Gripped with vengeful passion, The Queen of the Night  tears across the stage. She begins to sing her titular aria, one of the most famous sections  from Mozart’s beloved opera, "The Magic Flute." The orchestra fills the hall with music, but the queen’s voice soars above  the instruments. Its melody rings out  across thousands of patrons, reaching seats 40 meters away— all without any assistance  from a microphone. How is it possible that this single voice can be heard so clearly, above the strains  of dozens of instruments? The answer lies in the physics  of the human voice, and the carefully honed technique  of an expert opera singer. All the music in this opera house  originates from the vibrations created by instruments— whether it’s the strings of a violin  or the vocal folds of a performer. These vibrations send waves into the air,  which our brains interpret as sound. The frequency of these vibrations–– specifically, the number  of waves per second–– is how our brains determine  the pitch of a single note. But in fact, every note we hear is actually a combination  of multiple vibrations. Imagine a guitar string vibrating  at its lowest frequency. This is called the fundamental, and this low pitch is what our ears  mostly use to identify a note. But this lowest vibration triggers  additional frequencies called overtones, which layer on top of the fundamental. These overtones break down  into specific frequencies called harmonics, or partials— and manipulating them  is how opera singers work their magic. Every note has a set of frequencies  that comprise its harmonic series. The first partial vibrates  at twice the frequency of the fundamental. The next partial is three times  the fundamental’s frequency, and so on. Virtually all acoustic instruments  produce harmonic series, but each instrument’s shape and material changes the balance of its harmonics. For example, a flute emphasizes  the first few partials, but in a clarinet’s lowest register, the odd-numbered partials  resonate most strongly. The strength of various partials is part of what gives each instrument its unique sonic signature. It also affects an instrument’s ability  to stand out in a crowd, because our ears are more strongly  attuned to some frequencies than others. This is the key to an opera singer’s  power of projection. An operatic soprano— the highest of the four standard  voice parts— can produce notes  with fundamental frequencies ranging from 250 to 1,500 vibrations  per second. Human ears are most sensitive  to frequencies between 2,000 and 5,000  vibrations per second. So if the singer can bring out  the partials in this range, she can target a sensory sweet spot  where she’s most likely to be heard. Higher partials are also advantageous because there’s less competition  from the orchestra, whose overtones are weaker  at those frequencies. The result of emphasizing  these partials is a distinctive ringing timbre  called a singer’s squillo. Opera singers work for decades  to create their squillo. They can produce higher frequencies by modifying the shape and tension  in their vocal folds and vocal tract. And by shifting the position  of their tongues and lips, they accentuate some overtones  while dampening others. Singers also increase their range  of partials with vibrato— a musical effect in which a note  slightly oscillates in pitch. This creates a fuller sound  that rings out over the instruments’  comparatively narrow vibratos. Once they have the right partials, they employ other techniques  to boost their volume. Singers expand their lung capacity  and perfect their posture for consistent, controlled airflow. The concert hall helps as well, with rigid surfaces that reflect  sound waves towards the audience. All singers take advantage  of these techniques, but different vocal signatures  demand different physical preparation. A Wagnerian singer needs  to build up stamina to power through the composer’s  four-hour epics. While bel canto singers require  versatile vocal folds to vault through acrobatic arias. Biology also sets some limits— not every technique is feasible  for every set of muscles, and voices change as singers age. But whether in an opera hall  or a shower stall, these techniques can turn  un-amplified voices into thundering musical masterpieces.