The circuit was designed to work with an audio power amplifier which operated off +18v-0v-18v power rails. The actual voltage used is not too critical except that the feedback is referred to the LED chain which itself is anchored to a +12v rail, hence the separate stabilizer for this. It has one large advantage over most of the LED chips available - all the LEDs are in series so it only draws 20mA irrespective of the number of LEDs illuminated. source

This is a STEREO LED LEVEL METER. It’s the cheapest and best bar graph display available and best of all, it uses readily available components.You only need a handful of LEDs, 22 transistors, some resistors, diodes and a set of electros - it doesn’t require any chips.source

The LED meter is simpler and smaller than it’s analogue counterpart, and is very common in audio equipment. This version is based on a National Semiconductor IC, and uses the logarithmic version. Each LED operates with a 3dB difference from the previous one, and a jumper is provided to allow dot or bar mode.source