Hacker News Reader

>> John Chowning refined the concept, moved from frequency to phase modulation, and brought FM into the digital realm.

> ?? Chowning's paper doesn't mention phase modulation at all, does it? His equation is for frequency modulation. > >https://web.eecs.umich.edu/~fessler/course/100/misc/chowning... > > I would presume that the relationships between phase and frequency modulation were known a half-century before Chowning.

Chowning says his equation is for frequency modulation, but the equation is actually phase modulation.

Chowning's equation(1):

    e = A sin(𝛼t + I sinβt)

That's phase modulation. Frequency modulation would be:

    e = A sin((𝛼 + I sinβt) t)

Very different.

That's okay; it's the first academic paper on the topic, and things were still a little wobbly.

After the paper, he and others refined the concept, moved from frequency to phase modulation, and built digital implementations.

Ah yes, that's right. The I sin Beta t is I sin(beta t), not I sin(Beta) t.

>> Given 1983 technology, it was very difficult to implement digital audio filters, which require millions of multiplication/accumulation operations a second.

> This seems high? A second-order digital filter requires what, about 4 stores, recalls, and multiplies per sample? This would seem to be in the same level of complexity as six carrier/modulator interactions; you have to do a multiply to do a lookup after all. Or is the issue that the multiplies had to be 12-16 bit?

For microprocessors in 1983, multiply instructions, if they existed at all, involved a lot of shift and add cycles. That took a long time.

A simple filter might need 4 multiplies and accumulates. Times 44,000 times a second, for each sample. Times the number of voices; 16 in the case of the DX7.

Now you are easily over a million multiplies a second.

And even though the original DX7 is 12 bits, I think you'd need those multiplies to be 16x16 bits for accumulated error issues.

So the DX7 was an alternative to having to implement digital filters in 1983 technology. They could introduce a digital synth at a very reasonable price.

> > FM synthesis, as such, was not new. The Buchla synthesizer featured it in the 60's.

> But the critical feature of FM synthesis that made it usable as a musical element was linear FM. Early synthesizers (like, I presume Buchla's) sported "FM" but it was exponential due to volt/oct.

No; the first Buchla oscillator, the 158, did indeed have linear FM.

And that was intentional. Early Buchla synths didn't have much going on in the filter department, so instead he made the oscillators extra expressive.

> No; the first Buchla oscillator, the 158, did indeed have linear FM.

Could you point to an authoritative source on this? The Model 100 owner's manual says this about the 158: "The frequency modulation control require an external signal input, which determines the rate (speed) of the frequency modulation (vibrato)...". The fact that it says "vibrato" would imply exponential FM, wouldn't it?

https://archive.org/details/synthmanual-buchla-100-owners-ma...

Actually, after watching this video (https://www.youtube.com/watch?v=49qyPIX61rg) I'm less convinced that the 158 had linear FM. As he turns the FM knob, the pitch changes. This would be expected for exponential FM.

Correction; the senator meant to say the Buchla 258 oscillator had linear FM.

(Although there were variations!)

The control voltage input goes through the exponential converter, and the FM input sets the bias of the exponential converter.

> This would seem to be in the same level of complexity as six carrier/modulator interactions; you have to do a multiply to do a lookup after all.

The Yamaha FM synthesis chips do zero multiplications. Everything is done with additions in log scale, with a lookup table for log-sine and another lookup table for exp. I’m unaware of a technique for implementing digital filters without multiplication.

I don’t know why lookup would require a multiplication. Recall that the Yamaha FM chips do not use interpolation.

> A second-order digital filter requires what, about 4 stores, recalls, and multiplies per sample?

This is true today using something like the Chamberlin form for a state variable filter. I don't think that level of optimization had been discovered yet in the DX7 timeframe.

Also, for adequate quality you want to oversample at least 2x, preferably at least 4x.

And 16 bits usually won't be enough headroom in a digital filter for good audio quality. Too much truncation.

Well, remember the DX7 was 12 bit.

Right. My point was, digital filters won't sound good with those constraints, so people weren't using them yet.

Not to overshadow the main idea. The DX7 was a heck of a milestone.