I've started writing on a blog post on these issues, following on from discussion in the topic that was originally about Bach.
Anway, J Menz insists that attention to voicing on a vertical level is a dirty and shameful thing for a pianist to consider, so I recorded a video to illustrate the destructive folly of this attitude.
The start features two segments played with no significant vertical hierarchy- with accompaniment played at around the same volume as bass and melody, as on his own performance. Then I played through to illustrate the difference to the sense of horizontal melody. The first clearly sounds like average amateur piano playing- with little to it but a series of plods. I actually couldn't help but start voicing the accompaniment some of the time, however, and probably should have used my digital with dynamics turned off, to illustrate it fully. The playthrough is by no means an ideal performance (I haven't practised the work but had played through once and then made the recording straight after in one take). However, I think it's pretty clear which one sounds horizontal and which one sounds vertical.
Like the first example, this sounds almost entirely vertical in conception- regardless of how strong the horizontal intentions were.
When you don't create and use to your ears to observe the quality of hierarchy between a primary voice and a secondary element, horizontal lines cannot even begin to get off the ground. You don't need to have a go at anyone for listening wrongly when you differentiate musical voices properly, as a foundation upon which to build horizontal phrases. Putting a singing line in the listeners head is something you earn by avoiding the competing sound of heavy accompaniment attacks, not something you earn by telling them they should listen horizontally. The first approach inspires vertical awareness in the listener (no matter how strongly the pianist imagines horizontal lines), the second inspires horizontal awareness. Putting together a pianistic sound is like an animator making a film. Obviously it's about the implied connection between frames, to make a smooth progression. But that doesn't mean you don't have to pay attention to both the inherent qualities of how you draw each character within individual frames, as well as how you imagine the frames might link into a whole. It's not much use if anyone looking at a particular frame can't tell which character is supposed to be donald duck and which one is supposed to be micky mouse.
nb. I'm not posting to this to try and say I'm a great pianist or to compete with anyone- but rather because I care so greatly about the issue of musical voicing in pianism and to proper understanding of how it functions. An ideal performance would feature even better differentiation between the lines than my playthrough. At around 2.24 and at many other momements of crescendo I got carried away in the horizontal motion of the lines and made very little differentiation between left hand bass and accompaniments. The horizontal attention to the main line allowed the accompaniment to become noisy (rather than carefully placed into the texture) and actually makes it sound too vertical. Anyway, the point is that I don't like seeing someone preaching about how awful it is to see the big picture from multiple viewpoints and trying to write off the validity of one of those fundamentally necessary viewpoints outright- and then demonstrating that they fall significantly short of basic musical standards, in a manner that is clearly associated to what they have refuse to make a place for on their musical radar. If such pianists as Cortot and Horowitz had taken such a small-minded attitude about the role of listening to interactions between voices in the moment, they would never have learned to either layer their sounds as they did, or to convey long musical lines as they did. You can't hope to produce multiple layers unless you actually listen to the interactions between voices. And you can't make meaningful horizontal lines in two things or more at once unless you can first tonally differentiate between those layers with complete control. Trying to hear things in an exclusively horizontal way does not inspire an unbiased listener to hear horizontally, if you don't bother to pay more than the faintest shred of attention to differentiation between parts (by using the ears to observe yourself, rather than the imagination to create a throughly innacurate subjective picture for yourself alone).
I'm afraid that the old doctrine that horizontal is good and vertical is bad just doesn't hold an ounce of credibility (and ironically, that which is referred to as too "vertical" in conception often suffers precisely because no attention has been paid to making differentiations between vertical layers). Both elements have constant ongoing role in any half-decent pianism. The attention must be moved around between all kinds of different things, or the results sound like typical piano playing, not like deeper music making. A pianist who cannot yet use his hearing to pick up on serious voicing deficiency on a vertical level is not going to have much luck trying to make sophisticated balancing of multiple voices on a horizontal level.