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Can you provide an example that could be misread?

I think its quite easy to judge whether a downwards accent starts at the top of the line or at the middle, similarly for the upwards accent if it starts at the middle or at the bottom.

I may have made a mistake in assuming that the vertical line, because it was drawn in a different weight, was not part of the symbol. Without the line 1 & 4, 2 & 8 and 3 & 12 would rely on the vertical relationship with other symbols.

How would you misread the values? I suppose the symbols for 0x1/0x4 or 0x2/0x8 could be written sloppily enough to be confused, but it's no worse than trying to distinguish sloppily-written arabic numeral symbols. In fact, I suspect that these would be significantly easier to distinguish.

I think it would be relatively hard to misread. If you really wanted to make it clear the top and botom lines could be drawn horizontally.