An alternative to dedicated drivers and LED arrays is to make your own, borrowing the idea behind R2R ladders and flash ADCs. The output from the aforementioned edge detector is fed through something similar to an R2R ladder (not necessarily with equal value resistors), which provides a number of nodes with voltages from the input to ground. A FET can be selected such that its knee voltage or turn-on voltage is something manageable, like 0.5V to 1V, its source grounded and gate connected to the various R2R nodes. When a node exceeds the knee voltage, the FET turns on and drives an LED.
Sound amplitude is traditionally (and biologically!) logarithmic, so the voltage at which each should turn on is linear on a logarithmic scale. For an input of max 3.3V to light 10 LED's per channel logarithmically with voltage, assuming a knee voltage of 0.5V, the absolute node voltages will be: (MATLAB)
EDU>> logspace(log10(0.5),log10(3.3),10)
ans =
0.5 0.6166 0.7605 0.9379 1.1567 1.4265 1.7593 2.1697 2.6758 3.3
If one aims for a maximum current of ~1mA, total R2R resistance should be near 3.3kΩ. This reveals resistor values of: (use voltage divider iteratively)
R1 = 624.2 (620)
R2 = 506.1 (510)
R3 = 410.4 (430)
R4 = 332.8 (300)
R5 = 269.8 (270)
R6 = 218.8 (240)
R7 = 177.4 (160)
R8 = 143.9 (150)
R9 = 116.6 (120)
R10= 500 (500)
Note: standard 5% resistor values in brackets are not simply the closest match, but are calculated iteratively. To redo calculations with other standard values or specs, the formula is: Ri = RTOTAL x (1 - Vi / 3.3V) - {sum from 1 to i of Ri}, derived from voltage divider formula.
Final circuit will look something like this:

Another method of achieving this effect is to use diode drops. 3.3V can support about 8 Schottky drops (~0.4V) if transistor threshold voltage is less than or equal to 0.4V (otherwise, 7 drops). In a chain of 8 Schottky diodes, pull down voltages at each intermediate node with a resistor that will also function as a current limiter (allow something close to the test current from the datasheet to flow when diode is forward biased). Each node is then connected to transistors in the same way as above. Current through the diodes will change by over 8X, based on how many diodes are forward biased, so ensure each will work in all cases. This method is linear w.r.t. voltage or amplitude, which isn't quite authentic. Also, Schottky's are more expensive than 5% resistors...
A final hint -- one I haven't explored -- is to use the BE-drop in BJT transistors instead of Schottky diodes, saving several parts per LED but also having to deal with a larger diode drop and bipolars.