In a day, Vienna listens to blues one-seventh of the time, jazz one-tenth of the time, pop one-fifth of the time, and rock one-fourth of the time. Which kind of music does Vienna listen to the least?

The given time for different kinds of music are:

blues one-seventh of the time = $\frac{1}{7}\mathrm{th}$

jazz one-tenth of the time = $\frac{1}{10}\mathrm{th}$

pop one-fifth of the time = $\frac{1}{5}\mathrm{th}$

and rock one-fourth of the time = $\frac{1}{4}\mathrm{th}$

Here the numerators are the same i.e., 1 so the number with the greatest denominator will be the least.

So, $\frac{1}{10}\mathrm{th}$ is smaller than $\frac{1}{7}\mathrm{th},\frac{1}{5}\mathrm{th} \mathrm{and} \frac{1}{4}\mathrm{th}$.

Therefore, Vienna listens to jazz the least.