# Expedition 012

### 1. System name
Theme and Variations on the Golden Line

### 2. Pitch organization
Seven equal logarithmic divisions of the octave (7-TET). Every step is the irrational ratio 2^(1/7) ≈ 1.1041; no two pitches except the octaves form rational simple-integer ratios. The system is octave-repeating (two full octaves used). The *absence* of simple rational intervals is the system's signature — all intervals are irrational, all consonance is perceptual rather than acoustic.

The home pitch at 210 Hz is the tonic. Two other structural pitches function as semi-cadential landings: index 2 (2^(2/7) ≈ 1.219, a "near-minor-third") and index 4 (2^(4/7) ≈ 1.486, a "near-fifth").

### 3. Rhythmic organization
Additive 2+3+2+3+2 = 12 units at 140 ms unit. The irregular grouping produces a shuffled-triplet feel. Rhythmic ornament is dense and is the *only* ornament in the system — melodic ornament (grace notes, pitch bends) is prohibited. Long notes are habitually subdivided into rapid sub-groupings (duplets over triplets, ornaments of 3-against-2) with passing tones that do not belong to the scale-harmonic grammar but serve purely rhythmic function.

### 4. Formal structure
Theme and variations, through-composed. An introduction establishes the meter; the theme is stated plain; five variations transform it (rhythmic ornament, doubled speed, contour inversion, augmentation, fragmentation); a coda restates the theme plain and cadences on home. Each variation is self-contained but references the theme.

### 5. Texture and voicing
Soloist with accompaniment — one melodic lead (sung) and one membrane drum. Voice independence is high within this sparse texture: the soloist carries the pitched material and the drum carries the rhythmic commentary, and they alternate as much as overlap.

### 6. Ornament and inflection
Rhythmic-only. Ornament density is very high (~0.88 of notes receive some form of rhythmic elaboration).

### 7. Performance context
Ritual-religious, call-response. The soloist states material, the drum answers. The listener participates as ritual audience.

### 8. Relationship to neighboring systems
Shares with **Korean Pansori** the solo-voice-with-drum format, and the theme-and-variation (as narrative episodes) structure. Shares with **Tabla solo** the density and precision of rhythmic ornament. Shares with **Sufi Qawwali** the ritual call-response between voice and accompaniment. The unique synthesis: *irrational-interval theme and variations where the only permitted ornament is rhythmic density, and where the accompanist and soloist answer each other as near-equals*.

### 9. Audio specification

```json
{
  "duration_seconds": 72.0,
  "pitch_system": {
    "encoding": "ratio",
    "reference_hz": 210,
    "pitches": [
      1.0,
      1.1041,
      1.219,
      1.3459,
      1.486,
      1.6407,
      1.8114,
      2.0,
      2.0,
      2.2082,
      2.438,
      2.6918,
      2.972,
      3.2813,
      3.6229,
      4.0
    ],
    "octave_repeats": true
  },
  "rhythm_system": {
    "type": "additive",
    "groupings": [
      2,
      3,
      2,
      3,
      2
    ],
    "base_unit_ms": 140
  },
  "voices": [
    {
      "name": "soloist",
      "timbre": "vocal_male_low",
      "pitch_indices": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13
      ],
      "rhythm_role": "melodic_lead",
      "amplitude": 0.85,
      "spatial_position": [
        0.0,
        0.25
      ]
    },
    {
      "name": "drum",
      "timbre": "membrane_drum",
      "pitch_indices": [
        0
      ],
      "rhythm_role": "percussive",
      "amplitude": 0.7,
      "spatial_position": [
        -0.3,
        -0.3
      ]
    }
  ],
  "form": {
    "arc_type": "through_composed",
    "sections": [
      {
        "name": "introduction",
        "start_seconds": 0,
        "duration_seconds": 6,
        "character": "drum alone sets the additive meter",
        "chord_tones": [
          0
        ]
      },
      {
        "name": "theme_statement",
        "start_seconds": 6,
        "duration_seconds": 6,
        "character": "soloist states the theme plain",
        "chord_tones": [
          0,
          2,
          4
        ]
      },
      {
        "name": "var1_rhythmic_ornament",
        "start_seconds": 12,
        "duration_seconds": 11,
        "character": "theme densely ornamented rhythmically; drum triplets",
        "chord_tones": [
          0,
          2,
          4
        ]
      },
      {
        "name": "var2_double_speed",
        "start_seconds": 23,
        "duration_seconds": 11,
        "character": "theme at double speed; drum call-response",
        "chord_tones": [
          0,
          3,
          5
        ]
      },
      {
        "name": "var3_inversion",
        "start_seconds": 34,
        "duration_seconds": 9,
        "character": "theme contour mirrored",
        "chord_tones": [
          2,
          4,
          5
        ]
      },
      {
        "name": "var4_augmentation",
        "start_seconds": 43,
        "duration_seconds": 9,
        "character": "theme doubled in duration; percussion sparse",
        "chord_tones": [
          0,
          2,
          4
        ]
      },
      {
        "name": "var5_fragments",
        "start_seconds": 52,
        "duration_seconds": 11,
        "character": "theme fragments exchanged with drum",
        "chord_tones": [
          0,
          2,
          3,
          4,
          5
        ]
      },
      {
        "name": "coda",
        "start_seconds": 63,
        "duration_seconds": 9,
        "character": "plain theme returns; final drum flourish and tonic",
        "chord_tones": [
          0
        ]
      }
    ]
  },
  "ornamentation": {
    "density": 0.88,
    "rule": "Rhythmic ornament is dense. Long theme notes (\u22652 units) are subdivided into 2-3 rapid subdivisions with alternating passing pitch. The drum mirrors this density with triplets-against-duplets."
  },
  "auto_pedal": false,
  "events": [
    {
      "t": 0.0,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.85
    },
    {
      "t": 0.28,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 0.7,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 0.98,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 1.4,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 1.68,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.85
    },
    {
      "t": 1.96,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 2.38,
      "voice": "drum",
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      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 2.66,
      "voice": "drum",
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      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 3.08,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 3.36,
      "voice": "drum",
      "pitch_index": 0,
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      "amplitude": 0.85
    },
    {
      "t": 3.64,
      "voice": "drum",
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      "amplitude": 0.55
    },
    {
      "t": 4.06,
      "voice": "drum",
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      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 4.34,
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      "amplitude": 0.55
    },
    {
      "t": 4.76,
      "voice": "drum",
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      "duration_seconds": 0.08,
      "amplitude": 0.55
    },
    {
      "t": 6.0,
      "voice": "soloist",
      "pitch_index": 0,
      "duration_seconds": 0.399,
      "amplitude": 0.85
    },
    {
      "t": 6.42,
      "voice": "soloist",
      "pitch_index": 2,
      "duration_seconds": 0.266,
      "amplitude": 0.85
    },
    {
      "t": 6.7,
      "voice": "soloist",
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      "duration_seconds": 0.266,
      "amplitude": 0.85
    },
    {
      "t": 6.98,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.85
    },
    {
      "t": 7.12,
      "voice": "soloist",
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      "duration_seconds": 0.399,
      "amplitude": 0.85
    },
    {
      "t": 7.54,
      "voice": "soloist",
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      "duration_seconds": 0.266,
      "amplitude": 0.85
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    {
      "t": 7.82,
      "voice": "soloist",
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      "duration_seconds": 0.266,
      "amplitude": 0.85
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    {
      "t": 8.1,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.85
    },
    {
      "t": 8.24,
      "voice": "soloist",
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      "duration_seconds": 0.266,
      "amplitude": 0.85
    },
    {
      "t": 8.52,
      "voice": "soloist",
      "pitch_index": 0,
      "duration_seconds": 0.532,
      "amplitude": 0.85
    },
    {
      "t": 5.04,
      "voice": "drum",
      "pitch_index": 0,
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      "amplitude": 0.7
    },
    {
      "t": 5.32,
      "voice": "drum",
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      "amplitude": 0.45
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    {
      "t": 5.74,
      "voice": "drum",
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      "amplitude": 0.45
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    {
      "t": 6.02,
      "voice": "drum",
      "pitch_index": 0,
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      "amplitude": 0.45
    },
    {
      "t": 6.44,
      "voice": "drum",
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      "amplitude": 0.45
    },
    {
      "t": 6.72,
      "voice": "drum",
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      "amplitude": 0.7
    },
    {
      "t": 7.0,
      "voice": "drum",
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      "amplitude": 0.45
    },
    {
      "t": 7.42,
      "voice": "drum",
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    {
      "t": 7.7,
      "voice": "drum",
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      "amplitude": 0.45
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    {
      "t": 8.12,
      "voice": "drum",
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    {
      "t": 8.4,
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    {
      "t": 9.1,
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      "t": 9.38,
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      "t": 9.8,
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    {
      "t": 10.08,
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      "t": 10.36,
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    {
      "t": 10.78,
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      "t": 12.14,
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      "t": 12.42,
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      "t": 35.26,
      "voice": "soloist",
      "pitch_index": 7,
      "duration_seconds": 0.133,
      "amplitude": 0.82
    },
    {
      "t": 35.4,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.82
    },
    {
      "t": 35.54,
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      "amplitude": 0.82
    },
    {
      "t": 35.68,
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    },
    {
      "t": 35.82,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.82
    },
    {
      "t": 35.96,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.82
    },
    {
      "t": 36.1,
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      "duration_seconds": 0.133,
      "amplitude": 0.82
    },
    {
      "t": 36.24,
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      "amplitude": 0.82
    },
    {
      "t": 36.38,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.82
    },
    {
      "t": 36.52,
      "voice": "soloist",
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      "duration_seconds": 0.133,
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    },
    {
      "t": 36.66,
      "voice": "soloist",
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      "duration_seconds": 0.532,
      "amplitude": 0.82
    },
    {
      "t": 34.0,
      "voice": "drum",
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      "duration_seconds": 0.07,
      "amplitude": 0.7
    },
    {
      "t": 34.28,
      "voice": "drum",
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      "duration_seconds": 0.07,
      "amplitude": 0.5
    },
    {
      "t": 34.7,
      "voice": "drum",
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      "amplitude": 0.5
    },
    {
      "t": 34.98,
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    },
    {
      "t": 35.4,
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      "amplitude": 0.5
    },
    {
      "t": 35.68,
      "voice": "drum",
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      "amplitude": 0.7
    },
    {
      "t": 35.96,
      "voice": "drum",
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      "amplitude": 0.5
    },
    {
      "t": 36.38,
      "voice": "drum",
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    },
    {
      "t": 36.66,
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    },
    {
      "t": 37.08,
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    },
    {
      "t": 37.36,
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      "amplitude": 0.7
    },
    {
      "t": 37.64,
      "voice": "drum",
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    },
    {
      "t": 38.06,
      "voice": "drum",
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    },
    {
      "t": 38.34,
      "voice": "drum",
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    },
    {
      "t": 38.76,
      "voice": "drum",
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      "amplitude": 0.5
    },
    {
      "t": 39.04,
      "voice": "drum",
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      "amplitude": 0.7
    },
    {
      "t": 39.32,
      "voice": "drum",
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      "amplitude": 0.5
    },
    {
      "t": 39.74,
      "voice": "drum",
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      "amplitude": 0.5
    },
    {
      "t": 40.02,
      "voice": "drum",
      "pitch_index": 0,
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      "amplitude": 0.5
    },
    {
      "t": 40.44,
      "voice": "drum",
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      "amplitude": 0.5
    },
    {
      "t": 40.72,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.07,
      "amplitude": 0.7
    },
    {
      "t": 41.0,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.07,
      "amplitude": 0.5
    },
    {
      "t": 41.42,
      "voice": "drum",
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      "duration_seconds": 0.07,
      "amplitude": 0.5
    },
    {
      "t": 41.7,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.07,
      "amplitude": 0.5
    },
    {
      "t": 43.0,
      "voice": "soloist",
      "pitch_index": 0,
      "duration_seconds": 0.798,
      "amplitude": 0.88
    },
    {
      "t": 43.84,
      "voice": "soloist",
      "pitch_index": 2,
      "duration_seconds": 0.532,
      "amplitude": 0.88
    },
    {
      "t": 44.4,
      "voice": "soloist",
      "pitch_index": 4,
      "duration_seconds": 0.532,
      "amplitude": 0.88
    },
    {
      "t": 44.96,
      "voice": "soloist",
      "pitch_index": 3,
      "duration_seconds": 0.266,
      "amplitude": 0.88
    },
    {
      "t": 45.24,
      "voice": "soloist",
      "pitch_index": 5,
      "duration_seconds": 0.798,
      "amplitude": 0.88
    },
    {
      "t": 46.08,
      "voice": "soloist",
      "pitch_index": 4,
      "duration_seconds": 0.532,
      "amplitude": 0.88
    },
    {
      "t": 46.64,
      "voice": "soloist",
      "pitch_index": 2,
      "duration_seconds": 0.532,
      "amplitude": 0.88
    },
    {
      "t": 47.2,
      "voice": "soloist",
      "pitch_index": 3,
      "duration_seconds": 0.266,
      "amplitude": 0.88
    },
    {
      "t": 47.48,
      "voice": "soloist",
      "pitch_index": 2,
      "duration_seconds": 0.532,
      "amplitude": 0.88
    },
    {
      "t": 48.04,
      "voice": "soloist",
      "pitch_index": 0,
      "duration_seconds": 1.064,
      "amplitude": 0.88
    },
    {
      "t": 43.0,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.1,
      "amplitude": 0.85
    },
    {
      "t": 44.68,
      "voice": "drum",
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      "duration_seconds": 0.1,
      "amplitude": 0.85
    },
    {
      "t": 46.36,
      "voice": "drum",
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      "duration_seconds": 0.1,
      "amplitude": 0.85
    },
    {
      "t": 48.04,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.1,
      "amplitude": 0.85
    },
    {
      "t": 49.72,
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      "duration_seconds": 0.1,
      "amplitude": 0.85
    },
    {
      "t": 51.4,
      "voice": "drum",
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      "duration_seconds": 0.1,
      "amplitude": 0.85
    },
    {
      "t": 52.0,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.8
    },
    {
      "t": 52.14,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.8
    },
    {
      "t": 52.28,
      "voice": "soloist",
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      "amplitude": 0.8
    },
    {
      "t": 52.42,
      "voice": "soloist",
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      "amplitude": 0.8
    },
    {
      "t": 52.56,
      "voice": "soloist",
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      "duration_seconds": 0.133,
      "amplitude": 0.8
    },
    {
      "t": 52.7,
      "voice": "soloist",
      "pitch_index": 4,
      "duration_seconds": 0.133,
      "amplitude": 0.8
    },
    {
      "t": 52.84,
      "voice": "soloist",
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      "amplitude": 0.8
    },
    {
      "t": 52.98,
      "voice": "soloist",
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      "amplitude": 0.8
    },
    {
      "t": 53.263,
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      "amplitude": 0.65
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    {
      "t": 53.382,
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    },
    {
      "t": 53.501,
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    {
      "t": 53.62,
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    },
    {
      "t": 53.839,
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      "amplitude": 0.8
    },
    {
      "t": 53.979,
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      "amplitude": 0.8
    },
    {
      "t": 54.119,
      "voice": "soloist",
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      "amplitude": 0.8
    },
    {
      "t": 54.259,
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      "amplitude": 0.8
    },
    {
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      "amplitude": 0.65
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    {
      "t": 54.661,
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    {
      "t": 54.78,
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    {
      "t": 54.899,
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    },
    {
      "t": 55.118,
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      "amplitude": 0.8
    },
    {
      "t": 55.258,
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      "amplitude": 0.8
    },
    {
      "t": 55.398,
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      "amplitude": 0.8
    },
    {
      "t": 55.538,
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    {
      "t": 55.678,
      "voice": "soloist",
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    {
      "t": 55.961,
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    {
      "t": 56.08,
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    {
      "t": 56.199,
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    {
      "t": 56.318,
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    {
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    {
      "t": 56.817,
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    {
      "t": 56.957,
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    {
      "t": 57.097,
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    },
    {
      "t": 57.237,
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    {
      "t": 57.52,
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    {
      "t": 57.639,
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    },
    {
      "t": 57.758,
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    {
      "t": 57.877,
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    {
      "t": 63.0,
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      "duration_seconds": 0.399,
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    {
      "t": 63.42,
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      "duration_seconds": 0.266,
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    {
      "t": 63.7,
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    },
    {
      "t": 63.98,
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      "amplitude": 0.8
    },
    {
      "t": 64.12,
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      "duration_seconds": 0.399,
      "amplitude": 0.8
    },
    {
      "t": 64.54,
      "voice": "soloist",
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      "duration_seconds": 0.266,
      "amplitude": 0.8
    },
    {
      "t": 64.82,
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      "duration_seconds": 0.266,
      "amplitude": 0.8
    },
    {
      "t": 65.1,
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      "duration_seconds": 0.133,
      "amplitude": 0.8
    },
    {
      "t": 65.24,
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      "duration_seconds": 0.266,
      "amplitude": 0.8
    },
    {
      "t": 65.52,
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      "amplitude": 0.8
    },
    {
      "t": 68.5,
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      "duration_seconds": 0.07,
      "amplitude": 0.5
    },
    {
      "t": 68.57,
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      "duration_seconds": 0.07,
      "amplitude": 0.52
    },
    {
      "t": 68.64,
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      "duration_seconds": 0.07,
      "amplitude": 0.54
    },
    {
      "t": 68.71,
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      "pitch_index": 0,
      "duration_seconds": 0.07,
      "amplitude": 0.56
    },
    {
      "t": 68.78,
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      "pitch_index": 0,
      "duration_seconds": 0.07,
      "amplitude": 0.5800000000000001
    },
    {
      "t": 68.85,
      "voice": "drum",
      "pitch_index": 0,
      "duration_seconds": 0.2,
      "amplitude": 0.9
    },
    {
      "t": 70.0,
      "voice": "soloist",
      "pitch_index": 0,
      "duration_seconds": 2.5,
      "amplitude": 0.7
    }
  ]
}
```

### 10. Field note
7-TET has no pure fifth, no pure fourth. The ear hears the piece and gropes for consonance that never quite lands. What resolves the piece is not harmonic arrival but rhythmic arrival: the drum stops on the same beat the voice lands on home, and the ear accepts this coincidence as consonance.