specific frequencies, the fundamental and overtones, with no energy in between.
      Thus, under the simplistic sine wave model, it is possible that many musical sounds would not have overtones exactly at or very near the 3080 Hz point (to use our example) where the Tamino crossover creates its worst case 180 degree polarity inversion in its severe phase rotation of 360 degrees, and hence all such musical sounds would escape at least the worst and most peculiar sounding sonic consequences of the 180 degree point in the Tamino's 360 degree phase rotation. But, under the truer transient model, virtually all musical sounds would suffer some of the worst and most peculiar adverse sonic consequences from this 180 degree frequency, since virtually all musical sounds have energy at every frequency (and fraction of frequency) in an infinitely dense spectral content, which of course would include this worst case 180 degree frequency (3080 Hz in our example).
      Indeed, every musical sound, that has at least some spectral content at or above 3080 Hz (to use our example), would have an infinitely dense spectral content that includes 3080 Hz, and would therefore be colored by the Tamino crossover's worst case polarity inversion at 3080 Hz. Since the musical spectrum extends up to 20,000 Hz, you can see that virtually all musical sounds would have at least some spectral energy above 3080 Hz. Imagine what music would sound like if your audio system's frequency response cut off above 3080 Hz, as if the loudspeaker system's tweeter were totally disconnected. Virtually all musical sounds would be severely changed. This tells you that virtually all musical sounds contain spectral energy above 3080 Hz. And this in turn tells you that virtually all musical sounds, as transients, would contain some infinitely dense spectral energy both at and near the Tamino's worst case 3080 Hz point. So virtually all musical sounds will be modified by the colorations resulting from the Tamino's worst case 180 degree polarity inversion at 3080 Hz, and will also be modified by its colorations nearby, including the phasey quality and the recessed tonal balance, resulting from the severe and severely varying phase rotations from 0 to 360 degrees, in the region near 3080 Hz.

-- Critical Bands of Human Hearing

      The waveform analysis above, showing the notch in the musical waveform, is sufficient to explain the midrange colorations heard from the Tamino, both the phasey quality and the recessed tonal balance in the midrange. But the actual sound of the Tamino's coloration, as we humans actually perceive it, is probably made even worse than the waveform analysis implies, because of the way that human hearing works. We humans tend to hear the tonal balance of any broadband signal in terms of what are called critical bands. What does this mean? Because of the way our hearing works, we can't hear every individual frequency, contained in the spectral energy of a broadband signal, as a separate individual frequency. Instead, our hearing lumps together all the spectral energy contained in each critical band, and we only perceive how much energy there is in aggregate, within each critical band. The bandwidth of each critical band of human hearing is about 1/10 octave wide. This means that our perception of the tonal balance of a broadband signal groups together the energy within a 1/10 octave span, and can only assess how much energy there seems to be in that total span, not how much there is at specific individual frequencies.
      Now, as we saw above, the truer transient model of music shows that a music signal is indeed a broadband signal (as is random noise), with an infinitely dense distribution of spectral energy. The notch in the mountain waveform, created by the Tamino crossover's phase rotation to 180 degrees (on its way to 360 degrees), occurs at a specific frequency, and hence at a specific point in time on the mountain waveform seen in the time domain. But our human hearing limits us to perceiving and assessing the aggregate spectral energy over a 1/10 octave span, not at a specific frequency. This means that our hearing is limited to perceiving and assessing the amount of spectral energy, i.e. the tonal balance, over a span of time of the mountain waveform (since time is the same thing as the defined construct we call frequency, and is simply the mathematical inverse of frequency). In other words, our hearing mechanism probably doesn't hear just the narrow notch in the mountain waveform as such, but instead groups it together with temporally nearby portions of the mountain waveform.
      But that's bad news, because it means that our hearing mechanism lumps together the 180 degree inverted polarity portion of the mountain waveform, where the narrow notch is, with temporally adjacent portions that have more correct phase polarity, and algebraically sums them together, for our aural assessment of tonal balance in that general spectral region corresponding to that general temporal region of the mountain waveform. When you algebraically add an inverted polarity segment to a correct (or more correct) polarity segment, they cancel, leaving nothing or next to nothing. Thus, as human hearing perceives the sonic consequences of the Tamino's midrange phase rotation through 180 degrees, there could be almost complete cancellation of midrange energy in that whole critical band around the 3080 Hz point where the phase rotation passes through 180 degrees. Therefore, our human hearing could perceive and assess the Tamino as having a very severe hole or dropout in its tonal balance, in this critical band of the midrange. Note that a conventional sine wave or FFT measurement of the Tamino's frequency response would not show this cancellation effect as we humans hear it, and so would not show the true severity of the Tamino's tonal balance recession in the midrange as we humans hear it.

-- Phasiness from Music's Dynamic Changes

      We've just seen how the tonal balance aspect of the Tamino's midrange coloration is probably made worse by the way human hearing works, worse than our static waveform analysis would suggest. What about the other aspect of the Tamino'smidrange coloration that we reported hearing, the ghostlike or phasey quality? That too is made worse than our previous static waveform analysis suggests, but it is made worse by a different factor. To see this, we have to look at the music waveform dynamically instead of statically. The music waveform is constantly changing, so each mountain waveform will be different than the previous mountain waveform. Thus, even though the crossover phase rotation causing the notch might stay constant with respect to a static frequency axis on a static graph, when we look at a dynamically changing music waveform in the time domain, we see that the notch itself, and its relationship to each mountain waveform, will dynamically keep changing, as the shape of the music's mountain waveform keeps changing. In effect, the look of the notch, and where it appears in each mountain waveform, and how it affects the shape of each mountain waveform, will keep changing, as the mountain waveform keeps changing underfoot in reflection of the fact that the music keeps changing.
      Since the effective shape of the phasey notch, and its effect upon the mountain waveform shape, keeps changing, the phasey sonic quality it produces will keep changing. The sonic relationship, between what's in phase and what's out of phase, will keep changing as the music itself keeps dynamically changing. And a changing phasey quality is much more audibly noticeable than a constant phasey quality would be. The most popularly known example of a highly audible changing phasey quality is the 1959 hit song by Toni Fisher, The Big Hurt, which climbed to #3 on the Billboard chart. The accompanying music of The Big Hurt has a constantly changing phasey quality, achieved in the studio by an artificial technique called flanging. This constantly changing phasey quality is so highly audible that it is the star sonic feature of the music in The Big Hurt, and attracted a lot of attention as such. You can approximately mimic the sound of this flanging, this dynamically changing phasiness, by saying " shwwsh-shwwsh- shwwsh-shwwsh." Thus, the Tamino's phasey coloration is audibly more prominent because it seems to keep shifting and changing its effect upon the music, as the music waveform keeps changing underfoot.

-- Destructive Interference from Non-Matched Drivers

      In addition to all the above factors, there's yet another factor that conspires to make the Tamino's midrange coloration even worse. Throughout the above discussion, we tacitly assumed that the third order crossover network was electrically perfectly symmetrical, and that the two drivers were identical and perfectly matched, so that perfect summation between the two drivers would occur throughout the crossover region. Such is not the case, and this causes new midrange coloration problems, in addition to all the above midrange coloration problems (which would arise even if the drivers were identical and perfectly matched).
      This has particularly striking implications for the Tamino's performance through its crossover region, because the steep, radical phase changes through the crossover region, of the chosen third order crossover design in this loudspeaker, place extra demands (beyond those in most other loudspeakers) on realizing perfect matching and perfect summation from the two drivers that jointly contribute to the total system output as the system goes through its wild phase rotation. Because both drivers are simultaneously being put through phase changes that are very steep and rapid, these two drivers must match perfectly, not just in their amplitude but also in the phase of their response output, so that their outputs when combined will yield the desired result, as seen in both the time and frequency domains, as the whole system goes through its wild ride in the crossover region.
      As a crude analogy, imagine first two objects (say two roller coaster cars) coasting side by side through the vacuum of outer space, in a straight line, at the same speed. It doesn't much matter if the two objects are mismatched in mass, size, frontal area, etc. - they will still continue to coast along side by side, and will continue to present a united, matched front. But now put these same two objects, these two roller coaster cars, on a wild roller coaster ride down here on earth, say on identical parallel tracks. On this wild ride, these two objects are subject to wild and rapidly changing forces of all kinds, and these forces will soon elicit very different, mismatched performances from the two roller coaster cars, if there is the slightest mismatch in their mass, frontal area, wheel friction, etc. -- and one of the cars will charge ahead of the other, so they won't present a united front anymore This latter environment, with its wild changes, is much more critical of exact matching between the two objects, just as the Tamino's third order crossover design is.
      In the Tamino, the tweeter has an electrical third order high pass filter feeding it, but the woofer/midrange does not. For the Tamino's woofer midrange, there is electrically only a single pole filter, and the remaining 2 poles for the third order low pass filter are achieved simply by the natural mechanical rolloff of the woofer/midrange driver itself. Furthermore, the drivers are very mismatched in dimension, radiation behavior, etc. In this case, the tweeter is the more perfect driver in the crossover region, behaving like a piston and having a wide, uniform radiation pattern. But, in this same crossover region, the woofer/midrange, although an excellent unit for its ilk, nevertheless is necessarily (by the laws of physics) notably imperfect, and in two distinct ways.
      Firstly, because the woofer/midrange has a much larger diaphragm than the tweeter, its radiation pattern is very different, and it is operating non-pistonically in breakup mode, unlike the comparatively perfect tweeter in this region. Secondly, because the woofer/midrange driver is operating in breakup mode throughout the crossover region, its amplitude and phase response is naturally quite irregular, so its 2 pole contribution to the third order crossover filter from its mechanical behavior is quite imperfect, and is quite mismatched to what ideally should be a complementary contribution of the nearly perfect electrical third order filter feeding the tweeter.
      This means that the acoustic outputs of the tweeter and woofer/midrange will not sum perfectly as they ideally should, as the Tamino goes through the dramatic and sudden 360 degree phase rotation changes through its crossover region. In short, there will very likely be some extra, unwanted interference patterns between the two drivers through the crossover region, causing imperfections in the Tamino's total midrange midrange output that go beyond the imperfections discussed above, when we were tacitly assuming two identical drivers and two perfectly complementary electrical third order filters that would sum perfectly. For instance, when the tweeter is outputting an exactly 180 degree phase inverted signal component at exactly 3080 Hz (again, per our example here), the woofer/midrange, instead of putting out the same signal that would perfectly complement the tweeter's output here, would probably put out the wrong signal amplitude and the wrong signal phase, because it is operating in its non-pistonic breakup region, where it has irregular amplitude response and irregular phase response. Thus, the output of the two drivers could destructively interfere, instead of summing properly as they ideally should. This interference between the two drivers is doubly problematic here, because the woofer's irregular behavior forms 2 poles of its third order filter, and also further because the woofer's output would be irregular even if it were being fed by a perfect electrical third order filter.
      The manufacturer's frequency response plot of the Tamino's output shows hill and valley irregularities in the 2-4 kHz region where we hear the midrange coloration, so this is already evidence of the woofer/midrange's imperfections in contributing properly to the steep changes through the crossover region. But there is yet stronger evidence that the inevitable driver and network mismatch is an important factor worsening the Tamino's midrange coloration. As noted above, we found that the Tamino is very critical of exact horizontal angle, and that its sound changes notably if you change the horizontal listening axis by merely a fraction of a degree. Now, both drivers have reasonably good overall radiation patterns, since they both have small diaphragms, so they both exhibit uniformly excellent behavior over a relatively wide horizontal frontal angle.
      What then could explain the sonic differences we heard when horizontally rotating the Tamino by mere fractions of a degree of arc? Interference patterns. Interference patterns due to precisely this factor under discussion here, namely that the necessarily imperfect, irregular breakup behavior of the woofer/midrange, through the severe phase rotation of the crossover region, does not sum properly with the far more perfect output from the tweeter.
      As noted, there might be destructive interference, hence partial (or even total) cancellation at a certain frequency, where for instance the tweeter might be outputting a 180 degree inverted signal, but the woofer/midrange, because it is breaking up, is putting out some signal say in a positive phase, so the two driver outputs algebraically add, producing drastically reduced or even zero output at that frequency. Because the Tamino's front panel is tilted backward to achieve temporal alignment, when you rotate the Tamino even slightly, you change the relative distance of the two drivers to the listener, so you change the relative arrival times. And, precisely because the two drivers are destructively interfering instead of properly summing, changing the relative arrival times of the two drivers in turn changes the exact point in the music's temporal waveform where the destructive interfernce and cancellation occurs, hence it also changes the exact frequency at which the cancellation occurs (since time and frequency are the same thing, just mathematically inverted).
      Changing the frequency of a cancellation notch is of course highly audible, since different parts of the music, and different instruments or different musical overtones, are suddenly, mysteriously zeroed out (or significantly diminished) when you rotate the Tamino even slightly - while other parts of the music that were previously inaudible or subdued suddenly come into prominence. Thus, the extreme sensitivity of the Tamino to exact horizontal rotational orientation is proof corroborating the important role that this destructive interference factor plays in the basic midrange coloration we heard in the Tamino.
      There's further corroborative proof from the center channel Tamino. In our research explorations, we found that the center channel Tamino is even more sensitive to exact horizontal orientation, evincing even greater sonic changes for a given slight amount of horizontal rotation, including a pronounced midrange honk at merely 10 degrees or so off axis that the standard Tamino did not have. Why should this be so? After all, the center channel Tamino has the same crossover network as the standard Tamino, and the same two drivers spaced the same distance apart on the front panel.
      The only answer that could explain this different behavior of the center channel model is the fact that, on the center channel Tamino, the front panel is raked backward more than on the standard Tamino. This greater slant means that, for a given delta change in the degree of loudspeaker horizontal rotation, the center channel Tamino creates a greater delta difference in the relative distance of the two drivers to the listener, hence a greater delta differnce in the relative arrival times from the two drivers, hence a greater sensitivity to the destructive interference between the two drivers, for a given degree of horizontal rotation.
      Thus, this increased sensitivity of the center channel Tamino to exact rotational orientation acts as further corroborative proof that the factor of destructive interference is significantly at work here, due to the imperfect summing of the two drivers through the wild phase rotation through the crossover region, where exact summing is so important due to the steepness of the phase rotation.
      That's why we recommend that you take the time to exactly orient the horizontal rotation of every Tamino in your surround array, so that each points precisely at the central listening hot seat. We think that the Tamino sounds its best, its most transparent and open and airy, with this precise orientation (and you can listen for these sonic qualities as a guide to precisely optimizing each within a fraction of one degree of arc). But, more importantly, you want every Tamino in your surround array to be delivering the same sonic portrait, in order to achieve the best spatial imaging. You don't want the left Tamino to be horizontally aligned so its destructive interference notches out the music at a different frequency than the right Tamino, for that would seriously degrade spatial imaging.
      Note that listening to a Tamino from exactly in front does not cure the destructive interference phenomenon, so it still takes place at some frequency. But, if you precisely align all your Taminos so that you are sitting precisely aligned with every one, you at least know that all of them are creating their destructive interference notch at the same frequency (at least within the tolerance of

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