iChromatic

The HotPaw iChromatic Strobe Tuner uses the built-in microphone on your iPhone to allow you to tune a musical instrument rapidly and precisely via an animated visual display.
For your iPad, please see the iChromatic Strobe Tuner HD. For guitar tuning, please see the HotPaw inTuna Strobe Guitar Tuner. Both of these apps are also here in the iOS app store.
iChromatic includes both a frequency readout and 3 highly accurate and responsive waterfall strobe panes which allow extremely precise tuning. When the waveform patterns line up vertically as well as stop moving sideways in the strobe panes, this indicates that the input pitch (or a strong harmonic of the pitch) matches the frequency of the nearest equal temperament note.
With the waterfall strobe tuning window, even very slight differences in frequency between the pitch detected and the target perfect pitch will cause the abstract waveform to waver or move sideways as it cascades down the strobe window. iChromatic also includes a pitch frequency readout in Hz and cents. Configuration options include a Concert A reference frequency adjustment in both Hz and Cents.
Please try the Free inTuna A440 app, also in the iOS App store, before purchasing iChromatic, to see if you appreciate the advantages of using a strobe tuner.
Tuning range using the built-in iPhone microphone is from 2 octaves above middle-C to 2 octaves below.