Oh my God. You did this. You walked into a math problem disguised as a song and you fixed it with ratios — curious, careful, brilliant. Ratios run rhythm and harmony: you learned that rhythm is how many of something compared to the beat and harmony is how frequencies compare. You rebuilt a Pythagorean 7‑note C scale, simplified ratios, and used rounding rules to turn decimals back into neat fractions. Beautiful work.
Exemplary achievement — you showed method and heart. Your calculations were accurate: halving a string doubled frequency (C 261.63 → 523.26 Hz), 2/3 length gave the 3:2 fifth (G ≈ 392.445 Hz), and you correctly reduced notes into the C octave to recreate C, D, E, F, G, A, B, C with thoughtful rounding. You named interval ratios (1:2, 3:2, 4:3, 8:9, 16:27, 128:243) and explained why small integers sound consonant and larger ratios create beating and roughness.
ACARA v9 aligned: you demonstrated proportional reasoning in mathematics, explored musical elements and historical tuning ideas in The Arts, and strengthened general capabilities — numeracy, critical and creative thinking, and communication. You showed each step: setup, multiply by 3/2 for fifths, octave‑reduce by ÷2 when needed, and explain the listening evidence.
Specific strengths: accurate inverse relationships (length ↔ frequency), correct octave adjustment, clear linking of math to listening, and tidy communication of steps and results. You answered word problems with mathematical justification and musical sense. You recognized which ratios you liked (1:2, 3:2, 3:4, 8:9) and why, and which felt rougher (16:27, 128:243).
Final note: Exemplary. That word fits. Keep listening. Keep calculating. Keep composing. Oh my God — bravo. You met and stretched the ACARA v9 expectations and did it with curiosity and flair.
— Your teacher (proud, slightly dramatic, and very impressed)