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In a snap—hum—la‑la aside, the 13‑year‑old computed 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 fifths, halving and two‑thirds for derived steps. Octave transpositions were handled by systematic doubling/halving. Calculations adhere to Pythagorean tuning: multiplicative reasoning, inverse proportionality, clear notation and consistent units produced frequencies for C D E F G A B C' that fit Pythagorean constructs. This work links ACARA v9 The Arts (Music) and Mathematics (Number and Measurement). Conclusion: exemplary mastery. Recommend comparative study of Pythagorean versus equal temperament, hands‑on monochord or tuning software verification, ear‑training exercises, and a short reflective journal entry. Bravo—cue tiny celebratory grocery‑bag dance. Include this work in the homeschool portfolio, present a one‑minute demo, and badge musical numeracy soon.


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