The Yamaha DX7 synthesizer's clever exponential circuit, reverse-engineered

https://www.righto.com/2021/11/reverse-engineering-yamaha-dx7_28.html

by picture • 5 years ago

271 65 5 years ago

kens4• 5 years ago

Author here if anyone has questions about this classic synthesizer's internals.

yowlingcat• 5 years ago

Wow, very cool! The DX7 is one of my favorite synthesizers of all time, and its spiritual successor (in software form), FM8 is the one I've used the most for the past decade and a half in my compositions. Thank you for the incredible work breaking things down to the gate level -- if only this were around during the time I was taking my analog + digital electronics and computer organization class, I may have done a different final project!

You allude that you'll get to this in your next post of the series, but here's my question: what are the biggest differences in tone between the DX7 and current emulators such as FM8 and Dexed (both of which I believe can read DX7 patches)? And if present, where do they come from?

Thanks again for this write-up on one of my favorite machines.

pantulis• 5 years ago

I'd like to add to the list Korg's own FM implementation MOD-7

kens4• 5 years ago

Strangely, I haven't used any of the emulators or a DX7, so I can't comment on the differences in tone.

raphlinus2• 5 years ago

I believe you will find two main sources of differences in tone between the various DX7 emulators. One is that there are fairly major differences between the original DX7 and the DX7 II (I used the latter for the original engine now adapted in Dexed). The other is the analog filter on output, approximately a 16kHz lowpass filter designed to reduce artifacts from the DAC (this is replaced by a more general Moog-style filter in the Android implementation but present as an accurate emulation in Dexed).

I think Dexed is quite accurate, but this work will allow the authors to take it to the next level. I suspect most people won't be able to hear the difference, however.

raphlinus2• 5 years ago

The specific thing I've found least documented, yet most important for the distinctive percussive attacks of the DX7, is a random variation of the pitch envelope for the first few milliseconds of the note. That's almost short enough it could be done in the firmware, but I believe it might be in the hardware. It's not present in the msfa source, but might have been recovered by later Dexed authors (I haven't carefully looked at their code).

If you get to the envelope hardware, you'll find it's just as clever as the exponential and sine generators. There's some info at [1], but it doesn't capture every single thing I found - there are cases where there is a slight amount of additional noise in the amplitude, I'm not sure whether intentional to give more character or an unintentional artifact. That's also missing from the msfa source.

[1] https://github.com/google/music-synthesizer-for-android/blob...

ETA: Also see https://levien.com/dx7-envelope.html for a somewhat interactive JavaScript implementation of the envelope algorithm. This accurately emulates the envelope shape and quantization of the DX7 (ie it uses the same reduced number of bits to drive its state machine), but I do not claim it is bit-perfect.

kens4• 5 years ago

I haven't looked at the envelope chip, but I hope to examine it at some point.

analog31• 5 years ago

Interesting, hammond organs had a similar effect due to bad key contacts and leaky capacitors. Simulated by Korg of course.

turdnagel• 5 years ago

How good is Chipsynth OPS7’s emulation? https://www.plogue.com/products/chipsynth-ops7.html

ajxs5• 5 years ago

It's arguably the most 'authentic' emulation available. The amount of work they've put into the project of emulating the DX7's various nuances is enormous.

odiroot• 5 years ago

I've heard Yamaha needed to put a lot of R&D work into producing these digital FM chips.

I wonder if they (or any other manufacturer) ever attempted the same with purely analogue chips. I'm aware that FM has very narrow sweet spots and probably the analogue oscillator drift would make this idea totally impractical.

ssalazar2• 5 years ago

I do wonder if DCOs (much less susceptible to drift) would be more amenable to analog FM, though they were not common for musical instruments during the DX7's early R&D phase.

That said, it seems like music manufacturers were searching for a musically useful, cost-effective digital synthesizer around this time. Early digital synths like the Synclavier and Fairlight CMI were prodigiously expensive, while analog synths in the DX7's price range were saddled with few/no polyphonic voices and/or limited single oscillator designs. The DX7, with a varied tonal palette and 16 voices, must have seemed luxurious at the time.

klodolph3• 5 years ago

The other factor is the sheer number of oscillators you'd need to get polyphony. The DX7 has 6 oscillators per voice. With 16 voices, that's 96 oscillators. Typical polyphonic analog synthesizers have two. You occasionally see three. Polyphony is often lower. 8 voices is fairly common, but you saw smaller units... Prophet 5 was 5-voice, and Oberheim's OB-X was available in 4, 6, or 8 voice versions.

The DX7 had somewhere between 9 and 12 times as many oscillators, depending on which of those lines you compare it to.

ajxs5• 5 years ago

This isn't quite FM, though Jean-Claude Risset from Bell Laboratories did some contemporary experiments using additive synthesis with analog oscillators to achieve similar complex tones. I'm guessing that Yamaha probably experimented with all kinds of interesting prototypes before developing the VLSI FM chips that would go into their earliest FM synthesisers. It was a very large investment for them as a company, so they likely tried all kinds of things first with existing technology they had on hand.

boomlinde• 5 years ago

Analog FM is not so unusual, but it's usually "real" FM, e.g. a modulation of pitch or linear frequency, and it's not so easy to tame into consistent musical pitches.

"Yamaha style" FM is however more of a kind of phase modulation. The operators are sine tables driven by phase counters, and the outputs of the modulators are scaled and summed with the phase counter of the carrier before the sum goes into the carrier wavetable. So you modulate the phase irrespective of frequency, e.g.

  modulator(phase) = sin(phase * modulator_multiplier) * modulator_amplitude
  carrier(phase) = sin(phase * carrier_multiplier + modulator) * carrier_amplitude

I suppose this could be replicated in the analog domain. A phase counter could simply be a ramping sawtooth waveform. Summing modulator outputs would be as simple as mixing. The hardest part I think would be to replicate the wavetable. You'd need a waveshaper that basically does f(x) = sin(x). There is an oscillator on the market that I think does everything except the waveshaping in the analog domain: https://wmdevices.com/products/phase-displacement-oscillator...

ChuckMcM• 5 years ago

Another great write-up Ken, I'm wondering how the DX-11 differed (it was introduced after the DX7 and I've got a TX-11 (tone module)). The logarithm trick looks like it would fit easily in a small FPGA too!

ajxs5• 5 years ago

I haven't peered under the hood of the DX11, I do have a TX81Z though which is the rack-mounted equivalent. I'm pretty sure the fundamental design would be more-or-less identical. There definitely would have been many small improvements in the design between the DX7, and the DX11. Aside from the DX11 supporting different waveforms (actually truncated sine waves), people have said that the large difference in sound between the successive generations of Yamaha's FM synths comes from using a more abridged sine table. The shorter the table, the more thin, and metallic the sound.

S_A_P2• 5 years ago

The DX-7 has 6 operators per voice and 16 note polyphony. The DX-11 is a 4 operator synth but with 8 voice poly, but is multitimbral, where the DX-7 is monotimbral. I think both have their advantages and most of the time 4 operators are enough. I’ve been looking for a Yamaha FS-1 which was the 1990s return to FM synthesis for Yamaha. It’s a rare-ish classic that I wish Yamaha would reissue.

knob• 5 years ago

This was fascinating to read. Thank you for taking the time to post it up!!

kbob• 5 years ago

Are there resources for delta encoding transcendental functions in general? A fast, compact tanh() function would be great for making ladder filters in an FPGA.

EarlKing3• 5 years ago

It's really starting to scare me how many of my personal interests manage to crop up as articles here.

SavantIdiot3• 5 years ago

We're not as unique as we like to believe. I bet there are probably just ~400 different archetypal people that read HN.

S_A_P2• 5 years ago

Yeah, I’m willing to bet that most folks here are either into music/audio, photography, video production, or building gear and software that supports these endeavors in some way. I know a lot of people who code, but few of them visit this site. The ones that do fall into one of those categories.

EarlKing3• 5 years ago

Well, yes, but it can get eerie when I suddenly start seeing articles aimed at a very specific machine I happen to have recently begun playing^H^H^Hworking with (i.e. the DX7).

Hmmmm....

I REALLY LOVE THE ROLAND D-50. GOSH, IT SURE WOULD BE NICE IF THERE WAS AN OPEN SOURCE EMULATOR FOR IT...

...and now we wait.

dave_sid• 5 years ago

So cool an article about synths is at the top of HN.

throwawaysea2• 5 years ago

Can someone explain what a synthesizer is to a non musician? It looks like a keyboard to me. Do the two terms mean something different? Also, in today’s world, do these need to exist in the same form? That is, can’t all these sounds simply be digitally produced rather than relying on circuitry? Why aren’t all new keyboards (or those other things DJs have on stage) simply software, maybe with a custom input device for easier live use?

jacquesm8• 5 years ago

A synthesizer is a device that creates waveforms of a musical nature that do not have a natural equivalent.

throwawaysea2• 5 years ago

Is it not possible to have a fully digital (built in software) synthesizer?

recursive• 5 years ago

The synthesizer is the part that makes the waveform. Some of them have keyboards attached. Some don't. Some performers do indeed use a MIDI controller and VST plugins on a laptop.

The main problem with this is that software runs on computers, and sufficiently portable computers are generally just not reliable enough for a lot of live performances.

ssalazar2• 5 years ago

That is, can’t all these sounds simply be digitally produced rather than relying on circuitry?

Even for an almost fully digital synth like the DX7 a bit-accurate emulation is difficult (there is a rich discussion of this in one of the other threads here). For analog synthesizers, there is a lot of character and nuance in the individual circuits that are difficult to capture in a digital model, across all possible configurations. In the mix of a full song though, its not often that people can notice the difference.

Aliasing--the introduction of extra unwanted and generally non-harmonic frequencies--is also really hard to avoid in digital systems. For more esoteric instruments like Eurorack modules or Moog modular synthesizers, the physical interface is an integral part of the instrument--software versions of these exist but are obviously very different to interact with using a mouse or touchscreen.

Why aren’t all new keyboards (or those other things DJs have on stage) simply software, maybe with a custom input device for easier live use?

For live use this is very common nowadays, though physical single purpose keyboards (even fully digital ones) still are used widely. In a fast moving stage show you may not want to mess around with the complexity of a full personal computer setup. In modern operating systems, even with 100s of processes competing for CPU time, real-time audio may rarely drop out (the result of which is audible clicks and pops), but even this is too risky for a big professional live show.

adgjlsfhk1• 5 years ago

I honestly dont understand why none of the main consumer operating systems are optimized for low latency. outside servers, I feel like I would gladly take an OS that made my computer 2x slower, but never had a pause of more than half a ms or so.

ajuc• 5 years ago

Synthesizer is the part that creates the sound, keyboard is the part that tells synthesizer what note to play, when, for how long, and possibly at what volume. Sometimes people call the whole thing keyboard cause its the most distinctive part of it, but you can use the same keyboard connected to different synthesizers and synthesizers can exist without keyboards.

What's important about synthesizers is the fact that for the first time in history it allowed musicians to control the "character" of sound gradually in new dimensions (the parameters that let you distinguish the same note played on piano, flute, guitar, violin, etc.), creating sounds that were impossible previously and even changing the character of the sound in real-time as another dimension of artistic expression. It's like you played a long note on violin and it morphed slowly over time into a flute and then some instrument that doesn't exist. You couldn't do it before and all these new possibilities and constraints changed music.

Also the particular UI of some synthesizers allowed easy exploration of these new dimensions and that's important too. It's one thing to be able to play any waveform you want (you can do that by editing .wav file in hex editor), it's another to have several knobs and sliders and hear the differences in real-time when you tinker with them.

We can simulate all of this in software but not 100% perfectly.

klodolph3• 5 years ago

Can someone explain what a synthesizer is to a non musician?

Keyboard = input device, usually generates MIDI. Synthesizer = creates sounds from scratch, usually generates audio from MIDI.

Some keyboards are not synthesizers (sometimes called a "master keyboard") and you have to plug them into something in order to get sound. Some synthesizers are not keyboards, and you have to plug something into them to control them. For example, the DX7 is both a synthesizer and a keyboard. The TX-802 is a synthesizer but not a keyboard... it is kind of like two DX7s in a 2U rack-mount unit without a keyboard. The Akai MPK249 is a keyboard but not a synthesizer. You can buy a TX-802 and an Akai MPK249 and plug them into each other, and it's kind of like having a DX7.

Also, in today’s world, do these need to exist in the same form? That is, can’t all these sounds simply be digitally produced rather than relying on circuitry?

Circuit emulation has varying degrees of accuracy. I like to think of digital synthesizers as computers that don't ever need software updates, and are therefore more reliable than software running on a computer. They also often have purpose-built UIs (knobs, buttons, sliders) which are critical to some people using them.

If you are going to make a custom input device, why not just make the custom input device and the synthesizer one single package? This is called a "sound module" -- something that makes sounds but does not have a keyboard attached. They come in both rack-mount and desktop versions.

jerrysievert2• 5 years ago

Why aren’t all new keyboards (or those other things DJs have on stage) simply software, maybe with a custom input device for easier live use?

there are some sounds that rely on certain electronic oddities from weird components that cannot easily be modeled in software. some Russian transistors that are used for the polivoks filters are some that I can think of off the top of my head.

personally, I've built a ton of software simulations of hardware equipment, but I still have a tx81z sitting around, and a rack full of eurorack gear. there are just some things I can't get quite right, and some weird things that I doubt I could ever reproduce[1].

we can't accurately model a SID chip in software or fpga due to its weird quirkiness under electrical load, some of the less sane chips are even harder. that's why there's such a demand for weird things that use older chips[2].

1. https://www.nonlinearcircuits.com/modules/p/brain-custard

2. https://www.youtube.com/watch?v=NrZZiTpK3f0&t=112s

Bxbo• 5 years ago

Fourier, 200 years ago showed you can create a curve of any shape you can imagine by adding Sine Waves. The synth applies that to music and speech.

But the concept is applied in hundreds of fields as you move from curve, to planes to volumes.

The key magic is the sine wave which unlike other curves on differentiation any number of times always produces a sine way due it's deep connection to anything in nature that Repeats.

tasty_freeze• 5 years ago

Sine waves are convenient, but aren't at all necessary for a fourier transformation. The requirements are that you have a set of functions which are all pairwise orthogonal which also form a complete basis set.

At least, that is what I recall from my EE classes 35 years ago.

airstrike• 5 years ago

Since the article didn't appear to include any samples, I resorted to Goodolegoogle and found this: https://www.youtube.com/watch?v=U7Xnr0m-elw

geephroh• 5 years ago

Thanks to the OP for the memories. Worked and scrimped for the DX100 when I was in high school. That keyboard, my buddy's CZ-101, his brother's TR-505, plus copious hair mousse were the recipe for some of the best and worst Depeche Mode covers of all time.

The Yamaha DX7 synthesizer's clever exponential circuit, reverse-engineered

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