The Mechanism · Gated-generation receipt

gen-define-equal-temperament-tuning-and-give-one-short-worked-ex-d2d6

stable pending witness
2026-05-29 05:55:55 UTC · anthropic/claude-sonnet-4-5

Prompt

Define equal temperament tuning and give one short worked example.
66 chars

Generation

# Equal Temperament Tuning **Equal temperament** is a tuning system where the octave is divided into equal frequency ratios. In 12-tone equal temperament (12-TET), the most common system, the octave is divided into 12 equal semitones. ## Key Formula Each semitone has a frequency ratio of **∛¹²2** (the 12th root of 2) ≈ 1.05946 ## Worked Example **Find the frequency of E4 (4 semitones above middle C)** Given: Middle C (C4) = 440 Hz × (9/16) = 261.63 Hz Since E4 is 4 semitones above C4: Frequency of E4 = 261.63 Hz × (∛¹²2)⁴ = 261.63 Hz × (2^(4/12)) = 261.63 Hz × 2^(1/3) = 261.63 Hz × 1.2599 **= 329.63 Hz** This system ensures that any sequence of 12 semitones exactly doubles the frequency (one octave), making all keys equally in tune—hence "equal temperament."
20 tokens in · 295 tokens out · 6928 ms · $0.0045

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
6936.6 ms
Base LLM
6927.8 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0045

Trail

05:55:55 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
05:55:55 red_gate decision=pass reason=no disqualifying input patterns detected
05:56:02 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=20 tokens_out=295 latency_ms=6927.8 cost_usd=0.0045
05:56:02 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:56:02 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:56:02 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:56:02 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:56:02 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:56:02 signed hash_algo=sha256 hash=sha256:7c591e827e6629056c2fe285fc7324f38e92da2793d7fe53e35fcfbb88392169

Content hash

sha256:7c591e827e6629056c2fe285fc7324f38e92da2793d7fe53e35fcfbb88392169

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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