I suppose that, having come this far, I might as well finish this series of posts, but I would urge any readers to please post on the forums (the thread will be linked to at the bottom of this article) with corrections or important information I've missed -- I'm sure there will be many omissions and errors as I move out of my comfort zone and start writing about the synths with which I am less familiar.
At any rate: FM
FM, as the name implies and as the manual (from which the above image is taken) asserts, provides "Four operator FM synthesis".
In case you missed the 80s, FM is short for Frequency Modulation; the basic idea is that a set of oscillators -- for some reason called "operators" in this context, and in the specific case of OP-1's FM engine, comprising four sine waves -- are set to modulate each others' pitch. This produces complex and rich timbres, which can tend towards the clangorous and inharmonic.
(In case it's not obvious by now, I'm far from an expert at FM synthesis; my only real experience has been the very simple 2-operator version which is featured in some virtual analog synths, where one oscillator can be used to modulate another's pitch.)
While FM (the synthesis method) is notorious for being complex and difficult to understand, FM (the OP-1 synth engine) is relatively straightforward and fairly simple to use.
Visually, the theme is a quartet of isometric wireframe cubes (or if you prefer to stay in 2D, hexagons) inside which the relative pitches of the operators are displayed, each with a different colour drawn from OP-1's set of four "cardinal colours": the ubiquitous blue, green, white, and orange.
Unlike the above image, which is sadly out-of-date (although still quite gorgeous), the current OP-1 software displays the blue operator's pitch as "B"; I believe this refers to it being the Base frequency, with all other operator's frequencies' being either a ratio (1/2, 1/4, 3/8, etc.) or a multiple (2, 3.5, 4, etc.) of this base frequency, which itself tracks the keyboard.
I have arduously compiled a list of frequency sets (Green) and topologies (White), here: http://op-101.blogspot.com/2011/09/fm-data.html
This synth engine is capable of a very broad range of sounds, from deep and solid bass, to blaring clangorous tones, to sharp noisey chaos.
Blue ("FM Amount"):
(Note that the manual incorrectly -- or perhaps obsoletely -- has the Blue, Green, and White parameters swapped around. I will use the names that the manual provides, but apply them to the current/correct coloured encoder)
Blue controls the level of each of the non-Base operators, i.e modulation depth if an operator is modulator (located at the start or middle of the signal chain), or volume if the operator is a carrier (located at the end of the signal chain). The White section below will deal with how to determine which operators are acting in which capacity.
Aurally this control sounds very similar to a non-resonant lowpass filter, with good reason -- as you increase Blue, "raising the cutoff" as it were, the modulation depth increases with the result that more and more high-frequency overtones are introduced into the sound. This is purely analogous though, not literally identical, for the nature in which the timbre changes when raising the FM Amount is much more complex and interesting than a plain filter sweep.
Graphically, increasing operator levels are represented as increasingly bright blue silhouettes around the cubes (or outlines around the hexagons if you prefer to see it that way -- but from now on I'll stick to the 3D interpretation).
At the minimum/CCW value, the level of all non-Base operators is 0 and you are left with Base providing a pure sine tone -- very useful in and of itself. As you begin to turn Blue CW, the operator levels increase and the sound starts to round out somewhat; the effect varies quite a bit depending on the values of the other parameters. Turning Blue further causes the former "roundness" to increase in intensity and sharpen, until at the maximum/CW setting you are left with a very aggressive and noisy/busy tone.
Green ("Freq."):
The Green control determines the relative frequencies of each operator. Rather than providing individual control over each operator's frequency, this parameter selects from a list of 102 unique "sets", with each set defining three values: the frequencies of the green, white, and orange operators relative to the Base frequency.
The sets are arranged hierarchically, and are unfortunately somewhat awkward to explain.
Starting at minimum/CCW and turning CW, the green operator's frequency increases, spanning 8 different values: 1/64, 3/32, 1/8, 5/16, 1/2, 5/8, 1, and 2. For each of these green frequencies, there are a range of white frequencies -- unlike green, the white operator's frequencies decrease with CW movement. Finally for each white value, there are one or more orange frequencies which seem to be arranged in more or less random order.
One analogy for this behaviour is a digital time display: hours:minutes:seconds. The seconds (orange operator frequency) will count upwards and once they reach 00:00:59 they will wrap around to 00:01:00, incrementing the minutes (white operator frequency). Eventually the minutes will wrap around from 00:59:59 to 01:00:00, incrementing the hours (green operator frequency). Rather than having 60 different values as in the case of time (00 through 59), the operator frequencies have 1-2 (orange), 12-14 (white), and 8 (green) different values that they can pass through.
The net effect is that as you spin Green CW, the orange operator changes rapidly (each movement of the encoder corresponds to a change in the orange frequency), the white operator changes after one or two encoder steps (after orange sweeps through its range for that particular value of white), and the green operator changes after 12-14 encoder steps (after white sweeps through its range for that particular value of green).
(I hope that this is clear -- it's absolutely obvious when looking at a table of frequencies, but unfortunately cumbersome to describe succinctly.)
While there is a definite numerical pattern to the layout of the frequency sets, this doesn't translate to any particular order in terms of timbre -- the sound varies wildly even between adjacent values of the Green parameter, from melodic and harmonious to discordant and clangorous.
Visually, this control is obvious: the numbers in each cube change as you select a different set of three non-Base frequencies.
White ("Topology"):
Hopefully the idea of topology -- in the parlance of the DX7, "algorithms" -- is self-evident: the four operators can be arranged in various patterns (technically, directed acyclic graphs) of modulator and carrier.
Visually, the relative location of the cubes indicates their current function: as far as I can tell, cubes which are diagonally adjacent in a "\" direction are modulator and carrier: the upper-left cube is the former while the lower-left cube is the latter. Cubes which are diagonally adjacent in a "/" direction are mixed together.
Operators in the middle of the graph are both modulator and carrier, while operators who have no neighbor below and right of them are "output" operators -- that's what you're actually hearing.
This means that the CCW-most setting of White is all operators in a serial configuration (orange->white->green->B) while the CW-most setting is a parallel configuration where all four operators are sent to the output directly without modulation.
IMPORTANT: the above information may be incorrect! The "parallel" topology mentioned above (White fully CW) makes me suspicious of my attempted explanation, because if I'm correct then it should sound like 4 sine waves mixed together... but to my ears it sounds more complex than that.
Possibly there is some amount of self-modulation happening at the orange end? The TX81Z (and AFAIK DX21) -- both 4op FM synths -- had self-modulation happening on one operator of all of their algorithms, as illustrated in the diagram near the top of this website. It's possible that TE have stolen a page from Yamaha but this is hidden to the user.
One final thing to note here is that the volume of the Base operator seems to vary depending on the topology; when there is more than one "output" operator, the level of B is reduced. This is only really apparent when Blue is turned fully CCW so that the synth is generating a pure sine tone. I would guess that when there is more than one output operator, the levels of each are reduced so that the level of their combined output isn't twice as loud as single-output-operator topologies.
I apologize for the sloppiness and vague guesswork in this section; I'm sure there are many inaccuracies, and if you're aware of any please do let me know -- as mentioned above, there will be a link to a forum thread included at the end of the article for further discussion and corrections.
Orange ("Detune"):
This parameter is obvious: it detunes the operators. This can be used to create extreme inharmonic sounds, or simply introduce some beating movement.
Visually, the amount of Detune is shown by the B and white cube being offset to the right (the latter more than the former) while the green and orange cube are offset to the left (again, the latter experiencing a greater amount of movement than the former).
It's unclear whether the visualization is a literal depiction of what's happening internally, or merely an illustrative metaphor; I suspect the latter, because while B moves visually as you turn Orange, with Blue fully CCW there is no audible change in the pitch of the sine tone that's produced.
Sadly my untrained ears are unable to determine which operators are detuned by how much in which direction, even using the simple "parallel" configurations (White fully CW). If anyone has a guess, please let me know!
Concluding
That brings us to the end of our look at OP-1's FM synth engine; again I must apologize for the relative lack of rigour and certainty I've brought to bare on it.
If you'd like to contribute or correct something, or just chat about FM, please stop by this forum thread and discuss to your heart's content! http://ohpeewon.com/discussion/231/op-101-fm
