how to download songs from itunes radio with airplay recorder (for mac )

This new Mac app lets you create local copies as songs stream by on iTunes Radio.

The AirPlay Recorder app was released last month for Android and now has come to OS X. It allows you to record a stream from iTunes Radio, saving songs for offline use. DoubleTwist AirPlay Recorder for Mac can be downloaded directly from the developer's site. You can try out the free version of the app, but it lets you record only the first 10 seconds of a song. The full version of AirPlay Recorder costs $9.99 and lets you record entire tracks. You'll need Mac OS X 10.7.3 or higher to run the app.
When you launch AirPlay Recorder, it adds itself as an option to the AirPlay menu. Select it as your AirPlay output choice and it will record songs as they play on iTunes Radio. The app creates a Recorder folder in your Music folder where it puts copies of the songs it downloads.

AirPlay Recorder records songs in real time, and it can't record a song that is playing before it is selected as your AirPlay option. Thus, you can't choose which songs to record during an iTunes Radio stream, but can record them only as they stream by. Also, because AirPlay Recorder must be selected as your AirPlay output, you can't listen to songs and record them at the same time. On a positive note, AirPlay Recorder recognizes ads as being too short to be a song and doesn't record them.
One question remains: Is this legal? Addressing this concern, company co-founder and President Monique Farantzos told Engadget in January when the Android app launched, "Recording has been around for decades, from audio cassettes (remember mixtapes?) to TuneIn radio's recording feature. Given that Apple built their iPod empire on letting millions of people rip CDs based on fair use, we don't see how they could object to this app