# pitch vs playback rate

Let's say I have an audio sample, whose pitch is known to be C4 (don't wanna go in detail here, let's say I just sampled a tuned piano playing the C4 key).

The rules of the game are: I can only change the sample playback rate by any ratio. No pitchshifter module, no frequency analysis. If I set the playbackrate to 2.0, for example, the sample is played back at twice its speed. If I set it to 0.5, the sample is played back at half its speed, and so on. This changes the playback time as well as the sample pitch.

If I wanted to generate any arbitrary "note" from this sample, what is the relation between the playback rate and the sample pitch? For example, I know that C4 fundamental frequency is 261.63 Hz. What playback rate should I set to make the sample "sound like" a C#4/Db4 (277.18 Hz) or a D4 (293.66 Hz)? What is the general, formulaic, relationship?

• Very interesting topic. So do you have any issues with the duration of the note changing based on the pitch? – user2718 Feb 1 '13 at 22:50

For example, if your C4 note was sampled at 48kHz, you'll need to play it back at $48000 \times \frac{277.18}{261.63} = 50.85kHz$ to make it sound like a C#4.