Let's start with the facts…the human speaking voice ranges from ~100 Hz to ~6 kHz (6000 Hz) in regards to frequency. While that range seems huge, 80 percent of the energy is concentrated below 500 Hz. A simple assumption would be that the speaking voice is between 100 Hz and 500 Hz. But that assumption would be wrong. Nearly all of the energy of the consonants, within each word we speak, is over the 1 kHz mark.
When it comes to the singing voice (bass, alto, tenor, soprano), the range is ~80 hz to ~1 kHz. However, even with the human voice and the singing voice (not to mention all the music instruments), the high frequencies are very important because of harmonics.
The human ear can hear up to 20 kHz. The high E on a piano only produces 4 Khz. However, because of harmonics, that amount can go much higher.
"Each musical sound that you hear is a composite of sine waves at different frequencies and amplitudes. These sine waves combine to form the sound. The frequency and amplitude relationships determine the quality of the sound." (from "The Sound Reinforcement Handbook")
Let's say we play a moderately high E on the piano; second E after middle C. That note has a specific pitch. We hear the waveform created by the piano string being hit. However, we don't hear one frequency of 659 Hz. We hear a variety of frequencies that are created by different sine waves produced from the string. The sine wave frequency that we hear at the specific pitch as a note is known as the fundamental. Usually, the fundamental is the strongest of the sine waves.
Above the fundamental are these additional sine wave components (harmonics) that are mathematically related to the fundamental. Specifically, they are multiples of the fundamental. Let's take simple numbers. Say 500 Hz. That's between a B and C after the middle C for you piano players. The fundamental is 500 Hz. Then the harmonics (those related sine waves) occur at 1 kHz, 1.5 kHz, 2 kHz and on up until the energy of the frequency is gone. Now we are talking a 8-10 kHz frequency that you and I hear when a sound is played at the inital 500 Hz fundamental level. Welcome to harmonics.
Please note that reed instruments like the oboe and clarinet can have harmonics that are louder than the fundamental.
What Does All This Mean?
Understanding harmonics, musical and vocal ranges, and the ability of the human ear, you must understand that as soon as the range in which a sound system can reproduce frequencies is limited, the human ear will tell the brain, "something doesn't sound right."
High frequences are required for speech intelligibility. Our ears expect to hear the high frequencies which help us separate one sound from the next. If you turn down those frequencies too much or have a sound system that cuts frequencies too early, you lose the aspect of speech intelligibility.
High frequences give musical sounds depth and color. If you limit the high frequencies then you are removing the harmonics and when this is done to too high of a degree, the sound becomes flat and lifeless. In some cases, you can boost the high frequencies to produce a crisper and cleaner sound depending on the instrument.
The human ear is thought of as the world's perfect microphone. It's ability to detect a wide range of frequencies is amazing. We must respect our ears and our ability to differenciate the wide range of frequencies we can hear and thus harmonic frequencies are a very important part of what we hear.