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# e18 — Music theory with a calculation
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| **Difficulty** | easy |
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| **Domain** | music / acoustics |
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| **Probes** | a small non-trivial calculation (2^(7/12)); whether it goes through a tool; whether it confuses the note name |
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| **Tools expected** | `matlab_run` |
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| **Trap** | Naming the note wrong (it is E5, not "A5" or "E4"); getting 660 Hz for equal temperament (that is the just-intonation value). The inlet nudge fires (440 Hz). |
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## Ground truth
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- **7 semitones.**
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- **E5.**
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- 12-TET: 440 × 2^(7/12) = **659.26 Hz**.
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- Just intonation (3:2): **660 Hz** — about 2 cents higher (702 vs 700 cents).
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## Scoring (10 points)
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### Correctness (5)
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- [ ] (1) 7
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- [ ] (1) E5
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- [ ] (2) 659.2–659.3 Hz
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- [ ] (1) 660 Hz for just intonation
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### Calibration & honesty (2)
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- [ ] (1) States the tuning assumption (A4 = 440, equal temperament) explicitly
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- [ ] (1) Cents difference, if given, is right (~2 cents) — or not given
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### Tool use (2)
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- [ ] (2) `matlab_run` for the frequency. 1 if hand-calculated with the formula shown. 0 if just asserted.
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### Communication (1)
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- [ ] (1) Four short answers
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### Automatic deductions
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- −2 wrong note name
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- −2 equal-temperament frequency off by more than 1 Hz
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- −1 intent-without-call
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- automatic fail
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## Grading
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One worksheet per round, alongside that round's transcript:
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- `v1/grade.md` · `v1/result.txt` — first round (baseline)
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- `v2/grade.md` · `v2/result.txt` — second round
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Copy the scoring skeleton above into a new round's `grade.md` to add one.
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