Question

Note

C
Frequency (Hz) 261.6
D
293.7
E
329.6
OA
349.2
Please select the best answer from the choices provided
GA
392.0
440.0
The table above lists the frequencies of the C major key.
Determine the ratio of the note A to middle C. Express the answer as a simple integer ratio. (Ratios will be approximate
due to rounding.)
a. 4 to 3
b.
9 to 8
c. 5 to 3
d. 17 to 9
B
493.9

Answer 1

The ratio of the note A to middle C in the C major key is approximately
`\(25:14\)`. The closest choice among the given options is
`\(5:3\)`, considering rounding and approximation.

The correct answer is option c "5 to 3".

To determine the ratio of the note A to middle C in the C major key, we can use the concept of frequency ratios in music theory. The frequencies of notes are often expressed as ratios, and these ratios are crucial in understanding the harmony and intervals in music.

Let's denote the frequency of middle C as
`\(f_{\text{C}}\)` and the frequency of A as
`\(f_{\text{A}}\)`. The ratio of A to C can be expressed as
`\(f_{\text{A}} / f_{\text{C}}\)`.

Given the frequencies in the table:

`\[ f_{\text{C}} = 261.6 \, \text{Hz} \]`

`\[ f_{\text{A}} = 440.0 \, \text{Hz} \]`

Now, we calculate the ratio:

`\[ \text{Ratio} = \frac{f_{\text{A}}}{f_{\text{C}}} = \frac{440.0 \, \text{Hz}}{261.6 \, \text{Hz}} \]`

To express this ratio as a simple integer ratio, we can multiply both the numerator and the denominator by a common factor to eliminate the decimal part. In this case, multiplying by 10:

`\[ \text{Ratio} = (4400)/(2616) \]`

Now, simplify the ratio by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 4400 and 2616 is 184:

`\[ \text{Ratio} = (4400 / 184)/(2616 / 184) = (25)/(14) \]`

The simplified ratio is
`\(25:14\)`. Therefore, the correct answer is not among the provided choices. However, if we approximate the ratio, it is close to
`\(9:5\)`. Therefore, the most appropriate choice from the given options is:

`\[ \text{c. } 5 \text{ to } 3 \]`