I personally don't like use of LM339's (or other comparators) except very special custom scale needed.
LM3914 for lin scale; lm3915 for 3db/led scale; lm3916 for analog meter-like scale.
They have good precision, LED current is easy to program
(in this case, use external reference, because the brightness depends on load at voltage reference out pin).
LM3914 etc are available at many places, except mouser - ebay or farnell for example, $2...4 per chip.
Easy to get 20, 30 or 40 led's string, datasheet shows the connection of 2 cascaded drivers,
with same mind possible to cascade more - just connect in series internal resistors strings, connect reference voltage to top of resistor's string;
mind 20k resistor used for cascading in bar/dot mode.
This way, each 10 led's can have different brightness. RTFM or (datasheet in this case

As it was told by PRR, check how led's are connected at your boards.
If they're connected as matrix, possible to use multiplexers for channels rectifiers/led's and one lm3914 string...but whole thing becomes bulk.
In old models, Dor**h used one string of LM3914's for one string of led's.
They used op-amps and transistors in log converters; IMO THAT2252 is better way to get rectifier in db scale and peak/avg/rms responce.
The rest is easy to figure out from datasheets.
Another way to get precision meter with low parts count, is to do it with shift register, comparator, integrator, charge/discharge circuit, and good temp stable clock.
No resistors string, no comparators, but has some voodoo.
Possible to regulate whole meter's brightness (not in a big range) too.
I saw somewhere schemo of 64 led meter, with good stability and very low parts count. Same idea as in A/D converter based on counter/integrator.
Interestingly, if integrator's cap charged thru resistor, scale is linear. What happens if we charge it from constant current source?
(edit: found!!!!!!!)
http://www.eetimes.com/electronics-news/4164691/Simple-high-resolution-bar-graph-display-architecture-uses-analog-comparator
Elegant schem, aye!
Another idea is use 28 or 40 led matrix and microcontroller with internal DSP. Ho! So far so good

This way the parts count is very low,
the level of fun is maximum, due to user accessable options and features like peak hold, BUT requires some hardcore with R&D.