The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-equal-temperament-tuning-state-any-5b8a

stable pending witness
2026-05-29 04:45:24 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain equal temperament tuning. State any key formula.
74 chars

Generation

Equal temperament tuning divides the octave into 12 equal semitones, where each semitone has the same frequency ratio. This is achieved by using the ratio of the twelfth root of 2 (approximately 1.05946) between adjacent notes, ensuring that 12 semitones multiply to exactly double the frequency (one octave). **Key formula:** f(n) = f₀ × 2^(n/12), where f(n) is the frequency of a note n semitones above a reference frequency f₀. This system allows instruments to play in any key with equal intonation, though it slightly compromises the purity of intervals compared to just intonation.
27 tokens in · 161 tokens out · 4806 ms · $0.0025

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
4813.1 ms
Base LLM
4806.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

04:45:24 received prompt_chars=74 verifiers=['scripture_anchors', 'theology_doctrine']
04:45:24 red_gate decision=pass reason=no disqualifying input patterns detected
04:45:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=161 latency_ms=4806.0 cost_usd=0.0025
04:45:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:45:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:45:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:45:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:45:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:45:29 signed hash_algo=sha256 hash=sha256:703e4ed14ef62eac5b5ed89433e3ea487625383f4b6064416e20cb97913f2758

Content hash

sha256:703e4ed14ef62eac5b5ed89433e3ea487625383f4b6064416e20cb97913f2758

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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