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Chapter 4

FM synthesis

Operators, algorithms, ratios and envelopes — the DX7 engine, explained.

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In this chapter · 14
  1. 4.1How FM works, in five minutes
  2. 4.2Algorithms
  3. 4.3Feedback
  4. 4.4EDIT mode: getting around
  5. 4.5Operator tuning and level
  6. 4.6Operator envelopes: rates and levels
  7. 4.7Velocity, LFO sensitivity and fixed frequency
  8. 4.8Keyboard scaling
  9. 4.9The pitch envelope
  10. 4.10Voice settings: algorithm, feedback, sync and transpose
  11. 4.11Muting an operator
  12. 4.12Mono and poly
  13. 4.13Glide
  14. 4.14Recipes: three sounds from scratch
4.1BasicsManual §3.2 p.7

How FM works, in five minutes

Every FM-1 sound is built from six operators, OP1 to OP6. Each operator is a sine-wave oscillator with its own envelope and level. On its own a sine wave is the plainest sound there is; FM gets its character from operators changing each other.

Carrier
An operator you hear. Its output goes to the speaker, and its level is a volume.
Modulator
An operator you don’t hear directly. It wobbles the pitch of another operator so fast that you hear a new tone colour instead of vibrato. Its level sets how bright or harsh the result is.
Algorithm
The wiring: which operators are carriers, which modulate which, and where the feedback loop sits. The FM-1 has 32. See Algorithms.
Ratio
Each operator’s frequency as a multiple of the note you play. Whole-number ratios give harmonic, musical tones; odd ratios give bells and metal. See Operator tuning and level.

Three things to remember

  • A modulator’s level is the main brightness control — more level, more harmonics.
  • A modulator’s envelope is a filter envelope in disguise: a fast decay on a modulator gives the pluck of an electric piano or bass.
  • A modulator’s ratio decides which harmonics appear, so it changes the character, not just the brightness.

From the community

FM-1: A full FM synthesizer for $67

David Hilowitz Music

Composer-friendly overview of what you actually get as a full FM synth for the price.

M-Vave FM-1 Guide, Part 2 | Basic Operator Controls, Intro to FM, and two simple Patches

MiyafujiP

Part 2 of a methodical series: output level, coarse ratio, carriers vs modulators, detune and two starter patches.

4.2BasicsManual §1 p.1, §3.1 p.5

Algorithms

An algorithm decides how the six operators connect: which ones you hear and which ones modulate others. Turning ALGORITHM picks one of 32 and shows its diagram for about a second — carriers along the bottom, modulators stacked above the operators they feed, and a line marking the feedback loop.

Key combinations

Turn ALGORITHM
Selects algorithm 1–32 and shows its diagram.

Reading a diagram

  • More carriers, more organ. Algorithms with many operators along the bottom behave like additive organs: each carrier adds its own tone.
  • Tall stacks, more growl. A chain of modulators feeding one carrier gives the most complex, aggressive tones.
  • Pairs in parallel. Two or three short stacks side by side are the classic way to layer two sounds, such as a tine and a body in an electric piano.

The same setting appears as Algorithm on the voice settings page in EDIT mode — see Voice settings: algorithm, feedback, sync and transpose.

From the community

M-Vave FM-1 Guide, Part 2 | Basic Operator Controls, Intro to FM, and two simple Patches

MiyafujiP

Part 2 of a methodical series: output level, coarse ratio, carriers vs modulators, detune and two starter patches.

4.3IntermediateManual §3.1 p.5, §4.2 p.12

Feedback

In each algorithm diagram, one operator has a loop drawn back into itself: that operator modulates its own pitch. Feedback sets how much, from 0 (none) to 7. Moderate amounts turn a sine into something close to a sawtooth; the top values break up into noise, which is useful for breath, wind and percussion.

Find it

  1. Press EDIT.
  2. Press GLO KEY on the keyboard.
  3. Turn KNOB 2 to set Feedback.

From the community

M-Vave FM-1 Guide, Part 4 | Feedback, and some more patches

MiyafujiP

Part 4: operator feedback explained with more example patches.

4.4BasicsManual §3.2 p.7, §4.2 p.12

EDIT mode: getting around

EDIT mode is where you change the sound itself rather than shape it from outside. Pressing EDIT turns the ten labelled black keys into a menu: the eight that pick a section blink, the one you are editing lights solid, and SELECT turns that section’s pages. Each operator remembers the page you last left it on.

  1. Press EDIT.
  2. Press a labelled key — OP1–OP6, PIT or GLO KEY — to choose what to edit.
  3. Turn SELECT to page through its parameters. An operator has six pages.
  4. Turn KNOB 1–KNOB 4 to edit the parameters on the page, left to right.
  5. Press EDIT again to go back home, and save to keep the result.

Keys in EDIT mode

EDIT
Enters EDIT mode, or leaves it for the home screen.
EDIT, then OP1–OP6
Selects an operator to edit, on the page you last used for it.
EDIT, then hold OP1–OP6
Mutes that operator until you change preset.
EDIT, then PIT
Selects the pitch envelope.
EDIT, then GLO KEY
Selects the voice settings: algorithm, feedback, oscillator sync and transpose, then the preset tools.
EDIT, then MONO
Switches to mono: one note at a time.
EDIT, then POLY
Switches to poly.

An operator’s six pages

PageParameters (knobs 1–4)Covered in
1 · Tuning & levelDetune, FreqCoarse, FreqFine, Out LevelOperator tuning and level
2 · EnvelopeRate 1–Rate 4Operator envelopes: rates and levels
3 · EnvelopeLevel 1–Level 4Operator envelopes: rates and levels
4 · Sensitivity & modeA ModSens, KeyVelocity, OscModeVelocity, LFO sensitivity and fixed frequency
5 · Keyboard scalingL Depth, R Depth, BreakPointKeyboard scaling
6 · Keyboard scalingL Curve, R Curve, RateScaleKeyboard scaling

From the community

Rambling About: M-Vave FM-1 with tafony

tafony

Relaxed tour with handy chapters, ending in a patch built from scratch.

4.5IntermediateManual §3.1 p.4

Operator tuning and level

Page 1 holds the two settings you will touch most. The frequency settings decide which harmonics an operator adds; Out Level decides how much. For a carrier, Out Level is its volume in the mix. For a modulator it is the modulation depth — the main brightness control.

EDIT · Operator · page 1 · tuning and levelPress EDIT, then OP1–OP6. Turn SELECT to page 1.

Detune

A small offset from the exact ratio, for slow beating between operators. 0 is in tune.

KNOB 1Range −7–+7

Ratios that work

  • Carrier 1, modulator 1 — the bright, buzzy basis of brass and basses.
  • Carrier 1, modulator 2 — hollower, like a square wave: clarinets and reeds.
  • Carrier 1, modulator 14 — the metallic tine of a classic FM electric piano when the modulator decays fast.
  • Non-whole ratios (move FreqFine off zero) — bells, gongs and clangs.

From the community

  • Some Dexed patches with operator detune sounded wrong on V15 because the FM-1 calculated detune differently. Owners report that V16 matches Dexed, so update before judging imported banks. via Elektronauts: M-VAVE FM-1 thread

M-Vave FM-1 Guide, Part 2 | Basic Operator Controls, Intro to FM, and two simple Patches

MiyafujiP

Part 2 of a methodical series: output level, coarse ratio, carriers vs modulators, detune and two starter patches.

M-Vave FM-1 Guide, Part 3 | Frequency Fine Control, Inharmonics and a simple Bell Patch

MiyafujiP

Part 3: fine frequency control, inharmonic ratios and building a simple bell.

4.6IntermediateManual §3.1 p.4

Operator envelopes: rates and levels

Each operator’s envelope has four levels (where it goes) and four rates (how fast it gets there), all 0–99, on pages 2 and 3. A higher rate is faster. It works like the DX7’s, which is why DX7 patches load and play as they should.

How the stages run

  • When you press a key, the envelope moves to Level 1 at Rate 1, then to Level 2 at Rate 2, then to Level 3 at Rate 3.
  • It stays at Level 3 while you hold the key — that is the sustain.
  • When you let go, it moves to Level 4 at Rate 4. Level 4 is normally 0, so the note dies away.
EDIT · Operator · page 2 · envelope ratesPress EDIT, then OP1–OP6. Turn SELECT to page 2.

Rate 1

Speed of the first stage, from key press towards Level 1 — the attack. Higher is faster.

KNOB 1Range 0–99

EDIT · Operator · page 3 · envelope levelsPress EDIT, then OP1–OP6. Turn SELECT to page 3.

Level 1

The level the attack reaches.

KNOB 1Range 0–99

From the community

M-Vave FM-1 | Guide for the Envelopes and Patch Initialization

MiyafujiP

Clear explanation of the DX7-style rate/level envelopes plus where the hidden patch-init function lives.

4.7IntermediateManual §3.1 p.4

Velocity, LFO sensitivity and fixed frequency

Page 4 decides how an operator responds. KeyVelocity makes it react to how hard you play, A ModSens lets the LFO move its level, and OscMode switches it between following the keyboard and holding one fixed pitch — useful for drum hits and noisy attacks.

EDIT · Operator · page 4 · sensitivity and modePress EDIT, then OP1–OP6. Turn SELECT to page 4.

A ModSensAmplitude modulation sensitivity

How much the LFO’s AMD affects this operator. 0 ignores it; on a modulator it gives a wah-like movement, on a carrier tremolo.

KNOB 1Range 0–3

From the community

M-Vave FM-1 Guide, Part 5 | LFO, Fixed Frequency Mode and Rate Scaling

MiyafujiP

Part 5: LFO, fixed-frequency operators and rate scaling.

4.8AdvancedManual §3.1 p.4

Keyboard scaling

Real instruments change across their range: high piano notes are brighter and shorter, low ones darker and longer. Keyboard scaling lets each operator do the same. You choose a BreakPoint note, then how much the level changes as you play further to the left or right of it, and along which curve.

EDIT · Operator · page 5 · level scalingPress EDIT, then OP1–OP6. Turn SELECT to page 5.

L DepthLeft depth

How strongly the level changes for notes below the break point.

KNOB 1Range 0–99

EDIT · Operator · page 6 · curves and rate scalingPress EDIT, then OP1–OP6. Turn SELECT to page 6.

L CurveLeft curve

Whether the level falls (−) or rises (+) below the break point, along a linear or exponential curve.

KNOB 1Range −LN / −EX / +LN / +EX

Curves

−LN / +LN
Linear: the level falls (−) or rises (+) steadily as you move away from the break point.
−EX / +EX
Exponential: hardly any change near the break point, then a steep fall (−) or rise (+) further out.

From the community

M-Vave FM-1 Guide, Part 5 | LFO, Fixed Frequency Mode and Rate Scaling

MiyafujiP

Part 5: LFO, fixed-frequency operators and rate scaling.

4.9IntermediateManual §3.1 p.5, §4.2 p.12

The pitch envelope

The pitch envelope bends the pitch of the whole sound over time. It uses the same four-rates, four-levels design as the operator envelopes, but its levels are pitches rather than volumes. Use it for the pitch drop of a tom, a blip at the start of a synth brass note, or a slow, unsettling drift.

Key combinations

EDIT, then PIT
Selects the pitch envelope.
EDIT · Pitch envelope · page 1 · ratesPress EDIT, then PIT. Turn SELECT to page 1.

Rate 1

Speed of the first pitch stage after the key press.

KNOB 1Range 0–99

EDIT · Pitch envelope · page 2 · levelsPress EDIT, then PIT. Turn SELECT to page 2.

Level 1

The pitch reached after the first stage.

KNOB 1Range 0–99

4.10IntermediateManual §3.1 p.5, §4.2 p.12

Voice settings: algorithm, feedback, sync and transpose

Press EDIT, then GLO KEY, for the settings that belong to the whole preset. They are saved with it, unlike the global settings behind the GLO button. Page 2 holds the preset tools — Init Voice, Rename and Copy Voice — covered in Init, rename and copy a preset.

EDIT · Voice settings · page 1Press EDIT, then GLO KEY.

Algorithm

The operator wiring — the same setting as turning ALGORITHM.

KNOB 1Range 1–32

4.11IntermediateFirmware V15+Manual §3.2 p.7

Muting an operator

Taking an operator out is the fastest way to understand a patch: mute a modulator and you hear the tone it was colouring; mute a carrier and a whole layer disappears.

Key combinations

EDIT, then hold OP1–OP6
Mutes that operator until you change preset.

From the community

M-VAVE FM-1 V15 Firmware Update | New Glide, Sequencer Features & MIDI CC Control

M-VAVE

Official V15 tour: glide, init/rename/copy voice, operator mute, sequencer long notes and chaining, and the first CC guide.

4.12BasicsManual §3.2 p.7, §4.2 p.12

Mono and poly

In POLY the FM-1 plays chords: up to 12 notes at once on V15, and on V16 up to 20 notes shared between all eight Voices (see Eight Voices, 20 notes). In MONO it plays one note: press a new key and it takes over from the old one (last-note priority). Mono suits basses and leads, and it is the only mode where Glide works.

Key combinations

EDIT, then MONO
Switches to mono.
EDIT, then POLY
Switches to poly.

In EDIT mode the LED of the active mode lights solid and the other blinks, so you can see which you are in.

4.13IntermediateFirmware V15+Manual §3.2 p.8

Glide

Glide makes the pitch slide from one note to the next instead of jumping. It only works in MONO. On V15 it is a global setting on page 2 of GLO; on V16 each Voice has its own glide page (see Voice setup in GLO).

V15: GLO page 2

GlideTrigger mode
Full Time glides into every note. Fingered glides only when you play legato — pressing the new key before letting go of the old one.Knob 3Range Full Time / Fingered
Glide ValGlide time
How long the slide takes, up to one second.Knob 4Range 0–100 (0–1 s)

From the community

M-VAVE FM-1 V15 Firmware Update | New Glide, Sequencer Features & MIDI CC Control

M-VAVE

Official V15 tour: glide, init/rename/copy voice, operator mute, sequencer long notes and chaining, and the first CC guide.

4.14Advanced

Recipes: three sounds from scratch

These recipes combine the steps in this chapter into three classic FM sounds. Each uses a two-operator stack. Start with Init Voice on a preset you can spare (Init, rename and copy a preset), and set the Out Level of every operator you are not using to 0.

Electric piano tine

  1. Pick an algorithm whose diagram has a modulator sitting directly on a carrier.
  2. Carrier: FreqCoarse 1, a fast attack (Rate 1 high, Level 1 99), then a slow fall through Rate 2 and Rate 3 to a low Level 3, and a medium Rate 4 release.
  3. Modulator: FreqCoarse 14 for the metallic tine, Out Level around the middle, and an envelope that decays quickly to Level 3 0.
  4. Give the modulator some KeyVelocity so harder playing brings out more tine.
  5. Finish with a little chorus in The effect chain.

Plucked bass

  1. Use the same two-operator stack, with both operators at FreqCoarse 1.
  2. Modulator: a high Out Level and a quick decay, so each note starts bright and turns round.
  3. Raise Feedback on the voice settings page for extra grit.
  4. Switch to MONO, add a short Fingered Glide, and press OCT- once or twice.

Bell

  1. Carrier: FreqCoarse 1 and a long, slow decay with Level 3 at 0, so the note rings out even while you hold the key.
  2. Modulator: FreqCoarse 3 with FreqFine moved off zero for a clangorous, inharmonic tone, and a slightly shorter decay than the carrier.
  3. Add reverb in The effect chain.