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Octave = Double the Period

A-Level Music Technology | 2.5 Numeracy

Octave Period Trainer

Explore the mathematical relationship between frequency and period

Part 1
Foundation Concepts

Understanding Waveform Diagrams

Before you can draw transposed waveforms, you need to understand what each axis represents. Click each card to reveal the key concepts.

TIME
X-Axis: Time
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X-Axis: Time
The horizontal axis represents TIME (milliseconds or seconds). Shows how the waveform changes over time.
Key: Period is measured along the X-axis. Lower pitch = wider cycles along the X-axis.
AMPLITUDE
Y-Axis: Amplitude
Click to reveal
Y-Axis: Amplitude
The vertical axis represents AMPLITUDE (air pressure displacement or voltage). Shows the strength of the signal.
Key: Amplitude determines LOUDNESS, not pitch. Changing octave does NOT change amplitude.
T
Period (T)
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Period (T)
The time for ONE complete cycle of the waveform. Measured in seconds or milliseconds.
Key: Period = 1 / Frequency. Lower frequency = longer period = wider cycles.
4 cycles = 4Hz
Frequency (f)
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Frequency (f)
The number of complete cycles per second. Measured in Hertz (Hz).
Key: Frequency = 1 / Period. Higher frequency = higher pitch = more cycles per second.
x2 = octave up
Octave
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Octave
A doubling or halving of frequency. Going up one octave = frequency x 2. Going down = frequency / 2.
Key: Octave up = period HALVES. Octave down = period DOUBLES.
Cards Revealed
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📝Waveform Axes - Key Definitions
WAVEFORM DIAGRAM AXES:

• X-Axis (Horizontal): TIME - measured in milliseconds (ms) or seconds (s). Period is measured along this axis.

• Y-Axis (Vertical): AMPLITUDE - the strength of the signal. Determines LOUDNESS, not pitch.

CRITICAL RULE: Pitch changes affect the X-axis (time/period). Loudness changes affect the Y-axis (amplitude). They are independent!
⭐Period and Frequency Relationship
THE FUNDAMENTAL RELATIONSHIP:

Period (T) = 1 / Frequency (f)
Frequency (f) = 1 / Period (T)

• Higher frequency = shorter period = narrower cycles
• Lower frequency = longer period = wider cycles

OCTAVE RELATIONSHIP:
• Octave UP = frequency x 2 = period / 2
• Octave DOWN = frequency / 2 = period x 2
A-Level Music Technology | Component 4: Producing and Analysing | 2.5 Numeracy

What you learned

  • ✓Understand the relationship between frequency and period
  • ✓Recognise how octave changes affect waveform appearance
  • ✓Calculate period from frequency (T = 1/f)
  • ✓Draw waveforms at different octaves with correct cycle counts
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