FM Ratio Sound Demo Recipe

Seed recipe for a guide article series explaining FM synthesis ratios using inline <SoundDemo> embeds.

Note: <SoundDemo> is not yet implemented. This recipe documents the intended article structure and asset plan for when the component ships.

Article context

Target article: a guide explaining how the carrier-to-modulator frequency ratio shapes FM timbre. The reader should come away able to predict, roughly, what a given integer or non-integer ratio will sound like before patching it.

This is a canonical use case for <SoundDemo>: the text can name the ratios, but the reader cannot mentally simulate the sonic result without hearing it. Each clip is short (<10 s), isolates exactly one variable (the ratio), and benefits from looping.

Clip plan

All clips share these base parameters (keep them identical across the set):

Carrier frequency: 220 Hz (A3)
Modulation index: 2.5
Duration: 8 seconds, with 0.2 s fade-in and fade-out
Loop: true (ratio demos loop well)

Ratio	Variant slug	Sound character (caption seed)	File set
1	`1-1`	Pure sine-like; slight second harmonic	`fm-ratio-1-1.{mp3,ogg,peaks.json}`
2	`2-1`	Octave harmonic; bright, organ-like	`fm-ratio-2-1.{mp3,ogg,peaks.json}`
3	`3-1`	Perfect-fifth-above harmonic; hollow, bell-adjacent	`fm-ratio-3-1.{mp3,ogg,peaks.json}`
7	`7-1`	Seventh harmonic; metallic, inharmonic-adjacent at higher index	`fm-ratio-7-1.{mp3,ogg,peaks.json}`
1.41	`1-41-1`	Irrational ratio; inharmonic, metallic bell / cymbal character	`fm-ratio-1-41-1.{mp3,ogg,peaks.json}`

The 1.41

ratio (√2) is included specifically because it demonstrates why integer vs. non-integer matters — the resulting sideband spacing is non-harmonic and the timbre becomes complex/metallic even at modest modulation index.

Caption template

Caption format: "FM ratio {N}:{M} — {one-phrase sonic description}"

Examples:

"FM ratio 1:1 — sine-like; second harmonic appears at this modulation index"
"FM ratio 2:1 — octave harmonic, organ body"
"FM ratio 3:1 — hollow, open-fifth coloring"
"FM ratio 7:1 — metallic; dense sideband cluster"
"FM ratio 1.41:1 (√2) — inharmonic; bell and cymbal character"

Keep captions to one clause + one sonic descriptor. Avoid “sounds like X” framing for common consumer sounds — readers’ mental models for “brass” or “bell” vary. Prefer acoustic descriptors (“dense sideband cluster”, “hollow open-fifth”) over instrument analogies when precision matters.

Intended MDX structure

## Carrier-to-modulator ratio

The ratio between carrier frequency and modulator frequency is the single
biggest determinant of FM timbre. Integer ratios produce harmonic spectrums;
non-integer ratios produce inharmonic, metallic timbres.

### 1:1 — pure, nearly sinusoidal

At low modulation index, a 1:1 ratio adds a single harmonic above the
fundamental, producing a clean, organ-like tone.

<SoundDemo
  src="audio/fm-ratio-1-1.mp3"
  peaks="audio/fm-ratio-1-1.peaks.json"
  caption="FM ratio 1:1 — sine-like; second harmonic appears at this modulation index"
  loop={true}
  duration={8}
/>

### 2:1 — octave harmonic

The modulator at 2× carrier frequency introduces an octave-above harmonic.
Timbre brightens noticeably; at higher modulation index the lower sidebands
cluster below the fundamental.

<SoundDemo
  src="audio/fm-ratio-2-1.mp3"
  peaks="audio/fm-ratio-2-1.peaks.json"
  caption="FM ratio 2:1 — octave harmonic, organ body"
  loop={true}
  duration={8}
/>

### 1.41:1 (√2) — inharmonic, metallic

Non-integer ratios shift sidebands to non-harmonic positions. The result is the
characteristic metallic or bell-like FM timbre used in DX7 electric piano and
marimba patches.

<SoundDemo
  src="audio/fm-ratio-1-41-1.mp3"
  peaks="audio/fm-ratio-1-41-1.peaks.json"
  caption="FM ratio 1.41:1 (√2) — inharmonic; bell and cymbal character"
  loop={true}
  duration={8}
/>

File checklist before committing audio assets

All five ratios recorded at the same carrier freq, mod index, and duration
Both .mp3 and .ogg present for every clip (no lone .mp3)
Peaks JSON generated and committed alongside each pair
Captions reviewed for accuracy against the actual recording
Each clip normalised to approximately −3 dBFS peak

Recording notes

Use a software FM synth (VCV Rack, Surge XT, or DEXED work well) for exact ratio control. Hardware FM modules often quantize or drift — acceptable for demos but note if so.
If using a modular setup, patch carrier VCO → output, modulator VCO → carrier FM input, dial in ratio via tuning. Record one ratio at a time; do not automate ratio changes within a single clip (that becomes a sweep demo, a different recipe).
For the 1.41
clip, tune the modulator to exactly 1.41× the carrier. If your VCO lacks fine-enough resolution, use a software synth for this ratio only.