This statement comes up a lot in the discussions on these boards, and it is wrong. A flat-but-narrow hone and a convex hone are not 'the same' functionally to the razor, not by a long shot. Any German engineer would chortle at the suggestion. There are two important principles of the convex hone; a flat-but-narrow hone addresses one of them.
Only a hone which is curved in the long axis changes the shape of the bevel of a razor - if the hone's concave it will make the bevel convex, and if the hone's convex it will make the bevel concave. That's a critical consideration as to why the master grinders use them. The convex stone made convex in both the X and Y axis makes the bevel itself ever so slightly curved inward, reduces the cutting angle slightly, and *ALSO* functions as a narrow hone.
To best illustrate this to readers here with words rather than images/drawings, first imagine a 75mm x 200mm hone made cylindrical with a curvature imparted exclusively on the short 75mm axis (the 200mm axis still dead flat), with you honing normally, strokes going up and down the 200mm axis. Entirely depending upon the diameter of the curve imparted to the 75mm axis of the stone, this could "basically function as a narrow hone" as the above quoted tireless worker on this topic posits, or not change things at all. If the diameter of the curve was 150mm, a small percentage of the razor's cutting edge would be touching a small percentage of the 75mm axis just like with a narrow hone, allowing you to use that 'advantage' to 'ride in frowns and overgrown areas'....if on the other hand the diameter used equaled the Earth's diameter, it would not function differently than a flat stone. It is all about the diameter of the curve.
Now, imagine a 75mm x 200mm hone which has been made cylindrical with the curvature imparted exclusively on the 200mm axis instead of the 75mm axis, which is now dead flat as measured directly across the 75mm axis at any given line. Depending upon the diameter of the curve given to the 200mm side, the hone could function much differently in the way it grinds a bevel plane upon the razor; if the diameter was the same as the Earth it would seem to be immeasurably different from a flat stone, and if the diameter was short enough it would make a bevel so curved inward that the steel could not hold up to task. It is all about the diameter.
Hones used by master grinders worldwide since the late 19th century are given upward curvature in both their short and long axis so that, yes, the contact patch is isolated to solve problem razors, but also for the advantage of a concave and more acute bevel form.
Fine by me if one says they're not important enough to consider as they've used flat all this time just fine, and believe me if you're starting a business to make money as your main objective, telling people that black is white is not your best business move! The reason I'm selling these is that I'm forty-six years young and have put straight razors to hones since my 10th grade 'metal shop' class where a cool old country boy teacher introduced me to Arks and coticules and nothing changed the outcomes as dramatically as addressing the *shape* of that which I sharpened (and, by extension, therefore that which sharpens them), which I didn't dare to try until I was forty-two (I was thirty-six when I first saw one in person, and thus knew they existed). Don't want to buy them? No worries. Nobody's getting rich off of these. Want to make your own? I truly hope you do, because I'd feel good about peoples' habits changing en masse from something I took the time to suggest which was used by the actual producers for about 130yrs before I did so [hopefully it was suggested at retail level at some time in the Victorian era, but I'll presume my shop's the first to do so in the internet age].
But don't sell this story that they're just the same as anything that's flat along one axis and narrow upon the other - you belittle the reliability in your own name when you do that. They are marginally different things - a margin that is important to some and not to others.
What I don't read often here on these forums (actually, I have not yet read it once) is of any experienced person who has used both and ultimately preferred a flat stone.
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