Teacher comments (Ally McBeal cadence):
Oh — the monochord hums, we lean in. You found 1:2 — crisp; you doubled 261.63 to get 523.26 Hz — bravo, you hear the octave. You said pitch doubles when the string is halved — exactly right. Your 2/3 calculation for G (261.63 × 3/2 = 392.45 Hz) — lovely, correct. The Pythagorean C scale you listed is very near the expected values (small rounding differences are fine).
Where the music stumbles: the interval ratios. To get each interval, divide C by the other note, then simplify to a small whole-number ratio from Pythagorean tuning. Correct simplified interval ratios are: C:D = 8/9, C:E = 64/81, C:F = 3/4, C:G = 2/3, C:A = 16/27, C:B = 128/243, C:C = 1/2. Practice: compute decimal (C ÷ note), then match to nearest small fraction (use powers of 2 and 3).
Parent comments (Ally McBeal cadence):
Dear heart, you listened to Pythagoras and learned well. You answered bravely. A few fractions wandered off-stage — not a problem — we’ll rehearse the method: divide, get a decimal, then convert to a simplified fraction (look for 2, 3, 4, 8, 9, 16, 27, 81 patterns). Celebrate the correct ideas and guide the fraction work gently.
Next steps & curriculum mapping:
This task builds proportional reasoning, fractional simplification and using measurement units (Hz), aligning with ACARA v9 goals for Years 8–10: understanding ratio and proportion, applying real-world measurement and converting between representations. The lesson meets and in parts exceeds expectations by combining mathematical reasoning with scientific measurement and historical context. Suggested practice: three worked examples converting decimals to Pythagorean fractions, and a short worksheet on simplifying ratios.