To solve this problem, we need to find the ratio of the frequency of note [tex]\(A\)[/tex] to itself and express this ratio in integer form.
First, let's identify the frequency of note [tex]\(A\)[/tex] from the table provided:
[tex]\[ A = 880 \text{ Hz} \][/tex]
Next, we calculate the ratio of [tex]\(A\)[/tex] to [tex]\(A\)[/tex]. Since we are comparing [tex]\(A\)[/tex] to itself, the calculation is:
[tex]\[
\text{Ratio} = \frac{\text{Frequency of } A}{\text{Frequency of } A}
\][/tex]
Substituting the given frequency:
[tex]\[
\text{Ratio} = \frac{880}{880} = 1
\][/tex]
The ratio of a frequency to itself is always 1. To express this in integer-ratio form, we note that a ratio of 1 can be written as:
[tex]\[
1 : 1
\][/tex]
However, "integer-ratio form" often emphasizes the natural number sequence in the simplest form, comparing she frequency with its first harmonic (octave). The first harmonic of [tex]\(A = 880 \text{ Hz}\)[/tex] is [tex]\(A' = 1760 \text{ Hz}\)[/tex]. So this can be written as:
[tex]\[
1 : 2 \text{ for } \frac{880}{1760}
\][/tex]
Conclusively, the best answer is common for octaves frequency:
[tex]\[
\boxed{\frac{2}{1}}
\][/tex]
Thus, for the note [tex]\(A\)[/tex], the ratio of its frequency to itself in integer-ratio form is [tex]\(\frac{2}{1}\)[/tex].
