Gyrators are synthetic inductors, which are often used to form bandpass filters. As shown in the two examples here, the active buffering device can be a transistor or op-amp. This type of bandpass filter is commonly used in graphic equalizers and other frequency control circuits such as tone controls.
In the gyrator frequency calculator here, enter the values of R1, R2, C1 and C2 then hit the Calculate button to use the calculator. The center frequency of the bandpass filter will be displayed as well as the Q (bandwidth).
The passband will be narrow if the Q is high. A typical 1/3 octave bandpass will have a Q of about 4.3 and a 2/3 octave filter Q value could be around 2.4.