Phase modulation or frequency modulation?

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Unread post by Fozzer » Fri Jan 30, 2009 11:23 am

For me, the easiest to understand has always been Yamaha's "FM" Frequency Modulation used in the DX Synths... :D ...!

Four, or six, "Operators", all producing perfect Sine Waves, which can be arranged to produce a variety of sounds merely by "Modulating" them with each other, using different Frequencies and various "Effects".

It all seems nice and simple... :D ...!

Now, Derek has confused me even more, with my request for a description of Yamaha's Advanced Wave Memory; "AWM, and AWM2"!.... :cry: .... :lol: ...!

I partly gather that it involves using actual Sampling of real sounds, and then modifying them using Effects within the instrument?

...all fascinating "stuff"!...:D ...!

Paul...Sampling his Modulations... 8) ...!

Yamaha MO6, MM6,DX7,DX11,DX21,DX100,MK100,EMT 10,PSR 400,PSS 780,Roland GW-8L v2,Roland TR 505,Casio MT-205, Korg CX-3v2 dual manual (Hammond B3 clone) + Leslie 760/770,M-Audio Pro-keys 88, Key Rig,Cubase,Keyfax4.Various Guitars.Orchestral,Baroque,Renaissance,Medieval Instruments.....and a Petrol Lawn Mower...

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Unread post by Derek » Fri Jan 30, 2009 8:23 pm

Clyde wrote:What did you expect, for Yamaha to make sense? Derek, certainly you've read enough manuals comprised of "Yamahaese" to realize that it is never simple or direct with Yamaha, :lol: you just have to find out what is what on your own and move on! Seriously, I don't think any of the manufacturers have anything as cut and dried as we would like to see it. How many different versions were there of Rolands LA synthesis, all labeled LA. But somehow we struggle through it all and learn how to make it work.
I think Yammie manuals are pretty good compared to some others - apart from the Motif ES manual, which is awful!

You're quite right though, it's how it sounds that counts, which is why the Mellotron still rules when it comes to ethereal prog strings and choirs!

Derek Cook


Re: Phase modulation or frequency modulation?

Unread post by db7 » Mon Aug 26, 2013 11:42 am

Bumping with some clarifications. This thread is 5th on Google for Yamaha phase modulation, after all!
xpi0t0s wrote:So by taking y=sin(Ax + Lsin(Bx)) where A=carrier freq, B=modulator freq, L=modulator level we get (a) LFO/siren effects AND (b) waves that match FM synthesis by simply adjusting A, B and L. So if this is NOT frequency modulation but really phase modulation I must be missing something; anyone know what?
Yes. If the carrier and the modulator are pure sinusoidal functions (sine or cosine), frequency modulation and phase modulation produce mathematically identical results.

So, you may see results that suggest the synth literally uses FM, but in fact, you would see the same results if it used PM. And both careful investigation of the chips involved and relevantly designed tests combining operators would prove that Yamaha definitely used PM in all of their synths, not FM.

PM is preferable for synthesis because, compared to FM, PM does not cause ops with self-feedback to drift in pitch, it avoids problems when an operator contains a DC offset, and possibly other advantages of which I am unaware. A constant offset in phase simply causes a wave of the same frequency with a constant displacement in phase. A constant offset in frequency, on the other hand, is not so benevolent.

Here, read this good article by someone else: ... hnologies/

Clearly, once the waveform of any operator becomes non-sinusoidal, things get less clear-cut and less directly comparable. Still, the resulting PM can often be converted to FM. However, how many people really want to look that deeply into it? :P It is interesting. But my brain can only process the first few formulae before giving up. :lol:

I give a more mechanistic explanation of how waveforms are read and modulated at the end of this post.
Fozzer wrote:...whilst we are on the subject of FM (Yamaha's Frequency Modulation) and PM (Casio's Phase Modulation)...
Casio called their method phase distortion (PD), not PM. But it does still involve altering the phase of a sine wave, i.e. the point at which it is sampled. However, they do not allow freely configurable PM as Yamaha do: AFAIK, there are only 8 pre-defined ways to distort the instantaneous phase of the stored sine, resulting in 8 pre-defined waveforms. Some things will be easier in PD, but many things will be more difficult, and it certainly is not equivalent, or directly comparable at all, to Yamaha-type PM in terms of its synthetic possibilities (rather than just its bare mathematical basis).
Derek wrote:Just to complicate matters, there are many synths that claim to be AWM2, but they all have different capabilities. […] So what really is AWM2? I saw a post on the internet once, which said that AWM was 12 bit samples and AWM2 was 16 bit samples, so is that all it's referring to (and not the synth engine that's mangling the samples)?
Not certain, but I think AWM2 is just an umbrella term referring to any sample-playback method by Yamaha that, above the original AWM, supports bit-depths of at least 16 bits (not just 12) and offers filters. Anything after that is just window-dressing, I guess.
Fozzer wrote:...can anyone describe for me, the details of Yamaha's AWM, and later AWM2 (Advanced Wave Memory)..?
Many of the most basic concepts are similar. Any method of sample-playback synthesis like this will simply have a waveform in memory and step through its individual samples at a particular rate that will provide the pitch requested, a.k.a. the key pressed. In other words, it will read out the waveform at sequential points in its phase, whose spacing in time is determined according to the frequency requested for that oscillator/element/whatever.

This is, in fact, what an isolated, non-modulated carrier in a PM synth by Yamaha does, but the waveform in question is not freely configurable, just a sine wave or one of the other shapes offered by chips like OPZ or OPL. The samples of that wave are stepped through at a speed that produces the requested frequency using an accumulator that stores the elapsed phase (a.k.a. the point within one cycle of the waveform) and is incremented to the next point at a rate that produces said frequency.

When you add modulation, the instantaneous phase used to determine what is output for a given sample is not only derived from the accumulator: it can also be increased or decreased by a modulating operator, depending on the instantaneous amplitude of the latter, which is converted to a displacement of phase forwards (positive amplitude) or backwards (negative amplitude) relative to the value in the accumulator. This changes the sample output by the op, and so the shape of the wave, and so the resulting sound.

And finally, closing with what I hope is a succinct explanation of the difference between PM and how real FM would work in a hypothetical comparable synth by Yamaha: In PM, the modulating wave displaces the instantaneous phase of the modulated wave, while the latter’s accumulated phase determined by its fundamental frequency remains the same. In FM, the modulating wave directly alters the frequency of its target. Thus, literal FM enables drift in pitch and other instabilities, such as those I mentioned before.

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Unread post by EX5_etc » Tue Aug 27, 2013 6:11 am

Clyde wrote:What did you expect, for Yamaha to make sense?
If Yamaha made sense all the time we would not have this forum to chat. So, it may be a good thing they did not always make sense.

I am not an expert on FM, PM or PD nor do I plan to become one any time soon. But having used a TG55 with AWM2 vs a PSR1000 with AWM (that was introduced after the TG55) I can definitely say that the clarity of any AWM2 sound is immediately evident over AWM. This cannot happen unless the samples are superior and in the case of AWM2 they are.

The attached picture is a low resolution scan of the SY55 brochure as well as the EX5 brochure. You may find it useful.



Motif XF6, SY99, SY85, QS300, PSR1000, WX5, EX5R, A5000, TG500, TG55, RM50, QY700, QY100, QX5FD, MJC8, YDP2006, REV500, EMP700, EQ500U, MCS2, AW16G, Axiom Pro 49 and a few other things by Behringer, Evolution, Philips, Tascam, Technical Pro, Yamaha, etc, etc,... I wish I had time to use all this stuff; I am not even pro. :-)


Re: Phase modulation or frequency modulation?

Unread post by db7 » Tue Aug 27, 2013 12:52 pm

Hooray, it seems I was right! :P

However, proving what you said about Yamaha not always making sense (I could write a lot about this, but maybe another time), the rightmost scan shows them taking what is clearly AWM2, due to the mention of filters and the EX5 being made long after AWM2 arrived, but calling it AWM without the qualifying number. At best, this is an ambiguous kind of simplification, which I’ve seen a lot in at least some of their documents.

Anyway, thanks for providing some very relevant evidence straight from the proverbial, and variably reliable, horse’s mouth!
I am not an expert on FM, PM or PD nor do I plan to become one any time soon.
Oh, all right… I’ll do it. :lol:

Edit: To supplement what I said in my last post about Phase Distortion—and provide an another phrasing of my explanation of how, in both PD and PM (but not FM, which Yamaha say when they really mean PM!), waveforms are read out using a frequency, which creates an accumulated phase, which an input signal modulates to an instantaneous phase—see this page I found later: ... dsynthesis And yes, the Casio CZ family offered 8 types of waveform created via PD: ... nthesizers

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