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A musical scale is a sequence of notes ordered by pitch. Musical scales form the foundation of melody and harmony in music.
Each step in the scale corresponds to a specific frequency.
Different scales can be used to create various kinds of musical expressions.
Typically, Western music employs the diatonic scale or the chromatic scale.
Understanding the arrangement of notes in a scale helps musicians know which notes will sound harmonious when played together.

Frequency doubling is a key concept in understanding musical scales and octaves.
When you double the frequency of a note, you move one octave higher on the musical scale.
This doubling of frequency creates a sense of similarity in the notes, though they are at different pitches.
For instance, if we start with a frequency of 100 Hz, doubling it to 200 Hz moves us one octave higher.
To move another octave higher, we double 200 Hz to reach 400 Hz.
This principle applies to all notes, making it easier to understand how scales work.

Practical example:
- Starting frequency: 100 Hz
- First octave: 100 Hz × 2 = 200 Hz
- Second octave: 200 Hz × 2 = 400 Hz
This simple process ensures we can predict the frequencies of notes in higher octaves accurately.

An octave is the interval between one musical pitch and another with double its frequency.
It is one of the most basic and important intervals in music.
When playing or singing, moving up one octave means you are doubling the frequency.
Conversely, moving down one octave means you are halving the frequency.

Let's explore an example using the exercise given:
- Given starting frequency: 100 Hz
- Doubling the frequency for the first octave gives 200 Hz
- Doubling again for the next octave results in 400 Hz

This step-by-step doubling makes it straightforward to determine the frequency of notes an octave or multiple octaves away.
Musically, notes an octave apart sound very similar, almost as if they are the same note but at different pitches.
This characteristic makes octaves fundamental to developing melodies and harmonies in music across various genres.