You are trying to detect the key signature or tonality. Audacity’s Change Pitch only attempts to detect the pitch of the first meaningful note in your selection - nothing more.
You can still detect tonality by ear in Audacity. Select a note (this works best for a solo piece). Play the note. You can tell the scale relationship of the note, for example it’s on the major third of the scale. Open Change Pitch and it gives you the detected pitch. For example, if it says “E” and you heard that the note is the major third, then the key signature is C Major.
That’s a very interesting application - the first one I’ve seen myself that attempts tonality detection. According to that page, a few applications like Audio Mixcraft 3 have licensed the app.
As you may have noticed, there is an online demo of the app that accepts at least MP3 - you have to sign up and log in to upload files:
sonicAPI.com -- audio processing web service .
I assume the “tuning frequency” it detects is the pitch of the A4 (middle A) in the song. If so, you can select middle A in the Audacity waves once you know the key signature and Change Pitch will show you its frequency.
Gale