Efficiency is defined (as a
specification) as 1 watt/1 meter. Sensitivity is defined as 2.83Volts/1 meter. But you aren't wrong:
Efficiency and sensitivity conversion - loudspeaker percent and dB per watt and meter dB/W/m loudspeaker efficiency versus sensitivity vs speaker sensitivity 1 watt = 2,83 volt box chart - sengpielaudio Eberhard Sengpiel
www.sengpielaudio.com
-except that in this case I was using efficiency as the defined
specification- so I was using it correctly.
An easier way to look at this is sensitivity is based on voltage, since its fairly easy to get a solid state amp to behave as a voltage source; this spec took over in loudspeakers starting in the early 1980s.
Efficiency was used prior to that since tube amps do not always act as voltage sources; if they have no feedback at all they tend to act more like a power source. For more on this see:
Voltage Paradigm vs. Power Paradigm. Competing Paradigms in Amplifier and Loudspeaker Design, Test, and Measurement.
www.atma-sphere.com
SETs tend to be Power Paradigm devices and the speakers they drive are often designed with that in mind (although the designer may not have been thinking of the amp as a power source so much as he was thinking about getting the speaker to sound right with a given amplifier).
Sounds like that would violate Kirchoff's Law (the law of energy conservation). The part which seems problematic is the '+6dB' thing. First you cut the impedance in half, which requires 2x power rather than 1x power. That increases the sensitivity by 3dB since double the power is 3dB.
Where does the rest of the energy come from?