On how we hear
How low (high) can you go?
Obviously there is considerable controversy on the subject of audiophilia merits. Nays are prone to take the approach of "why bother". Human hearing is limited to detecting 20kHz sounds at best. More often, less than 15kHz. Therefore, using linear-up-to-40kHz tweeters surely must be pointless. Must it not?
Well, this turns-out not to be the case. A bit of Do-Re-Mi basics will explain why. Any musician knows his "perfect octave" (from Latin "octavus" - "eighth"). Octave spans seven distinct tones, the eighth, final one being the start of the next, higher octave. Each tone within the octave has it's own distinct sound frequency. Eighth tone has double frequency of the first one.
What is relevant to our hearing-limits-discussion here, is this ratio of octave frequencies from from first, to last note, equals times two. The octave top frequency is always two times the octave bottom frequency. If the highest sound frequency (we could hear in our prime young age) was close to 20kHz, this (topmost) octave begins at some 10kHz. Previous octave, ending at 10kHz, starts at 5kHz then. The preceding one 5kHz to 2.5kHz, and so on-and-on.
The whole audible sound frequency spectrum 20Hz-to-20.000Hz span (measured in octaves) is a bit less than 10 octaves. Applying the octave measurement to our original subject of human-hearing-limits, it turns out we can never miss more than a part of the top-most octave. Nine, or so octaves always remain. The aging loss of high-frequency sensitivity indeed looks like almost half of the range loss superficially, but in actual fact, counting octave-wise, what always remains is more than 90% of the audible range (nine+ octaves).
Mathematicians call this way of presenting any span, with next data point double value of the previous, while always the same distance from the previous - "logarithmic". Forged from Greek "logos" and "arithmos", meaning "proportion" (or "ratio") and "number" respectively. On our graphical representation of the frequency spectra axis, all octaves are of the same length regardless of frequency span they represent. The bottom octave from 20Hz to 40Hz is only 20Hz "long", while the topmost from 10kHz to 20kHz is five hundred times more - 10.000Hz "long". Regardless of that, the human ear and brain perceive both having the same Do-Re-Mi span.
And then, there is the "phase"..
Where did the twig-snap sound come from?
Please excuse using "phase" word. For us, not-exactly-at-home in mathematics people, let's call it the millisecond difference between the arrival of the same sound at two distinct points in space. The sound travels through the air at a finite speed. It takes time for a sound to travel the distance from one point to another.
Applied to (these points being) our left and right ears, we hear the same sound in each ear at different times. One hears it first in the left ear if the sound comes from left. In the right ear for sound coming from right. We do this all the time. It is how one knows from which side of the dark-and-scary forest the wolf growled in the thick of the night. And stayed alive.
This is quite fascinating aspect of sound perception. We actually perceive the exact location of the sound source by hearing and measuring the sound arrival delay. The ears hear the same soundwave with a time-difference. Let us call this "phase shift".
It is not only us humans, animals can do it as well, think of bats. And foxes locating a mouse under the snow blanket.
Let's measure this..
The triangulation of the sound-source-location (by phase shift) is not fascinating only to audiophiles. The scientists have researched it thoroughly. There are a ton of research papers published on the subject. The gist of the various research attempts is the numbers they agree on.
Humans are not as-good-as-bats, of course, but according to Yamaha research, humans can hear 6 microsecond time-differences. Please note that 1 second divided by 6 microseconds translates to some 167,000 times. This is not equivalent to 167kHz, but consider the sensory resolution needed.
While the already stated concerns just "simple" sounds like twigs snapping in a dark-and-scary forest at night, and we know exactly where the sound came from, and from how far away, hearing complex sounds like music is more complex. Details are available from a paper in the Journal of the Audio Engineering Society, among others.
The gist the article is: the phase shift of both-base-and-harmonic sounds definitely do change the perceived timbre. The same also goes for the other sound aspects, audiophiles care about.
What if we filter away part of the spectrum?
In sound reproduction systems, we use to play our music, there are many frequency filters, be it low-pass, band-pass, or high-pass ones. There are some we did not intend to use, but could not avoid, as well. All system components (due to not being ideal) bring some low-passing or high-passing to the table.
Just think of the loudspeaker, be it two-way, or three-way, or many-way. Cross-over networks are full of frequency filters. Even wide-band (one-way) speakers cause filtering by nature of sound frequency out of reproducible limits.
What follows is a bit hard to understand to us-not-exactly-at-home in mathematics people. Any and all frequency filters cause phase shifts both well under and well above the frequency point (points) the filters work at.
So, for instance, if the tweeter (or tweeter filter) cuts the signal frequencies above certain point, the band under that point will be phase shifted. The closer the signal gets to the cut-off point, the greater the shift is. Therefore, we have to put the cut off point well above human hearing range. The farther away the cut-off point is (from the audible range) the less phase shift there will be within the audible range.
Danny Richie of GR Research has recently done an extensive three-part-Youtube-clip on the sound reproduction system imaging. The series addresses practical aspects of phase-related (and other) sound reproduction issues (first, second, and third).
Recommended to all.