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Below are the pitch ranges of some common musical instruments. The note names and octave numbers are written below the piano keyboard. Middle C and A440 are marked.
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This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.
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Every musician discovers early on that octaves are special.
Notes which are one or more octaves apart have the same note name – that in itself means a lot. Furthermore, changing octaves feels more like changing voice or register than going to a different note.
Why is this so?
When we play a note, a sound wave is produced. Each pitch produces a wave which vibrates at a certain frequency: the higher the pitch, the higher (greater) the frequency.
The frequency is measured in cycles (vibrations) per second, called Hertz, Hz for short. You may have heard of A440, the frequency tuners are calibrated to. 440 means 440 Hz. A440 vibrates 440 times per second.
Playing a note an octave higher doubles the frequency: an octave above A 440 Hz is A 880 Hz. As the frequency gets higher, the length of the wave becomes shorter, so double the frequency is half the wave length.
When we play these two notes together, the higher note’s sound wave fits exactly twice inside the lower note’s sound wave. No other combination of two notes has such a direct relationship between their sound waves as an octave. This perfect fit is why the higher note of an octave sounds like it fits inside the lower note: because it literally does.
Graph showing the sound waves of two notes an octave apart such as A440 and A880. Twice the frequency = half the wavelength
Low and high octaves are large and small versions of each other. A musical part can be played at a different octave without introducing any new notes: it will still fit all chords and other parts equally well.
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*Graphics taken from Music Theory De-mystified, my upcoming music theory book, due to be released late 2022.
