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The Numbers That Come Up

Topic 2.5 · Numeracy, free at full depth on the resource hub. Two of the chapter’s four rows are reproduced below, unchanged.

Row 1 · Pitch & Period

Pitch & Period

A4 is tuned to 440 Hz; an octave up doubles frequency (440 → 880 Hz), an octave down halves it (440 → 220 Hz). Period is the flip side of frequency (T = 1/f), so a handy shortcut is worth memorising: 1 kHz ⇄ 1 ms. A 250 Hz tone’s period follows the same rule: 1/250 = 0.004 s = 4 ms.

An A note at 440 Hz is transposed one octave up. What is the new frequency?

  • 880 Hz. One octave up doubles frequency: 440 × 2 = 880
  • 220 Hz. That is one octave down, the opposite direction
  • 440 Hz. An octave changes how a note is written, not its frequency

Correct: an octave up always doubles frequency, and an octave down always halves it (440 ÷ 2 = 220 Hz).

Row 3 · Tempo in Milliseconds

Tempo in Milliseconds

Every timed effect starts from one formula: one beat in milliseconds = 60,000 ÷ BPM. At 200 BPM, that’s 60,000 ÷ 200 = 300 ms. Divide, don’t guess. From there, dotted = ×1.5 and triplet = ×⅔ of any note value, whatever the tempo.

At 200 BPM, what is the value of one beat in milliseconds, and what is a dotted version of that value?

  • 300 ms for the plain beat (60,000 ÷ 200), and 450 ms dotted (300 × 1.5)
  • 200 ms for the plain beat, reading the BPM number directly
  • 300 ms plain, but 200 ms dotted, since dotted notes are shorter

Correct: 60,000 ÷ 200 = 300 ms, and dotted always means ×1.5 of the plain value.

Two more rows continue inside the full chapter (Decibels & Dynamic Range, and File Size) plus the worked exam anchor question that ties all four together.