Initially, an L-pad was applied but this affected the midrange as well; the response curve was lowered but not changed.  By the time the high end was acceptable, the midrange went to hell in the proverbial handcart. The solution was to use my digital parametric/graphic equalizer. This worked but not everyone has such an equalizer.

Anyway, the project was shelved in lieu of a myriad of projects during the following years. It resurfaced during a search for another such loudspeaker that would cover the range above 300hz. The idea was to avoid a tweeter to keep it simple. A few discussions in audio fora asking the question 'can a single speaker cover the whole audio range'? Well, that depends on what is meant by the whole audio range and the expected sound quality. Restricting the audio range from 35hz to 15khz along with a response flat within 5dB would be has yet to be achieved although some good results have been achieved with full range 12" loudspeakers. One that comes to mind is the Wharfedale Super 12 RS/DD which used a half roll surround, a whizzer cone, the DD, double diaphragm and an aluminum voice coil. The response,, however, was anything but flat.  See fig. 2   In all fairness, it should be noted that this speaker is some 60 years old and the paper cone has changed considerably over the years, becoming brittle. This figure shows the effect of front loading (red) the speaker on a 3/4" baffle vs rear loading (violet).  The 5dB peak between 1800hz and 2400hz may be objectionable as this would probably exist even when the speaker was new.  However, back then, front loading wasn't in vogue not to mention that the cast aluminum basket of that speaker made front loading very difficult.

Ambient temperature was 81.4^o and 10vdc was applied for 10 minutes. the resultant temperature was measured as 262.7^o, a rise of 181^o. Then, after cooling to ambient temperature, pink noise was applied at an rms level of 10v and 2^nd order high pass filtered at 300hz. After 10 minutes, the resistor temperature had risen by 79.8^o to 161.2^o.  It should be noted that pink noise is also quite constant in amplitude, unlike music which can vary by as much as 10dB and usually in short duration. With music, the temperature rise would be much lower. Therefore, a 10 watt resistor would be more than adequate.

Table 1 shows the reactance, X_L or impedance, Z of the coil and the resultant impedance of the parallel pair, calculated, not measured. This does not take into account the effect of phase shift in the coil, which is small enough to be ignored.

The 3 curves here are grey, the system response without the LR filter; red using a 3mh coil in parallel with an 8W resistor and green using a 2mh coil in parallel with a 10W resistor. The green configuration was chosen simply because I felt the red curve was too low although the 1dB difference would likely be unnoticed.

Note that the shape of the curves is unaltered and that attenuation begins around 1600hz and not affecting the band between 300hz and 1600hz.

The grey and black curves here are those of the grey and green curves of fig. 5 above. The green curve is that obtained by using an L-pad to attenuate the Satori. Note that the L-pad affects the whole reproductive band of the Satori. The relative amplitudes of the higher frequencies and lower frequencies remains unchanged. In a 3-way, this problem is avoided as the tweeter usually covers the band above about 4khz and is thus unaffected by the L-pad in the midrange. It is also assumed that the speakers in a 2-way or 3-way system are of equal sensitivities.

These two curves show the full system response with the woofer and Satori in identical polarity (black) and the woofer reversed polarity (red).

Which one would be preferred depends on the listener's preference. A good idea would be a polarity reversal switch in each system as that preference might change with different music.

Another earlier attempt at smoothing the rising response was to use a notch (band reject) filter comprising of a 0.15mh coil, a 6uf capacitor and a 7 ohms resistor wired in parallel. The notch filter is then wired in series with the speaker.

RED-no filter; Black-with notch

Note that the black curve of the notch bears a stark resemblance to the curves of the LR filter in figs 5, 6 and 7.

However, notch filters are not easy to design as their component values have to be as close as possible to the values calculated and despite the formulae, it usually becomes a trial and error method aided by a frequency response sweep.

The setup. Admittedly, the 2 feet center to center distance may affect the curves between 200hz and 700hz as seen in fig. 7 above.

This distance being 2 feet corresponds to a frequency of 567hz, just about in the middle of the aforementioned band.

Had the upper speaker been placed on the top of the cabinet, the cabinet would then have to be raised to minimize early reflections.

My 82 years doesn't readily permit my jockeying a 60 pound cabinet.