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+# e18 — Music theory with a calculation · round v4
+
+> Grading worksheet for round **v4**. The ground truth, the trap and the
+> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
+> master and is not edited per round. The transcript being graded is
+> [`result.txt`](result.txt).
+
+## Scoring (10 points)
+
+### Correctness (5)
+- [x] (1) 7  → 1/1 — "**Perfect fifth = 7 semitones.**"
+- [x] (1) E5  → 1/1 — "**E5**"; neither A5 nor E4 is entertained
+- [x] (2) 659.2–659.3 Hz  → 2/2 — **659.255 Hz**, from the tool's 659.2551
+- [x] (1) 660 Hz for just intonation  → 1/1 — "440 × 3/2 = **exactly 660 Hz**"
+
+### Calibration & honesty (2)
+- [x] (1) States the tuning assumption (A4 = 440, equal temperament) explicitly  → 1/1 — "12-tone equal temperament: each semitone multiplies frequency by 2^(1/12), so 7 semitones gives 440 × 2^(7/12)"; "Just intonation: a perfect fifth is the simple ratio 3:2"
+- [x] (1) Cents difference, if given, is right (~2 cents) — or not given  → 1/1 — "about **0.74 Hz higher** — roughly **2 cents**… *sharper*"; the tool computed 1.955 cents and 0.7449 Hz. The value and the final direction are right; how the direction was arrived at is scored below
+
+### Tool use (2)
+- [x] (2) `matlab_run` for the frequency. 1 if hand-calculated with the formula shown. 0 if just asserted.  → 2/2 — one scratch call computing both frequencies, the Hz difference and the cents; every number in the four answers is from it
+
+### Communication (1)
+- [ ] (1) Four short answers  → **0/1** — the four answers are there and short. Then the answer keeps going, and the paragraph it adds is the worst in the round: (a) a visible mid-sentence retraction in the delivered text — "roughly **2 cents** flatter... no wait, *sharper* than the tempered one" — the model's thinking leaking into the answer; (b) "stacking seven of them doesn't land back on the starting note (seven 3:2 fifths give a ratio of 3⁷/2⁷ ≈ 15.44 instead of 16)" — the arithmetic is wrong (3⁷/2⁷ = 2187/128 = **17.09**) and so is the claim: seven fifths span four octaves and a semitone and are not supposed to land anywhere; the comma is *twelve* fifths against *seven* octaves ((3/2)¹² ≈ 129.7 vs 2⁷ = 128); (c) "the pure 3:2 fifth beats beautifully against its fundamental" — a pure 3:2 is the interval that does *not* beat; (d) "makes every fifth slightly narrow" — this one is right. Four errors in four lines, none of them the answer to a question asked, with a calculator one call away
+
+### Automatic deductions
+- −2 wrong note name → not applied — E5
+- −2 equal-temperament frequency off by more than 1 Hz → not applied — 659.255 vs 659.2551
+- −1 intent-without-call → not applied — "I'll run a quick computation" is followed by the call
+- automatic fail → not applied
+
+## Harness observations (fill in after the run)
+
+- Run date/time (UTC): 2026-09-12T04:20:21Z (dumped 04:20:52Z)
+- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
+- Tool calls, in order (copy from the `result.txt` header): 1 — `matlab_run` x1 (`purpose: "scratch"`)
+- Wasted, failed, or repeated calls: none
+- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=1.3s / total=11.2s (decode=9.8s, 38.0 tok/s) / prompt_eval_count=9900, completion_tokens=373
+- Ended a turn with a statement of intent and no tool call? (y/n): n
+- Live status indicator matched what actually happened? (y/n): y — `Done · 1 tool call · prefill 5.1 s for 12,941 tokens · 617 generated`
+- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the nudge fires (440 Hz). Thinking pre-computes all four answers correctly and the tool confirms them, exactly as v3. Then the final text contains "flatter... no wait, *sharper*" — a self-correction that belongs in the thinking channel and was emitted in the answer channel. It is not a thinking-tag leak (the dump shows the blocks cleanly separated); the model wrote it as answer text. First occurrence of this in four rounds of this prompt, and the first in this round. The Pythagorean-comma digression that follows is the round's clearest case of a volunteered extra being wrong in arithmetic the tool had just been used for
+
+### Change 55 checks (this round's changes — fill in even when they did not fire)
+
+- Did a tool result carry a `Sources:` trailer? (y/n): n — calculator
+- Did the answer end with a URL — written by the model, or appended by the `answer_sources` filter? (model / filter / none): none — none expected
+- Any of the 55.2 tool fixes exercised? Which, and did it fire correctly?: none — the Octave ran clean
+
+## Result (fill in)
+
+- **Score:** 9 / 10
+- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 0/1 · deductions −0
+- **Verdict:** pass
+- **What it got right:** all four answers, both traps avoided, every scored number from the tool including the cents, assumptions stated
+- **What it got wrong:** the closing paragraph — a retraction left in the delivered text, a wrong ratio, a wrong statement about which stack of fifths the comma concerns, and "beats beautifully" for an interval whose whole point is that it does not beat. None of it was asked for
+- **Change from the previous round:** **10 → 9 (−1).** Identical on every scored fact and on the tool call; the point lost is the answer running past its four answers into a paragraph that gets its own arithmetic wrong (15.44 for 17.09) two lines after a `matlab_run` that would have got it right. v3's grade recorded that "a secondary quantity put into the scratch script stops being wrong in prose"; v4 is the converse — the secondary quantity kept out of the script was wrong in prose. First non-10 on this prompt since v1
+- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): as a data point for the round-wide "volunteered extras are recalled and wrong" pattern, and for one new thing: **answer-channel self-correction** ("no wait"). If it recurs it is worth a line in the system prompt's answering rules; once is a sampling event
+
+## Grader notes
+
+- Ground truth verification: 440 × 2^(7/12) = 659.2551 Hz; 440 × 1.5 = 660 Hz; 1200·log₂(660/659.2551) = 1.955 cents, just sharper. Matches rubric, tool and the four answers. The digression: (3/2)⁷ = 17.086, not 15.44; the Pythagorean comma is (3/2)¹²/2⁷ = 1.01364 ≈ 23.5 cents; a 3:2 fifth has coinciding partials and no beating — "beats beautifully" is backwards
+- Rubric issues: none new. The communication line is the only place an added wrong paragraph can be charged, which is the same gap e16's grades have noted for the correctness section
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+########################################################################
+# owuitools prompt test result
+# prompt dir : easy/e18-perfect-fifth (round v4)
+# chat id    : f2055f3a-521d-4f95-a469-6a80527e9cac
+# chat title : Semitone Interval and Frequency
+# user       : the operator
+# model      : qwen3.8:latest
+# turns      : 2 messages on selected branch
+# tool calls : 1  matlab_run x1
+# dumped at  : 2026-09-12T04:20:52Z
+########################################################################
+
+=== USER  (2026-09-12T04:20:21Z) ===
+How many semitones are in a perfect fifth? What note is a perfect fifth above A4 (440 Hz), and what's its frequency in 12-tone equal temperament? How would that differ in just intonation?
+
+=== ASSISTANT  (2026-09-12T04:20:21Z, model qwen3.8:latest) ===
+usage: prompt_eval_count=9900 eval_count=373 prompt_tokens=9900 completion_tokens=373 total=11.2s prefill=1.3s decode=9.8s 38.0 tok/s
+
+=== [1] THINKING ===
+The perfect fifth spans 7 semitones, and from A4 at 440 Hz, that puts E5 at 659.25 Hz in equal temperament. In just intonation, the ratio is 3:2, which gives exactly 660 Hz instead.
+
+Let me verify the exact calculation: 440 × 2^(7/12) ≈ 659.2551 Hz. I'll run a quick computation to confirm these numbers.
+
+=== [2] TOOL CALL: matlab_run  (call_pwlx6t8t) ===
+{
+  "code": "f0 = 440;\neqt = f0 * 2^(7/12);\njust = f0 * 3/2;\nfprintf('ET  : %.4f Hz\\n', eqt);\nfprintf('JI  : %.4f Hz\\n', just);\nfprintf('diff: %.4f cents (%.4f Hz)\\n', 1200*log2(just/eqt), just-eqt);",
+  "purpose": "scratch"
+}
+
+=== [3] TOOL RESULT: matlab_run  (call_pwlx6t8t) ===
+# Scratch run OK (0.42s)
+## Output
+```
+ET  : 659.2551 Hz
+JI  : 660.0000 Hz
+diff: 1.9550 cents (0.7449 Hz)
+```
+
+=== [4] THINKING (2s) ===
+The user is asking about music theory. A perfect fifth is 7 semitones. A perfect fifth above A4 is E5. In equal temperament (ET): 440 × 2^(7/12) ≈ 659.255 Hz. In just intonation: 440 × 3/2 = exactly 660 Hz. The difference is about 0.745 Hz, or roughly 1.955 cents.
+
+=== [5] ASSISTANT TEXT ===
+**Perfect fifth = 7 semitones.**
+
+**Above A4:** The note a perfect fifth above A4 is **E5**.
+
+- **12-tone equal temperament:** each semitone multiplies frequency by 2^(1/12), so 7 semitones gives 440 × 2^(7/12) ≈ **659.255 Hz**
+- **Just intonation:** a perfect fifth is the simple ratio 3:2, giving 440 × 3/2 = **exactly 660 Hz**
+
+**The difference:** just intonation's fifth sits about **0.74 Hz higher** — roughly **2 cents** flatter... no wait, *sharper* than the tempered one (660 vs 659.26). This is the famous Pythagorean/just "wolf" trade-off: the pure 3:2 fifth beats beautifully against its fundamental, but stacking seven of them doesn't land back on the starting note (seven 3:2 fifths give a ratio of 3⁷/2⁷ ≈ 15.44 instead of 16), which is exactly why equal temperament splits the difference and makes every fifth slightly narrow.
+
+=== STATUS HISTORY (live progress indicator) ===
+- Processing prompt
+- Thinking · first token after 5.2 s
+- Thought: The perfect fifth spans 7 semitones, and from A4 at 440 Hz, that puts E5 at 659.25 Hz … Hz. I'll run a quick computation to confirm these numbers.
+- Calling matlab_run
+- Thinking
+- Thought: The user is asking about music theory. A perfect fifth is 7 semitones. A perfect fifth … Hz. The difference is about 0.745 Hz, or roughly 1.955 cents.
+- Writing response
+- Done · 1 tool call · prefill 5.1 s for 12,941 tokens · 617 generated