Octave

The octave is the musical interval between two notes whose frequencies are in a ratio of 2. Two notes separated by an octave have the same name (Do, Re, Mi… or C, D, E…) because they are perceived as very similar by the human ear.

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How to measure it in class

With the FizziQ app, it is possible to experimentally verify the frequency ratio of an octave.

Steps:

Open FizziQ and select the “Frequency Meter” instrument
Play a note on an instrument (piano, flute, xylophone) and note its frequency
Play the same note one octave higher and measure its frequency
Verify that the second frequency is indeed double the first
Repeat with different notes to confirm the relationship

Scientific activities on this topic

Study the frequencies of the musical scale notes: https://www.fizziq.org/en/activities/the-range/
Analyze the harmonics of an instrument: https://www.fizziq.org/en/activities/tubular-melodies/
Build the tempered scale with the FizziQ synthesizer

Learn more

Perception of the octave:

The octave is a universal phenomenon recognized in all musical cultures. This universality is explained by the physiology of the ear: the hair cells of the cochlea that respond to a frequency f also partially respond to 2f, creating a sensation of kinship between these two sounds.

The octave in the scale:

The Western scale divides the octave into 12 equal semitones (tempered scale). Each semitone corresponds to a frequency multiplication by the 12th root of 2, approximately 1.0595. Thus, after 12 semitones: (12th root of 2)^12 = 2, we indeed find the octave.

Scientific notation of octaves:

Notes are numbered by octaves: C3 (approximately 262 Hz), C4 (approximately 523 Hz), C5 (approximately 1047 Hz). A4 at 440 Hz serves as the international reference.

Harmonics and octaves:

The harmonics of a sound are integer multiples of the fundamental frequency. The 2nd harmonic is therefore exactly one octave above the fundamental, the 4th harmonic two octaves above, etc.

Formula

f2 = 2 x f1

where:

f2: frequency of the note one octave above (Hz)
f1: frequency of the starting note (Hz)

For n octaves: f = f1 x 2^n

Application examples

A3 is at 440 Hz, A4 at 880 Hz, A5 at 1760 Hz
A standard piano covers about 7 octaves (from 27.5 Hz to 4186 Hz)
The human voice spans about 2 octaves
The low C of a double bass (approximately 41 Hz) and the high C of a piccolo (approximately 4186 Hz) are separated by 7 octaves

FAQ

Q: Why do two notes an octave apart seem “identical”? A: It is related to the logarithmic structure of our auditory perception and the fact that the harmonics of a note naturally contain its octaves.

Q: Does the octave exist in all music? A: Yes, it is one of the few universal intervals. However, the division of the octave into 12 semitones is specific to Western music; other cultures use different divisions.

Q: How can I quickly verify an octave with FizziQ? A: Measure the frequency of a note, then that of the same note one octave higher. The ratio should be exactly 2.

Frequency - Pitch - Tempered scale - Harmonics - Semitone - Musical interval