. Setup 1: oscillator with the carrier frequency and a oscillator modulating the carrier frequency.

Setup 2: two independent oscillators, one set to the carrier frequency and one with the modulation frequency.

Do we hear the same sound and/or timber?

In general, no. Frequency-modulating a carrier with a modulator doesn't give you a result that just contains the frequencies of the carrier and the modulator; normally, the output signal is seen as containing a number of side bands.

See https://www.soundonsound.com/techniques/introduction-frequency-modulation and https://www.sfu.ca/~truax/fmtut.html for more details on the maths.

I have the idea, that I can just play the sounds together to "simulate" a signal going through multiple modulators

That wouldn't be modulation at all, but simply mixing.

• Thank you. I will invest some more time to look at the maths, I think they would help me too to understand the side bands. Is it wrong to say FM means multiplying and mixing means adding? (sorry, that was the first idea just that came to my mind, bevor I could reserve some time for studying the maths behind instead of just reading about the waves and application). Jun 7 '20 at 12:55
• Ok, I think I got it (glad being corrected if not) for frequency modulation its not multiplication it is "recursion": `sin(2*Pi*Fc*t + I*sin(2*Pi*Fm*t)`.And playing two signals together, better refered as "mixing" is additive snythesis, where the cos() in sin() values are added up (sorry for this simplification of the fourier's expression). Jun 7 '20 at 17:46
• @spikey I'm not an expert on the maths of FM, but mixing does mean adding in the "time domain", and FM doesn't mean multiplying in the "time domain". You are right that mixing a number of sinusoids is effectively additive synthesis (which is more my bag than FM!) Jun 7 '20 at 19:34