# Expedition 002

### 1. System name
Gestural Path Lesson

### 2. Pitch organization
Pythagorean pitches generated by stacking perfect fifths (3:2 ratio) without reducing to the octave — the sequence spirals outward and never closes. A typical lesson uses nine pitches from the spiral, selected by the conductor for the particular geography being taught. The demonstration uses the contiguous section from (3/2)⁻² to (3/2)⁺⁶ relative to a 110 Hz reference: 49, 73, 110, 165, 248, 371, 557, 835, 1253 Hz. Interval hierarchy is near zero — no pitch is treated as a tonic. Pitches differ only in their direction on the spiral. Microtonality emerges naturally: adjacent pitches on the spiral span wide irregular intervals, and the Pythagorean comma accumulates across the selection, so no two intervals between adjacent pitches are exactly equal.

### 3. Rhythmic organization
Cyclical non-metric with a concealed pulse. The conductor holds a regular gesture-beat — approximately 72 per minute — which provides the spine for voice entries but is never audible as a beat. Against this spine, three to five responding voices interlock in polyrhythmic strata whose internal cycle-lengths are coprime with one another: the same rhythmic coincidence cannot recur within the duration of a single lesson. This is the source of the maximum polyrhythmic complexity — not simultaneous fast subdivisions, but non-recurring sparse events.

### 4. Formal structure
Through-composed narrative. Each piece traces a specific geographic route — a path between two named landmarks in the practitioner-teacher's territory. The arc has three movement-types: *approach* (slow pitch motion toward a destination pitch), *arrival* (voices converging near-unison on the destination), *departure* (voices spiraling outward into new territory). A lesson lasts 1–3 minutes and ends when the last landmark is reached. No lesson repeats; the route determines the form.

### 5. Texture and voicing
Call-and-response in a one-to-many structure. The conductor sings a short prompt, and three responding voices answer in heterophonic improvised variation. The responding voices are strongly independent — each chooses its own path through the conductor's prompt. Drone presence is minimal; when a voice holds a pitch longer than two seconds, other voices are expected to move.

### 6. Ornament and inflection
Ornament is obligatory but sparse. Each response must include one of three gestures: a trill at a direction-change on the spiral, a slide between landmark pitches, or a damped release at the end of the response. A response without one of the three is considered incomplete and is corrected.

### 7. Performance context
The system is pedagogical. A senior practitioner — the walker — teaches younger practitioners the shape of a territory by singing the routes between its features. Transmission is through the walker's gestures, which act as both conducting cue and mnemonic: the gesture for "bend in the river" differs from the gesture for "approach to the ridge." Over a course of study, a student memorizes dozens of paths; the full territory is carried in the voice.

### 8. Relationship to neighboring systems
Shares with Lachenmann's musique concrète instrumentale a non-tonic high-pitch-density acoustic approach, but diverges in being human vocal rather than prepared-instrument, and in having an explicit pedagogical function. Shares with IDM/glitch the maximum polyrhythmic complexity, but the polyrhythms arise from heterophonic voices with coprime cycle-lengths rather than from algorithmic manipulation. The sampled coordinate carried a tension between `ensemble_topology=solo` and `voice_count=0.70`; the system resolves this by treating the conductor as the singular authorial voice (thus solo) while the piece is realized through the responding ensemble.

### 9. Audio specification

```json
{
  "duration_seconds": 65,
  "pitch_system": {
    "encoding": "ratio",
    "reference_hz": 110,
    "pitches": [0.4444, 0.6667, 1.0, 1.5, 2.25, 3.375, 5.0625, 7.5938, 11.3906],
    "octave_repeats": false
  },
  "rhythm_system": {
    "type": "cyclical_nonmetric",
    "cycle_duration_seconds": 12,
    "event_density_per_cycle": 7,
    "cycle_count": 5
  },
  "voices": [
    {"name": "conductor", "timbre": "vocal_male_low", "pitch_indices": [2, 3, 4, 5, 6], "rhythm_role": "melodic_lead", "amplitude": 0.75, "spatial_position": [0.0, 0.3]},
    {"name": "resp_low", "timbre": "vocal_male_low", "pitch_indices": [0, 1, 2, 3], "rhythm_role": "breath_phrase", "amplitude": 0.55, "spatial_position": [-0.5, -0.1]},
    {"name": "resp_mid", "timbre": "vocal_female_high", "pitch_indices": [3, 4, 5, 6], "rhythm_role": "breath_phrase", "amplitude": 0.55, "spatial_position": [0.0, -0.2]},
    {"name": "resp_high", "timbre": "vocal_female_high", "pitch_indices": [5, 6, 7, 8], "rhythm_role": "breath_phrase", "amplitude": 0.5, "spatial_position": [0.5, -0.1]}
  ],
  "form": {
    "arc_type": "through_composed",
    "sections": [
      {"name": "approach", "start_seconds": 0, "duration_seconds": 24, "character": "slow motion toward destination; voices sparse"},
      {"name": "arrival", "start_seconds": 24, "duration_seconds": 18, "character": "voices converging on destination pitch"},
      {"name": "departure", "start_seconds": 42, "duration_seconds": 23, "character": "voices spiraling outward into new pitches"}
    ]
  },
  "ornamentation": {
    "density": 0.14,
    "rule": "Every response voice phrase ends with one of: trill, slide, or damped release. Otherwise no ornamentation."
  }
}
```

### 10. Field note
What registers first is that the voices never agree on where the tonic is — each takes its own pitch as the centre, and the listener is obliged to hear three centres at once.