7 ms·

> In mathematical terms, FM synthesis is achieved by using the instantaneous amplitude of a sound wave (the modulator) to adjust the rate of change in the phase

> In mathematical terms, FM synthesis is achieved by using the instantaneous amplitude of a sound wave (the modulator) to adjust the rate of change in the phase angle of another wave (the carrier). > As convoluted as this sounds, it makes more sense when visualised: [1] ...but does it?? [1] https://ajxs.me/static/img/articles/dx7_technical_analysis/frequency_modulation.jpg https://ajxs.me/static/img/articles/dx7_technical_analysis/f...

buildsjets 5y ago
If you understand Bessel Basis Functions, or the design and tuning of motorcycle carburetors, then it makes perfect sense. If you are uneducated on these and similar arithmatic summations of wave functions, then it will make no sense.
armchairhacker 5y ago
Idk what's going on with the modulated carrier in that image. Here's a better visualization: https://flypaper.soundfly.com/wp-content/uploads/2017/09/AM_FM.gif https://flypaper.soundfly.com/wp-content/uploads/2017/09/AM_... Notice how, when the modulator wave is at its top the FM wave is very short, and when the modulator wave is at its bottom the FM wave is very long. FM = adjust the frequency (width) of the carrier based on the absolute value of the modulator.
- ajxs 5y ago
  Author here: Thanks for pointing this mistake out! I'm not sure how I didn't validate this. I believe the mistake lies in the absolute value aspect of the formula. Unfortunately I can't find the script I used to create those diagrams. I've been meaning to revisit this article, and update it with some of my more recent discoveries. I'll make sure to update this when I do so!
  - metaphor 5y ago
    Link to the Chowning paper[1] is broken too; hazarding a guess that neither AES nor Prof. Fessler would mind. [1] https://web.eecs.umich.edu/~fessler/course/100/misc/chowning-73-tso.pdf https://web.eecs.umich.edu/~fessler/course/100/misc/chowning...
rcxdude 5y ago
"rate of change of the phase angle" is just a convoluted way of saying 'frequency'
- jacobvosmaer 5y ago
  I'm not sure. Intuitively I would think "phase angle" means "offset into the sine wave lookup table". If you step through the lookup table with constant size steps, you would get a sine wave. If the steps are not constant size then you get a distorted sine wave. The "rate of change of the phase angle" would then be the step size.
  - joeberon 5y ago
    "frequency" would mean the same thing in your weird practical analogy.
    - cto_of_antifa 5y ago
      Be polite, please.
  - rcxdude 5y ago
    This is exactly how direct digital synthesis works and the 'step size' is labelled 'frequency' (specifically, frequency in HZ = step size / size of table * update rate)
  - ajxs 5y ago
    Author here: This is one reason why I used that term. I was definitely thinking in terms of the 'phase accumulator' looking up the sin table. Everyone is absolutely right that this is the same as frequency. I think I was used that particular poetic flourish to emphasise how complicated the academic, mathematic explanation is, in contrast with the diagram. Quite likely I picked up that exact phrasing of "phase angle" from some academic literature in particular.
    - joeberon 5y ago
8bitsrule 5y ago
It helps me to think of the difference between AM and FM radio. In an AM radio signal, the frequency of the carrier is constant; the amplitude of the audio modulates the amplitude of the carrier. In an FM radio signal, the amplitude of the audio modulates the frequency of the carrier. That's the difference! In musical terms, I very much like some analog, and some FM, synthesizers. But certainly, back in the day, getting some rich sounds out of FM synths was a lot cheaper than analog. (Just in terms of the cost of patch cords alone ;-) Without Chowning there wouldn't have been a synthpop era!
ajuc 5y ago
> ...but does it?? I think in this case the clearest explanation is the equations + graphs: 1. modulator(t) = sin(t) 2. carrier(t) = sin(t*4) 3. result(t) = sin(t*4 + d modulator(t)/dt) = sin(t*4 + cos(t)) http://www.fooplot.com/#W3sidHlwZSI6MCwiZXEiOiI0K3NpbigxMCp4KSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MCwiZXEiOiIyK3NpbigoMTAvNCkqeCkiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoic2luKDEwKngrKDEwLzQpKmNvcygoMTAvNCkqeCkpIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTEzLjEzODg5MTIyMDA5Mjc0OSIsIjIuNzMwMjQ5NDA0OTA3MjA5IiwiLTIuNzIzOTczMjc0MjMwOTUiLCI3LjA0MTY1MTcyNTc2OTAyMiJdfV0- http://www.fooplot.com/#W3sidHlwZSI6MCwiZXEiOiI0K3NpbigxMCp4... EDIT: it's wrong, see below
- MauranKilom 5y ago
  I'm pretty sure you need an integral in there somewhere, no?

buildsjets 5y ago

If you understand Bessel Basis Functions, or the design and tuning of motorcycle carburetors, then it makes perfect sense. If you are uneducated on these and similar arithmatic summations of wave functions, then it will make no sense.

armchairhacker 5y ago

Idk what's going on with the modulated carrier in that image. Here's a better visualization: https://flypaper.soundfly.com/wp-content/uploads/2017/09/AM_FM.gif https://flypaper.soundfly.com/wp-content/uploads/2017/09/AM_... Notice how, when the modulator wave is at its top the FM wave is very short, and when the modulator wave is at its bottom the FM wave is very long. FM = adjust the frequency (width) of the carrier based on the absolute value of the modulator.

ajxs 5y ago
Author here: Thanks for pointing this mistake out! I'm not sure how I didn't validate this. I believe the mistake lies in the absolute value aspect of the formula. Unfortunately I can't find the script I used to create those diagrams. I've been meaning to revisit this article, and update it with some of my more recent discoveries. I'll make sure to update this when I do so!
- metaphor 5y ago
  Link to the Chowning paper[1] is broken too; hazarding a guess that neither AES nor Prof. Fessler would mind. [1] https://web.eecs.umich.edu/~fessler/course/100/misc/chowning-73-tso.pdf https://web.eecs.umich.edu/~fessler/course/100/misc/chowning...

rcxdude 5y ago

"rate of change of the phase angle" is just a convoluted way of saying 'frequency'

jacobvosmaer 5y ago
I'm not sure. Intuitively I would think "phase angle" means "offset into the sine wave lookup table". If you step through the lookup table with constant size steps, you would get a sine wave. If the steps are not constant size then you get a distorted sine wave. The "rate of change of the phase angle" would then be the step size.
- joeberon 5y ago
  "frequency" would mean the same thing in your weird practical analogy.
  - cto_of_antifa 5y ago
    Be polite, please.
- rcxdude 5y ago
  This is exactly how direct digital synthesis works and the 'step size' is labelled 'frequency' (specifically, frequency in HZ = step size / size of table * update rate)
- ajxs 5y ago
  Author here: This is one reason why I used that term. I was definitely thinking in terms of the 'phase accumulator' looking up the sin table. Everyone is absolutely right that this is the same as frequency. I think I was used that particular poetic flourish to emphasise how complicated the academic, mathematic explanation is, in contrast with the diagram. Quite likely I picked up that exact phrasing of "phase angle" from some academic literature in particular.
  - joeberon 5y ago

8bitsrule 5y ago

It helps me to think of the difference between AM and FM radio. In an AM radio signal, the frequency of the carrier is constant; the amplitude of the audio modulates the amplitude of the carrier. In an FM radio signal, the amplitude of the audio modulates the frequency of the carrier. That's the difference! In musical terms, I very much like some analog, and some FM, synthesizers. But certainly, back in the day, getting some rich sounds out of FM synths was a lot cheaper than analog. (Just in terms of the cost of patch cords alone ;-) Without Chowning there wouldn't have been a synthpop era!

ajuc 5y ago

> ...but does it?? I think in this case the clearest explanation is the equations + graphs: 1. modulator(t) = sin(t) 2. carrier(t) = sin(t*4) 3. result(t) = sin(t*4 + d modulator(t)/dt) = sin(t*4 + cos(t)) http://www.fooplot.com/#W3sidHlwZSI6MCwiZXEiOiI0K3NpbigxMCp4KSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MCwiZXEiOiIyK3NpbigoMTAvNCkqeCkiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoic2luKDEwKngrKDEwLzQpKmNvcygoMTAvNCkqeCkpIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTEzLjEzODg5MTIyMDA5Mjc0OSIsIjIuNzMwMjQ5NDA0OTA3MjA5IiwiLTIuNzIzOTczMjc0MjMwOTUiLCI3LjA0MTY1MTcyNTc2OTAyMiJdfV0- http://www.fooplot.com/#W3sidHlwZSI6MCwiZXEiOiI0K3NpbigxMCp4... EDIT: it's wrong, see below

MauranKilom 5y ago
I'm pretty sure you need an integral in there somewhere, no?