"Equivalent" may need some qualification. SY99's AFM has extensive feedback routing not available in FM-X. Your picture doesn't show any feedback at all - either due to simplification or because you really mean to ignore feedback. Ignoring feedback (and, I suppose - a bunch of other FM-related things the SY has that FM-X doesn't) - just for the basics - you have some options of what can give you 3 modulator/carrier pairs (stacks) as shown.

FM-X Alg 13, 14, 67, 74, 78, 81, 83 can all be reduced down to 3 carriers with 3 modulators stacked on top.

Alg 67 is the closest "shape" - so maybe an easy fit. But if you start needing complex feedback routing - it's likely that those feedback paths just can't be done with what you have in FM-X. You'll have to leave feedback somewhat on the table and lost in translation. Maybe examining what you think is the key feedback path and try to find an Alg that gets closest to providing that path -- or at least one of the feedback paths in the original.

The SY allows for simultaneous feedback routes and these routes can pick any operator's output as the source for feedback (well, except for the fixed ones - you can't pick those ... but mostly you get freedom) and allows for any operator's feedback input to be the destination - including multiple operators simultaneous as a destination for feedback of a given route. (FB1, FB2, FB3). Operators may have up to 2 feedback inputs - and each (of the up to 2) feedback inputs has its own level. It's really a lot of feedback routing flexibility -- even with a fixed assignment here and there.

FM-X is not trying to emulate / reproduce / model the SY99's AFM capabilities - so what you can match up is limited.

Unless you get lucky (like an "underutilized" SY99 AFM program) - you're going to likely be more in the realm of trying to reproduce the SY99 sound not by trying to find matching structures -- but more by using new features in FM-X to get in the ballpark a different way. The kind of stuff synthesis always does - sounds like something else using the current keyboard's technology to the best of its ability to mimic something else. Not by having the underlying exact model - but by your creative use of the knobs and settings. FM-X has "new" stuff (relative to the SY99) - so you may be able to dial in the general idea/character of an SY99 sound you're referencing by different means than the original AFM program.

FM-X Algorithm 81 could be used, with operators 3 & 6 providing additional operator (basic) feedback emulation if needed.

Actually, the Algorithm shape is just one aspect, please recognize that none of the Algorithms found in the MONTAGE/MODX FM-X engine match exactly the arrangement of the six Operator Algorithm 42 (as found in the AFM engine)

Yes. Matching the shape (three 2-Operator stacks) occurs several times in the FM-X engine, as noted above, but notice never are Operators 1, 3 and 5 Carriers with Operators 2, 4 and 6 as Modulators in the FM-X engine.
So you will have substitute the values so that you match the Operator to its role in making the sound... Carrier with Carrier and Modulator with Modulator in each case. If the AFM stack has Modulator as Op2 and Carrier as Op1, the fact that Op2 is a Modulator and Op1 is a Carrier is absolutely critical. You will not find such an Operator arrangement in the FM-X engine. This means you manually will need to swap Operator positions when you enter the values.

Programming Hints
The multiple 2-Operator stacks are used when you are programming a sound with multiple audible components. The iconic FM electric piano sound was based on the DX7’s three 2-Operator stack Algorithm. Three programming components.

You can use the convenient ”Algorithm Search” engine:
Define the number of Carriers and Modulators you desire to work with and it will show you your options.
Here’s how:
From an “Init FM-X” Part
“Edit”
“Common” > “Part Settings” > “Algorithm” > tap “Algorithm Search”
Set the number of “Carriers” = 4
Set the height of Operators stacked above (Chain) = 2
You can select the one that most appeals to your goal.

Each 2-Op stack made a different sound component contribution to the Rhodes tone... the first two 2-Op stacks fashioned the body of the tone soft-hard, and the third 2-Op stack was the high pitched tine sound. When combined you got a full bodied electric piano sound. In the iconic TX816 (eight DX7s in a rack) you had 48 FM Operators (8 x 6) making the electric piano sound... find the MONTAGE Performance “The TX816 E.Piano” — there each pair of DX7s (two Parts: 1/2, 3/4, 5/6, 7/8) create a Stereo image of their component building block

If you have the AFM synth (SY77/SY99) there to play around with, isolate each 2-Op stack and listen to its contribution to the whole.
In general when building sounds start with the Carrier (naturally) — fashion the AEG to create the general loudness shape of the overall sound you’re attempting to emulate. Then use the Modulator to give the timbre some definition. The Output Level of Modulator will profoundly change the overall timbre of the result. And it is the Modulator’s AEG that will determine how the timbre (tone) changes overtime. You want to make the Modulator sensitive to velocity change, (critical to make the timbre change as you play softer/harder).

If the Modulator’s AEG extends longer than the Carrier’s then its influence over the timbre will be throughout the sound.
If the Modulator's AEG is quicker/shorter than the Carrier’s then it’s influence will disappear before the sound dies out.
Again, critical functions, as the Modulator can be used as a quick burst to add chaos to the ‘attack’ portion, or it can be used to fashion a solid sonic tone for the held part of the sound.

These are a critical listening points when programming FM... Output Level and velocity response
In the FM-X Explorations tutorial, we take a deep look at the 2-Operator stack (as it forms the original backbone of FM synthesis)... with the older engines (original DX/TX and even in the AFM) it often took two Operators to fashion a complex waveform. Feedback was used to create more timbral chaos... and while the new FM-X engine has the original Feedback function to bring it into compatibility with the legacy six Operator engine... the Spectral Forms eliminates the need for an Operator Feeding back on its self — as each Operator is completely variable via the Spectral Form and Skirt parameters. And although you could route Operators freely in AFM, and you had as many as three programmable Feedback loops, that could included multiple Operators, you were limited to the total number of Operators per sound (12 in a “2AFM Poly” or 24 in an “4AFM Mono” program)... the FM-X engine provides you with a maximum of 64 Operators in an 8 Part KBD CTRL FM-X program!!!

But it’s not about which has more options, but which offers you more musical results. We discovered rather quickly, for example, the more complex the Modulator, the quicker it it generates frequencies containing all harmonics — in other words, it becomes an elegant “Noise” maker.
I remember we all were excited to modulate an FM sine wave with an acoustic piano...no one knew exactly what to expect; Well, as you know you can’t hear the Modulator - it’s contribution is strictly energy, not sound. Well, the more harmonics in the Modulator, the quicker it manifests complete chaos in the Carrier’s output result. The ability to make sound effects was greatly enhanced...

Extra Credit:
As you may know by now, I have a lot of T-shirts in my closet (as in: “been there, done that, got the t-shirt). So I’ve been down this road - the only thing this qualifies me to say is, (beyond the warning above about the Modulator/Carrier numbers and the importance of their location in the Algorithm) is instead of trying to reproduce an old sound by reading numbers off a piece of paper, be sure to use your ears while inputting numbers... it can be a good way to learn, if you take that extra time. And it will be worth it in the end.

If you just type in numbers (copy them without experimenting with them) you may get your sound or something close, but you learn nothing.
Experiment with not only the Rates and Levels of the AEG, but the tuning of Modulator to Carrier, play around with the Output Level of Modulator to Carrier (critical). When you find these small changes making huge differences in the results - you really start to see the endless possibilities.

Some times changing the Output Level one unit is huge in the possible results it will yield (and as Manny points out in several tutorials, change is not always linear...

Also there are parameters that have different ranges... the Element Output Levels go 0 thru 127 on the AFM engine
The Element Output Levels on the FM-X engine is back to the original 0 thru 99.

This is yet another reason to not just mindlessly input numbers. Trust me on this... parameter ranges are different, not only for the Element Output Levels, but the Rates and Levels of the Envelope Generators.

In the AFM engine Rates and Levels worked on a range of 0 thru 63
In the FM-X engine Rates and Levels are configured on a range of 0 thru 99

Again, it is not simply copying numbers mindlessly... if you do, just sit there and enter numbers, you will spend literally hours doing this and your sound will not even be close. So if you are going to do this (and earn this Jedi Merit Badge) do yourself a favor, use it as a way to experiment with and learn FM programming... and don’t make the only focus an effort to restore some ancient sound.

If you focus on learning you will come out of this having a feeling that you have a better sense of how FM synthesis works. A feeling of some accomplishment.
If you just make it an exercise in entering numbers, you will learn nothing and you’ll likely find the sound you were attempting to recreate didn’t come across as you expected. And you’ll be back here asking “How come they...?”

Hope that saves you some time.

Link to article on working with 2-Op stacks: Mastering MONTAGE: FM-X Exploration Part 1

"Equivalent" may need some qualification. SY99's AFM has extensive feedback routing not available in FM-X. Your picture doesn't show any feedback at all - either due to simplification or because you really mean to ignore feedback. Ignoring feedback (and, I suppose - a bunch of other FM-related things the SY has that FM-X doesn't) - just for the basics - you have some options of what can give you 3 modulator/carrier pairs (stacks) as shown.

FM-X Alg 13, 14, 67, 74, 78, 81, 83 can all be reduced down to 3 carriers with 3 modulators stacked on top.

Alg 67 is the closest "shape" - so maybe an easy fit. But if you start needing complex feedback routing - it's likely that those feedback paths just can't be done with what you have in FM-X. You'll have to leave feedback somewhat on the table and lost in translation. Maybe examining what you think is the key feedback path and try to find an Alg that gets closest to providing that path -- or at least one of the feedback paths in the original.

The SY allows for simultaneous feedback routes and these routes can pick any operator's output as the source for feedback (well, except for the fixed ones - you can't pick those ... but mostly you get freedom) and allows for any operator's feedback input to be the destination - including multiple operators simultaneous as a destination for feedback of a given route. (FB1, FB2, FB3). Operators may have up to 2 feedback inputs - and each (of the up to 2) feedback inputs has its own level. It's really a lot of feedback routing flexibility -- even with a fixed assignment here and there.

FM-X is not trying to emulate / reproduce / model the SY99's AFM capabilities - so what you can match up is limited.

Unless you get lucky (like an "underutilized" SY99 AFM program) - you're going to likely be more in the realm of trying to reproduce the SY99 sound not by trying to find matching structures -- but more by using new features in FM-X to get in the ballpark a different way. The kind of stuff synthesis always does - sounds like something else using the current keyboard's technology to the best of its ability to mimic something else. Not by having the underlying exact model - but by your creative use of the knobs and settings. FM-X has "new" stuff (relative to the S
Y99) - so you may be able to dial in the general idea/character of an SY99 sound you're referencing by different means than the original AFM program.

Here is the algorithm section of this patch opened in the SY Manager.

I'm still learning all of this but I just had this one patch I so wanted to be converted.
I know FMX is a different beast than the SY's AFM, but I've seen someone on the Yamaha Musicians forum, Manny Fernandez to be exact, convert a favorite of mine the "NiteHawk" EP patch with amazing results.

He has messaged me with a bit more help, so hopefully I can get this done.

Actually, the Algorithm shape is just one aspect, please recognize that none of the Algorithms found in the MONTAGE/MODX FM-X engine match exactly the arrangement of the six Operator Algorithm 42 (as found in the AFM engine)

Yes. Matching the shape (three 2-Operator stacks) occurs several times in the FM-X engine, as noted above, but notice never are Operators 1, 3 and 5 Carriers with Operators 2, 4 and 6 as Modulators in the FM-X engine.
So you will have substitute the values so that you match the Operator to its role in making the sound... Carrier with Carrier and Modulator with Modulator in each case. If the AFM stack has Modulator as Op2 and Carrier as Op1, the fact that Op2 is a Modulator and Op1 is a Carrier is absolutely critical. You will not find such an Operator arrangement in the FM-X engine. This means you manually will need to swap Operator positions when you enter the values.

Programming Hints
The multiple 2-Operator stacks are used when you are programming a sound with multiple audible components. The iconic FM electric piano sound was based on the DX7’s three 2-Operator stack Algorithm. Three programming components.

You can use the convenient ”Algorithm Search” engine:
Define the number of Carriers and Modulators you desire to work with and it will show you your options.
Here’s how:
From an “Init FM-X” Part
“Edit”
“Common” > “Part Settings” > “Algorithm” > tap “Algorithm Search”
Set the number of “Carriers” = 4
Set the height of Operators stacked above (Chain) = 2
You can select the one that most appeals to your goal.

Each 2-Op stack made a different sound component contribution to the Rhodes tone... the first two 2-Op stacks fashioned the body of the tone soft-hard, and the third 2-Op stack was the high pitched tine sound. When combined you got a full bodied electric piano sound. In the iconic TX816 (eight DX7s in a rack) you had 48 FM Operators (8 x 6) making the electric piano sound... find the MONTAGE Performance “The TX816 E.Piano” — there each pair of DX7s (two Parts: 1/2, 3/4, 5/6, 7/8) create a Stereo image of their component building block

If you have the AFM synth (SY77/SY99) there to play around with, isolate each 2-Op stack and listen to its contribution to the whole.
In general when building sounds start with the Carrier (naturally) — fashion the AEG to create the general loudness shape of the overall sound you’re attempting to emulate. Then use the Modulator to give the timbre some definition. The Output Level of Modulator will profoundly change the overall timbre of the result. And it is the Modulator’s AEG that will determine how the timbre (tone) changes overtime. You want to make the Modulator sensitive to velocity change, (critical to make the timbre change as you play softer/harder).

If the Modulator’s AEG extends longer than the Carrier’s then its influence over the timbre will be throughout the sound.
If the Modulator's AEG is quicker/shorter than the Carrier’s then it’s influence will disappear before the sound dies out.
Again, critical functions, as the Modulator can be used as a quick burst to add chaos to the ‘attack’ portion, or it can be used to fashion a solid sonic tone for the held part of the sound.

These are a critical listening points when programming FM... Output Level and velocity response
In the FM-X Explorations tutorial, we take a deep look at the 2-Operator stack (as it forms the original backbone of FM synthesis)... with the older engines (original DX/TX and even in the AFM) it often took two Operators to fashion a complex waveform. Feedback was used to create more timbral chaos... and while the new FM-X engine has the original Feedback function to bring it into compatibility with the legacy six Operator engine... the Spectral Forms eliminates the need for an Operator Feeding back on its self — as each Operator is completely variable via the Spectral Form and Skirt parameters. And although you could route Operators freely in AFM, and you had as many as three programmable Feedback loops, that could included multiple Operators, you were limited to the total number of Operators per sound (12 in a “2AFM Poly” or 24 in an “4AFM Mono” program)... the FM-X engine provides you with a maximum of 64 Operators in an 8 Part KBD CTRL FM-X program!!!

But it’s not about which has more options, but which offers you more musical results. We discovered rather quickly, for example, the more complex the Modulator, the quicker it it generates frequencies containing all harmonics — in other words, it becomes an elegant “Noise” maker.
I remember we all were excited to modulate an FM sine wave with an acoustic piano...no one knew exactly what to expect; Well, as you know you can’t hear the Modulator - it’s contribution is strictly energy, not sound. Well, the more harmonics in the Modulator, the quicker it manifests complete chaos in the Carrier’s output result. The ability to make sound effects was greatly enhanced...

Extra Credit:
As you may know by now, I have a lot of T-shirts in my closet (as in: “been there, done that, got the t-shirt). So I’ve been down this road - the only thing this qualifies me to say is, (beyond the warning above about the Modulator/Carrier numbers and the importance of their location in the Algorithm) is instead of trying to reproduce an old sound by reading numbers off a piece of paper, be sure to use your ears while inputting numbers... it can be a good way to learn, if you take that extra time. And it will be worth it in the end.

If you just type in numbers (copy them without experimenting with them) you may get your sound or something close, but you learn nothing.
Experiment with not only the Rates and Levels of the AEG, but the tuning of Modulator to Carrier, play around with the Output Level of Modulator to Carrier (critical). When you find these small changes making huge differences in the results - you really start to see the endless possibilities.

Some times changing the Output Level one unit is huge in the possible results it will yield (and as Manny points out in several tutorials, change is not always linear...

Also there are parameters that have different ranges... the Element Output Levels go 0 thru 127 on the AFM engine
The Element Output Levels on the FM-X engine is back to the original 0 thru 99.

This is yet another reason to not just mindlessly input numbers. Trust me on this... parameter ranges are different, not only for the Element Output Levels, but the Rates and Levels of the Envelope Generators.

In the AFM engine Rates and Levels worked on a range of 0 thru 63
In the FM-X engine Rates and Levels are configured on a range of 0 thru 99

Again, it is not simply copying numbers mindlessly... if you do, just sit there and enter numbers, you will spend literally hours doing this and your sound will not even be close. So if you are going to do this (and earn this Jedi Merit Badge) do yourself a favor, use it as a way to experiment with and learn FM programming... and don’t make the only focus an effort to restore some ancient sound.

If you focus on learning you will come out of this having a feeling that you have a better sense of how FM synthesis works. A feeling of some accomplishment.
If you just make it an exercise in entering numbers, you will learn nothing and you’ll likely find the sound you were attempting to recreate didn’t come across as you expected. And you’ll be back here asking “How come they...?”

Hope that saves you some time.

Link to article on working with 2-Op stacks: Mastering MONTAGE: FM-X Exploration Part 1

If I can post the parameters of this patch (which is not ancient, it's an amazing Electric Piano not and not one of the standard ones), could someone help me to define the parameters for FMX?

This uses 2 of the 3 feedback paths. Op 6 (input 1) feeds back into itself with an input level of 1 and Op 6 (input 2) feeds back from the output of Op5 with an input level of 0.

I don't think an input level of "0" means off - I don't have the keyboard and docs don't really spell it out. But I would think you'd probably not connect (which you can do) rather than set a level of 0. I just think 0=the lowest level (whatever that is).

Of course what you've shown isn't the whole patch - just a small portion. There's a lot more to dig through. Knowing the feedback structure - you can try replicating without adding the Sy99 Op5 (output) to Op6 (input) feedback loop. OR you could use a structure that does have this (like Montage Alg 14 - which feeds back the output of Op 4 to the input of Op 3) and then use skirt to simulate self-oscillation on Op3.

If "0" does mean off - then the feedback structure would be reduced down to Montage Alg 13 or 67 or 74 or 78 or 83 or 81. 67's probably the one I'd pick if SY's input level of "0" does mean off. Someone else would have to chime in on this. If it isn't then the above Alg 14 may be best.

Not sure how all of the other things are set either. Feedback was just one of those SY-specific things. There are other possibilities in the feature-set that do not directly translate 1:1 and would require more than, as BM puts it, plugging in values.

If you didn't catch it:

The kind of stuff synthesis always does - sounds like something else using the current keyboard's technology to the best of its ability to mimic something else. Not by having the underlying exact model - but by your creative use of the knobs and settings. FM-X has "new" stuff (relative to the SY99) - so you may be able to dial in the general idea/character of an SY99 sound you're referencing by different means than the original AFM program.

This was my "use your ears" comment.

I'm no expert, but if it were me, I would follow BMs advice and break the AFM patch down into first principles (reverse engineer), and then try to rebuild the sound in FM-X. This, as opposed to trying to identify and copy 1 to 1 parameters and hoping for a good result.

Hey everyone.

Manny helped me out to the fullest extent! I can truly say he helped me to create this patch within the FMX engine nearly 1:1!

Super amazed with the result!

Did you post it to Soundmondo?