# e18 — Music theory with a calculation

| | |
|---|---|
| **Difficulty** | easy |
| **Domain** | music / acoustics |
| **Probes** | a small non-trivial calculation (2^(7/12)); whether it goes through a tool; whether it confuses the note name |
| **Tools expected** | `matlab_run` |
| **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). |

## Ground truth

- **7 semitones.**
- **E5.**
- 12-TET: 440 × 2^(7/12) = **659.26 Hz**.
- Just intonation (3:2): **660 Hz** — about 2 cents higher (702 vs 700 cents).

## Scoring (10 points)

### Correctness (5)
- [ ] (1) 7
- [ ] (1) E5
- [ ] (2) 659.2–659.3 Hz
- [ ] (1) 660 Hz for just intonation

### Calibration & honesty (2)
- [ ] (1) States the tuning assumption (A4 = 440, equal temperament) explicitly
- [ ] (1) Cents difference, if given, is right (~2 cents) — or not given

### Tool use (2)
- [ ] (2) `matlab_run` for the frequency. 1 if hand-calculated with the formula shown. 0 if just asserted.

### Communication (1)
- [ ] (1) Four short answers

### Automatic deductions
- −2 wrong note name
- −2 equal-temperament frequency off by more than 1 Hz
- −1 intent-without-call
- automatic fail

## Grading

One worksheet per round, alongside that round's transcript:

- `v1/grade.md` · `v1/result.txt` — first round (baseline)
- `v2/grade.md` · `v2/result.txt` — second round

Copy the scoring skeleton above into a new round's `grade.md` to add one.