extremely high efficiency

Most of the figures quoted are sensitivity, not efficiency. They are an on axis spl measurement. Efficiency is a comparison of output power to input power. As such, increasing the directivity of a cabinet will increase the sensitivity, but not the efficiency.

I suspect that Danley like most other manufacturers derive their output figures from calculation. Given that the pdf, linked to, states that the cabinet uses 10 10” LF drivers, and 12 6” mid drivers, the figures show that the synergy horn is providing very little to the proceedings.

Take a single 10” driver, say a B&C 10HPL64. The rated sensitivity is 98.5dB/W/m call it 99 as we are into marketing BS. For every doubling of drive units the output goes up a theoretical 6dB, so: 

1 = 99, 2 = 105, 4 = 111, 8 = 117, plus a bit for the extra 2 drive units. (J8 claims 119) 

The drive units are rated at 400W music power (4000 total), so using a 10dB increase for every 10X power and 3dB per 2X: 

1 = 117, 10 = 127, 100 = 137, 1000 = 147, 2000 = 150, 4000 = 153 (J8 claims 153)

The thread starter was asking about efficient loudspeaker designs. The synergy horn was brought up as a possible solution. However, the figures of the product linked to, don’t support the notion of it being very efficient, unless by efficient you mean highest output from smallest box.

Additionally, if you also calculate a 6dB drop in sound level for each doubling of distance, at full chat this box should be able to produce 117dB at 64m.  Here in the UK, the HSE recommends that levels at events should not exceed LAeq of 107 dB (Events are not covered by Control of Noise at Work Regulations 2005 hence the recommendation). Situations where the closest listeners are over 100m away from the loudspeaker can’t be that plentiful.