C567 — Unify full half and quarter Key scales

Question

Do14,7 and3.5 require separate expansion laws?

Inputs

{
  "scales": [
    7,
    "7/2",
    "7/4"
  ]
}

Sources

[
  "File62 §8.3; File60 §7"
]

Opened utc

2026-09-28T00:15:57.467599+00:00

Results

{
  "input_output_gain": [
    [
      161,
      175,
      14
    ],
    [
      "161/2",
      "175/2",
      7
    ],
    [
      "161/4",
      "175/4",
      "7/2"
    ]
  ],
  "general_rule": "23u→25u, gain2u"
}

Finding

The three gains are scaled evaluations of E, not new Keys. They connect the161/175 Covenant unit to80.5/87.5 and40.25/43.75 duration units without making their event placements interchangeable.

Reassessment

Compare the two source routes from483 to490.

Checks

{
  "rule": true,
  "gains": true
}

Closed utc

2026-09-28T00:15:57.467964+00:00

Record provenance

Exact record hash: 0742ca056f0055f89dbf2ad53ec97c22107efb6313ba309b6f077554fd3c7bb3

Source journal: Research_Cycles/C0532_C0631/journal.json