Question 1a (ratio 1:2)
Oh my, sweet discovery! You wrote 1:2—crisp and correct. Celebrate that ratio connection between halving string length and octave. This meets ACARA v9 numeracy expectations for proportional reasoning and music awareness in The Arts. Keep noting whether ratios are written small-to-large or large-to-small, precise practice.
Question 1b (frequency 523.26 Hz)
Gosh, you multiplied and found 523.26 Hz — charmingly correct; halving the string doubles frequency into the octave above. This shows ACARA v9 skill with numerical computation and measurement. For music, label it 'high C' and watch rounding rules; two decimals work, but mention units explicitly next time.
Question 1c (pitch doubling)
You're right: pitch doubles when the string is halved, and your phrasing is succinctly musical. ACARA v9 alignment: proportional reasoning and scientific understanding of waves. Consider adding why frequency increases (inverse length relationship) and use technical words like 'frequency' and 'octave' — that precise vocabulary earns top rubric marks indeed.
Octave limits (261.63 to 523.26 Hz)
Nice, you correctly set the C octave limits: 261.63 Hz up to 523.26 Hz. Melody contained! This aligns to ACARA v9 numeracy and The Arts outcomes, showing understanding of bounds and unit consistency. Next step: annotate which is lower and upper and add 'Hz' each time to reinforce scientific notation.
2/3 split frequency (392.45 Hz)
Bravo — 392.45 Hz (rounded) is the 3/2 frequency result from making the string two-thirds as long. Nicely done. This matches ACARA v9 expectations for ratio application and measurement. One tip: show the arithmetic 261.63 × (3/2) = 392.445 then rounding rule used, for transparent method evidence. Keep that clarity.
Pythagorean C scale frequencies (list)
What a melodic spreadsheet — your Pythagorean C frequencies are accurate and nicely rounded. This demonstrates procedural fluency aligned to ACARA v9 numeracy and The Arts: follow-up. Celebrate your arithmetic and octave adjustments. Next, annotate where you halved or doubled frequencies and reference rounding rules to strengthen evidence of understanding.
Interval Ratio: C to D (student: wrote 261.63:294.33, then 4/5)
Oh, that little wobble: C to D as 261.63:294.34 simplifies to 8/9 (or invert to 9/8 for D over C). Your 4/5 is off. Aligns to ACARA v9 proportional reasoning—show division then fraction simplification and state which direction the ratio represents to avoid confusion. Explain units, rounding, and context, please.
Interval Ratio: C to E (student: wrote 261.63:331.13, then 4/5)
Lovely effort, but C to E should reduce to 64/81 (so E:C is 81/64), not 4/5. ACARA v9 numeracy asks for accurate fraction conversion from decimals — divide C by E, convert the decimal back to fraction, then simplify. Show steps and rounding method to meet rubric clarity expectations, please.
Interval Ratio: C to F (student: 3/4)
Bravo — C to F giving 3/4 is perfect; that fraction reflects Pythagorean fourth (F above C) and shows solid proportional manipulation. This aligns with ACARA v9 outcomes in number and measurement. Include simplified fraction and division steps. Also label direction (C:F or F:C) to remove ambiguity with clear notation.
Interval Ratio: C to G (student: left blank)
Ah, you left G blank — gentle nudge: C to G is 2/3 (or G to C is 3/2), because G equals C×3/2 before octave adjustment. ACARA v9 wants method and justification. Write the division, simplify the fraction, note whether you mean C:G or G:C, and include rounding rules please.
Interval Ratio: C to A (student: 3/5)
Warm applause for trying! C to A simplifies to 16/27 (so A:C is 27/16), not 3/5. ACARA v9 expectation: convert decimal division to exact fraction using powers of 3/2 chain. Show each multiplication by 3/2 or halving for octave, then simplify to demonstrate mastery and reasoning clarity and neat formatting.
Interval Ratio: C to B (student: 13/25)
Lovely attempt, but C to B should be 128/243 (so B:C is 243/128), reflecting three successive 3/2 multiplications with octave reductions. Your 13/25 is approximate; ACARA v9 recommends exact fractional expression from calculation. Show the 3/2 chain and halving steps, then simplify to that exact fraction for full rubric credit.
Interval Ratio: C to C (octave) (student: 1/2)
Yes! C to higher C is exactly 1:2 (or 1/2 depending on order), neatly capturing the octave. This matches ACARA v9 outcomes for ratio understanding and measurement precision. Recommend noting which note is numerator, stating 'C:C(high) = 1:2', and recording whether you applied rounding anywhere to strengthen evidence, thanks friend.