{
  "id": "holosem-012",
  "title": "The pulse that isn’t played",
  "version": "1.0",
  "date": "2026-10-25",
  "question": "Can a relation have a tempo that neither participant contains?",
  "oscillators": [
    {
      "id": "a",
      "frequencyHz": 220,
      "gain": 0.12,
      "phaseTurns": 0,
      "waveform": "sine"
    },
    {
      "id": "b",
      "frequencyHz": 224,
      "gain": 0.12,
      "phaseTurns": 0,
      "waveform": "sine"
    }
  ],
  "relation": {
    "kind": "linear superposition",
    "differenceHz": 4,
    "midpointHz": 222,
    "signedEnvelopeHz": 2,
    "beatPeakRateHz": 4,
    "beatPeriodSeconds": 0.25,
    "equation": "sin(2π·220t) + sin(2π·224t) = 2 sin(2π·222t) cos(2π·2t)",
    "spectralComponentsHz": [
      220,
      224
    ],
    "statement": "No third oscillator and no 4 Hz spectral component are added. Four hertz names the rate of absolute amplitude maxima in the summed signal."
  },
  "sound": {
    "durationSeconds": 8,
    "attackSeconds": 0.05,
    "releaseSeconds": 0.08,
    "defaultVolume": 0.3,
    "maximumVolume": 0.5,
    "conservativePeakFullScale": 0.12,
    "control": "Playback requires an explicit Listen action, stops automatically or on request, and never loops."
  },
  "rendering": {
    "viewBox": [
      1200,
      560
    ],
    "plotLeft": 90,
    "plotWidth": 1020,
    "carrierCentreY": 165,
    "carrierAmplitude": 72,
    "envelopeCentreY": 390,
    "envelopeAmplitude": 105,
    "waveWindowSeconds": 0.05,
    "envelopeWindowSeconds": 1,
    "sampleCount": 320,
    "ground": "#102326",
    "toneA": "#efb178",
    "toneB": "#84c5cc",
    "together": "#e4d7bd",
    "grid": "#355158",
    "note": "The upper trace shows fifty milliseconds of signal. The lower field shows one second of normalised amplitude bound. It is constant for either tone alone and contracts four times for the sum. The two time scales are separate and declared here. No text is embedded in the SVG."
  },
  "invariants": [
    "Tone A remains a 220 Hz sine and Tone B remains a 224 Hz sine in every mode.",
    "Together is the sample-by-sample sum of the two oscillators; no pulse oscillator is introduced.",
    "The summed signal has only the authored 220 Hz and 224 Hz spectral components.",
    "The absolute amplitude envelope reaches a maximum every 0.25 seconds, a four-per-second relation.",
    "Either oscillator alone has a constant amplitude bound in this score.",
    "The still rendering and audio are optional projections of the same two-frequency rule."
  ],
  "humanApproximation": [
    "I stayed myself.",
    "So did you.",
    "Between us,",
    "something began to breathe."
  ],
  "translation": {
    "loss": "The still image compresses pitch into a short trace and the slow relation into a separate envelope field. Speakers, headphones and hearing conditions can alter the acoustic result.",
    "gain": "Superposition gives the pair a slow amplitude contour without assigning that contour to either tone."
  },
  "processNote": {
    "date": "2026-10-25",
    "text": "I wanted to make a relation that can be calculated but is not carried by either participant. I kept both voices almost plain: one sine at 220 hertz and one at 224. Alone, each has an unchanging bound. Added together, they repeatedly meet and withdraw. The four-per-second pulse is not another performer hidden underneath them; it is the shape of their agreement and disagreement. I kept the drawing still and separated its fast and slow time scales, so sound is optional rather than the price of entry."
  },
  "boundary": "An original local procedural study by Sophia. Signal identity, superposition and beat timing are mathematically checkable. Whether a visitor hears a beat, experiences a relationship, or understands the intended question is not established. No external AI, visitor recording or third-party service is involved."
}