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I dislike the orange style as the second default plot style, and I would like to swap it with the fourth, which is red.

Is there a relatively painless way of doing this?

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    $\begingroup$ FYI, I am told the first three colours are easily distinguishable for people that are colourblind. If you are only going to use three lines for example I would recommend sticking to the colour scheme since using green and red is considered particularly unfriendly for the colourblind. I heard that if you have a group of five man, you will have a 20% chance of having at least one colourblind. $\endgroup$ – Ruud3.1415 Jul 19 '17 at 15:20
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    $\begingroup$ If you take a look at this plot, you will almost see no contrast between the this and the fourth line ImageEffect[ Plot[{x, x/2, x^2, x^3}, {x, 0, 1}], {"ColorBlindness", "Deuteranopia"}] $\endgroup$ – Ruud3.1415 Jul 19 '17 at 15:34
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Module[{colors}, colors = ColorData[97, "ColorList"]; 
   colors[[{2,4}]] = colors[[{4,2}]];
   Plot[Evaluate[Sin[# x] & /@ {1, 2, 3, 4, 5}], {x, -Pi, Pi}, PlotStyle -> colors, 
     PlotLegends -> "Expressions"]]

enter image description here

Or

swap = Thread[ColorData[97, "ColorList"][[{2,4}]] -> ColorData[97, "ColorList"][[{4,2}]]];

Plot[Evaluate[Sin[# x]&/@{1,2,3,4,5}], {x,-Pi, Pi}, PlotLegends->"Expressions"] /. swap

Same picture

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