Case: In the matter of the 13-year-old pupil’s Pythagorean tuning application.
Statement of Assessment: Pursuant to ACARA v9 homeschool music standards, the student constructed a Pythagorean C scale from Middle C (261.63 Hz) to C′ (523.26 Hz) using monochord ratios—1:2 for octaves, 3:2 for perfect fifths—and halving and two‑thirds operations to transpose across octaves. Calculations were shown stepwise in hertz with clear units and notation.
Findings of Fact: Frequencies for C, D, E, F, G, A, B and C′ align with Pythagorean ratios; octave doublings and reductions were systematic. Explanations demonstrated multiplicative reasoning and inverse proportionality linking frequency to string length.
Legal Conclusion: Methodology is transparent, coherent and accurate within the Pythagorean framework and meets ACARA v9 expectations.
Recommendation: Continue applied tuning exercises, formalise notation, compare with equal temperament.
Observational Note: In an Ally McBeal cadence the pupil’s whimsical reflective voice enriched technical rigor and merits praise. Highly recommended overall.