A musical scale is constructed by providing intermediate frequencies between a note and its octave which

Options

A. form an arithmetic progression
B. form a geometric progression
C. bear a simple ratio with their neighbours
D. form a harmonic progression

Answer

To solve the question regarding the construction of a musical scale with intermediate frequencies between a note and its octave, we will analyze the properties of octaves and the relationships between the frequencies.

### Step-by-Step Solution:

1. **Understanding Octaves**:
- An octave is defined as the interval between one musical pitch and another with double its frequency. For example, if a note has a frequency of 220 Hz, the note one octave higher will have a frequency of 440 Hz.

2. **Identifying Frequencies**:
- Let's denote a note as A with a frequency of 220 Hz. The next octave of A will be 440 Hz. The frequencies in between these two notes will be the intermediate frequencies.

3. **Intermediate Frequencies**:
- The intermediate frequencies between a note and its octave do not follow a simple arithmetic or geometric progression. Instead, they are spaced in a way that maintains a consistent ratio with their neighboring frequencies.

4. **Simple Ratio with Neighbors**:
- The intermediate frequencies will bear a simple ratio with their neighbors. This means that if you take any two adjacent frequencies, the ratio of their frequencies will be constant.

5. **Conclusion**:
- Based on the analysis, the correct answer to the question is that the intermediate frequencies "bear a simple ratio with the neighbors."

### Final Answer:
The correct option is: **C) bears a simple ratio with the neighbors.**