Excellent post
@napilopez, thank you.
It's informative to see the differences in ER and HR curves between these non-coaxial speakers and to see illustrated how this may translate into better (ie smoother horizontal off-axis) performance than the spinorama seems to suggest.
Having said that, I'd like to make one point that I see as fundamental to the discussion we're having:
Although in each of the examples you've illustrated, the HR and HRDI curves are much straighter/smoother than the ER and ERDI curves, in all cases, they follow essentially
the same line of best fit (which is what Olive used to calculate the target
slopes).
This is easily illustrated by the Q Acoustics, for example (but holds for multi-way direct radiators in general):
View attachment 64730
What does this tell us IMHO? That, although the ER/ERDI curves can
not tell us how
smooth the HR/HRDI curves of conventional direct-radiating loudspeakers will be, they
can tell us what its
slope will be.
This of course makes sense even in the absence of measurements: Although direct-radiating (non-coaxial) designs will tend to exhibit vertical off-axis cancellation at the XO points, they will nevertheless tend to exhibit similar directivity along both (all) axes throughout the rest of the spectrum.
Given this, we can only conclude that, in respect of direct-radiating multi-way speakers, although there may be little correlation in terms of
smoothness between ER/ERDI and HR/HRDI, there tends to be a very close correlation in terms of
slope.
In turn, from this it can be extrapolated that, in respect of such speakers (and ofc in respect of coaxials too), Olive's target
slopes are adequately descriptive in terms of HR/HRDI.*
*Again, of course, within the aforementioned (rather significant) limitations of the studies.