Laser Waves is a beautiful and accurate music visualizer.

Here is a short description of the app's visualizations:

BasicLasers : a colorful oscilloscope
PolarFFT : the frequency spectrum in a doughnut shape with low frequencies on the outer ring and the log of the higher frequencies on the inner ring
Spectrum : a plot of the frequency spectrum on logarithmic axis
Spiral : a curvy mapping of the fft to R^2
RetroWaves : a pixelated oscilloscope

The oscilloscope is likely the most accurate you can find on the app store. If you can find one that's more accurate then please let me know about it. LaserWaves comes with a colorful oscilloscope for free and includes the other visualizations as in-app purchases.

The purpose of the app is not to be a fully featured music player but instead to be a platform on which I can distribute my music related pixel art :) (including 3D ray-marched scenes in the future maybe)