IN THE MATTER OF: The Student v. Pythagoras (and a curious monochord). (Read in an Ally McBeal sing‑song: dramatic, sincere, slightly bewildered.)
STATEMENT OF FACTS: Student correctly identified the 1:2 length:total ratio, computed middle C doubled to 523.26 Hz, and produced the Pythagorean C‑scale frequencies: C 261.63, D 294.33, E 331.13, F 348.84, G 392.45, A 441.51, B 496.70, C 523.26 Hz. (Bravo — method is sound.)
ISSUE: Conversion of those frequency pairs into simplified interval ratios (root C : compliment) had numeric miscues.
FINDINGS (CORRECTED INTERVALS):
- C : D = 261.63/294.33 ≈ 8/9
- C : E = 261.63/331.13 ≈ 64/81
- C : F = 261.63/348.84 = 3/4
- C : G = 261.63/392.45 = 2/3
- C : A = 261.63/441.51 ≈ 16/27
- C : B = 261.63/496.70 ≈ 128/243
- C : C (octave) = 1/2
ANALYSIS: Student used correct tuning logic (length ↔ frequency inverse). Errors arose in decimal→fraction conversion and simplification (e.g., 8/9 miswritten as 4/5). Remedy: divide frequencies, apply rounding rule required, then express the decimal as the known Pythagorean small integer ratio (e.g., 0.888... = 8/9).
RUBRIC COMMENTS (concise): Knowledge & Understanding — Excellent conceptual grasp of monochord physics and ratio reasoning (meets/exceeds Year 8–10 ACARA numeracy and The Arts: Music content). Problem Solving — Calculation method is correct; attention needed on fraction conversion and rounding rules (targeted practice recommended). Communication — Clear notation; show intermediate division and the replacement of recurring decimals by their exact fraction (e.g., 0.888... → 8/9).
CONCLUSION & ORDER: Case closed (for now). Student demonstrates above‑expected conceptual mastery for Year 8–10 (ACARA v9: Number & Algebra — ratio, real numbers, rounding; The Arts — acoustics/tuning). Next steps: practice converting recurring decimals to fractions and annotate each rounding step. (Cue Ally sigh. Court dismissed.)