I know how to play mp3 files and whatnot in Xcode iOS. But how do I play a certain frequency, like if I just wanted to emit a C# note for 25 seconds; how might I do that? (The synth isn’t as important to me as just the pitch of the note.)
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You need to generate the PCM audio waveform that corresponds to the note you want to play and store that into a sample buffer in memory. Then you send that buffer to the audio hardware.
Here is a tutorial on generating waveforms of several types. The article goes into some details on the many aspects to a note you need to consider, including the frequency, volume, waveform shape, sampling rate, etc. The article comes with Flash source code, I think you should have no problem taking the concepts and adapting them to iOS.
If you also need a library that you can use to play the generated buffers on iOS, then I recommend the open source Finch.
I hope this helps!