SixOp: Six-Operator FM from INIT VOICE to Bells, Bass and Brass

Six sine waves and a routing map

An operator is a sine-wave oscillator with its own output level and its own envelope. Its frequency follows the played note through a ratio: at 1.00 it plays the note, at 2.00 an octave higher, at 0.50 an octave lower. The OPERATORS column lists all six, operator 6 at the top as on the original hardware, with on/off, ratio or fixed mode, Coarse, Fine, Detune, Level, velocity sensitivity, amplitude-modulation sensitivity and a small envelope picture.

The letter at the end of each row tells you the operator’s job in the current algorithm. A carrier (C) is mixed into the output, so its Level works like a volume control. A modulator (M) is never heard directly: it bends the phase of the operator below it, which adds new partials called sidebands. Raising a modulator’s Level makes the sound brighter and denser, not louder. Almost everything in FM follows from that difference.

Lesson 1: an electric piano from INIT VOICE

1. Choose Init voice in the voice menu. You hear one plain sine: operator 1 at Level 99 in algorithm 1, with an organ-like envelope that stays at full level until you let go of the key.
2. Step the algorithm to 5 on the ALG page: three pairs, each a modulator above a carrier, with operators 1, 3 and 5 as carriers. Raise Op2 Level to 72 at ratio 1.00 and the sine turns reedy, because operator 2 now modulates operator 1.
3. Give the pair a piano envelope: a fast first rate (96 and 95), a slower second and third rate and L3 at 0, so the note fades away even while it is held. Set Op2 Velocity to 6 so that harder notes are brighter.
4. Add the tine: operator 3 as a second carrier at Level 80, detuned by +2, and operator 4 above it at Coarse 14, Level 58 and Velocity 7, with L2 at 0 so its metallic edge lasts only a moment after each strike.

Play the example, then set Op2 Level to 0: the body of the piano becomes a pure sine while the tine remains. Try 90 and the attack starts to bark. Switch operator 4 off with its on button to hear the body without the tine, and compare soft and loud notes to hear how velocity sensitivity on a modulator changes tone rather than only volume.

Reading the 32 algorithms and feedback

An algorithm is a fixed wiring of the six operators. The ALG page draws it: operators stacked above another one modulate it, and the operators on the bottom row are carriers. Algorithm 1 has two carriers with a four-operator stack on one of them; algorithm 5 has three independent pairs; algorithm 32 makes all six operators carriers, which works like a six-drawbar organ of sine waves. Step through them with the arrows and watch which operators switch between C and M in the OPERATORS rows.

Every algorithm also has one feedback loop, drawn as a line looping back into an operator. Feedback (0 to 7, on the ALG page and in GLOBAL) lets that operator modulate itself: low values add a few harmonics, around 5 to 6 the sine leans toward a sawtooth, and at 7 it gets rough and noisy. Because the loop sits on a fixed operator, feedback only does something when that operator has some Level.

Lesson 2: bells from inharmonic ratios

Ratios that are whole numbers give harmonic, pitched tones. Other ratios give the clangorous partials of bells and metal. In this example operator 2 runs at 3.50 (Coarse 2 with Fine 75) and operator 4 at 4.23 (Coarse 3 with Fine 41): Fine multiplies Coarse by one plus Fine divided by 100. Both modulators have shorter decays than their carriers, so the strike is brighter than the ringing tail, as with a real bell.

Detune (-7 to +7) shifts an operator very slightly away from its ratio. Operator 3’s +3 makes it beat slowly against operator 1, which gives the tail life. Switching an operator’s mode from R to F makes it ignore the keyboard and play a fixed frequency; a fixed modulator gives every key a different spectrum, which is useful for drums and effects.

Four rates, four levels

Rates R1 to R4

Speeds from 0 (very slow) to 99 (immediate), not times. R1 moves toward L1 when a key goes down, R2 toward L2, R3 toward L3, and R4 toward L4 after release.

Levels L1 to L4

Targets from 0 to 99. L3 is where the envelope rests while a key is held; L4 is where it ends after release and also where the next note starts.

Rate Scl

Rate scaling (0 to 7) speeds up the envelope for higher notes, so treble notes of a piano or bell decay faster than bass notes.

On a carrier the envelope shapes loudness; on a modulator it shapes brightness over time. Open the ENV page, choose an operator by clicking its row and drag the handles or type the numbers. The pitch envelope (PITCH page) uses the same four rates and four levels, but its levels bend the pitch of the whole voice and 50 means no change.

Lesson 3: an FM bass with feedback, mono and glide

This bass uses algorithm 5 again, but only two of its pairs. Operators 2 and 1 give a punchy attack that settles to a rounder sustain, while operator 6 feeds back into itself at Feedback 6 and modulates operator 5, which adds a saw-like growl underneath. Turn Feedback down to 0 and the growl turns into a clean, hollow tone.

The voice is set to MONO in GLOBAL, so only one note sounds at a time, and Porta at 35 glides between them. In mono, Mode chooses Fingered (glide only when notes overlap) or Full (always glide); in poly it chooses Retain or Follow. The G button turns the glide into semitone steps. Voices sets how many notes can sound at once in POLY, up to 16, and PB sets the pitch-bend range.

Keyboard scaling and velocity

Keyboard level scaling (the KEYS page) changes an operator’s level across the keyboard. Choose a break point, then a depth and a curve for each side: -LIN and -EXP lower the level away from the break point, +LIN and +EXP raise it, with the exponential curves changing faster toward the extremes. Lowering a modulator toward the top of the keyboard keeps high notes from turning harsh; lowering a carrier evens out a sound that gets too loud in the bass.

Velocity (0 to 7) is set per operator as well. On a carrier it makes soft notes quieter; on a modulator it makes soft notes darker, which is usually what an expressive keyboard sound needs. AMS (0 to 3) sets how much the LFO’s amplitude modulation, and controllers assigned to Amp, affect that operator.

Lesson 4: a brass swell with the pitch EG and LFO

Algorithm 22 lets operator 6 modulate three carriers at once, so one envelope swells the brightness of a whole stack. The carriers attack at rate 62 and the modulators more slowly, at 48 and 45, so each chord first grows louder and then opens up, as brass players do. The pitch envelope starts at L4 47, slightly flat, and rises to 50 at rate 70, giving a short scoop into each note.

The LFO page sets one modulation oscillator for the voice: Wave (triangle, saw down, saw up, square, sine or sample and hold), Speed, Delay, PMD for pitch depth, AMD for amplitude depth, Key sync and PMS, the voice’s pitch-modulation sensitivity. Here a sine at Speed 34 waits for Delay 55 before a gentle vibrato (PMD 8, PMS 3) fades in, so short notes stay steady and long ones start to sing.

Lesson 5: modulating with the mod wheel

The Controllers button in GLOBAL opens the assignments for the mod wheel (MW), foot controller (FC), breath controller (BC) and aftertouch (AT). Each one has a Range and any combination of Pitch, Amp and EG Bias. Pitch and Amp raise the LFO’s pitch or amplitude depth up to the range as the controller moves, so the LFO’s own PMD and AMD act as a floor. EG Bias lowers the level of every operator whose AMS is above 0 steadily, without the LFO.

In this example the wheel is assigned to Pitch and Amp with Range 50 and is held at 60 percent. Operator 2 is a modulator with AMS 3, so the amplitude part makes its level, and therefore the tone, sway like a wah, while the pitch part adds vibrato. Set the Mod Wheel value to 0 and the note goes still; automate it in a clip to bring the movement in only where the phrase needs it. Aftertouch works the same way when your keyboard sends it.

Loading and importing DX7-compatible voices

The VOICE column on the left is SixOp’s librarian. The bank menu lists the factory banks (the four classic ROM banks plus public-domain banks contributed by the user community), your own imported banks and, once you have loaded an imported voice, the project’s bank. Click a voice to load it: all of its parameters land in the panel, ready to edit, and the display shows its name. Compare switches between your edits and the stored voice.

Import reads DX7-compatible .syx files: 32-voice bulk dumps (including files that hold several banks), raw 4096-byte voice data and single voices. You can also drop .syx files onto the Browser or onto the device. Imported banks are saved to your User Library, so they appear in SixOp’s bank menu in every project and in Ensemble’s FM6 parts. If a file’s checksum does not match, you are told so and can choose Load anyway. Save stores the current voice in your library, and the voice menu exports a voice or a whole bank as .syx again.

A good way to learn from a factory voice is to load it, open the ALG page and switch carriers off one at a time to hear what each contributes, then lower each modulator’s Level to hear what it adds. After a few voices you will start recognizing the same pairs, ratios and envelopes everywhere.