Hi yeah me again - I've got lots on my mind... I wondered if anybody knew how volume rises as more notes are added and how in turn we hear the result. If we take a piano for example that when played in a medium weight fashion on the right hand peaks out at -6db - what if we add the left hand in playing in exactly the same manner thus adding another 3 notes or so. How does the volume increase if at all? Basically I'm getting at the whole fundamental of amplitude - 12 instruments playing at a peak of -6db wont result in an overall volume of -6db - I'm presuming the result to be much more?? Is this peak versus rms? Anybody got any enlightenment here? Thanks alot Alex.

The difference in decibels between the two is defined to be 10 log (P2/P1) dB where the log is to base 10. If the second produces twice as much power than the first, the difference in dB is 10 log (P2/P1) = 10 log 2 = 3 dB. If the second had 10 times the power of the first, the difference in dB would be 10 log (P2/P1)= 10 log 10 = 10 dB. If the second had a million times the power of the first, the difference in dB would be 10 log (P2/P1) = 10 log 1000000 = 60 dB. The human ear is very sensitive to frequenties tough, the perception of a 3 db rise in the 2k-4khz will be much more noticible then a 3 db rise in 100hz-400hz. I hope this answers your question

Using your piano example, each time you double the number of notes played I would expect to see double the amount of power. This will show up on your meters as being 3db louder. Our perception of volume though is logarithmic, i.e. each 3db more and is sounds slightly louder. The frequency response of the ear is not flat though so that as the power level is decreased the lows and highs appear to be disproportionaly affected so that in the extreme that's all you can hear.

You need to calculate the RMS level by taking the amplitude of each 'note' (actually a complex waveform), squaring each, summing the squares, and taking the square root of all of that. That gives you one number (Root Mean Square or RMS) which is the simplest indication of total volume. However, since the ear is not constant in its perception of volume across frequency, not all notes of the same amplitude will have the same loudness to the ear. So, the RMS is a guide, not an absolute.