A musical scale that is not based on any one key-note but has the same character independent of the starting note is known as an equally tempered scale. If in this scale, an octave is divided into 12 half tones, what are the frequencies of the successive half-tones between a note of frequency 256 Hz and its octave ?

Explanation

To find the frequencies of the successive half-tones between a note of frequency 256 Hz and its octave (512 Hz) in an equally tempered scale, we can follow these steps:

### Step 1: Understand the relationship between frequencies in an octave
In an equally tempered scale, an octave is divided into 12 equal parts (half-tones). The frequency of the note after one octave is double the frequency of the starting note. Therefore, if the starting frequency is \( f_0 = 256 \) Hz, the frequency of the octave is:
\[ f_{octave} = 2 \times f_0 = 2 \times 256 = 512 \text{ Hz} \]

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