As you can notice, the dots of the dotted double line are joined by two very thin lines. Also the dashed-double line joins them automatically. Is there a way out to remove those unions? (I left knots there because I'd like this solution to be compatible with that package).
This is a zoom to the (relevant) issue of the following code:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{knots}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}
\clip (-4,1) rectangle (1,7);
\begin{knot}[
clip width=5 ,
scale =3,
clip radius=8pt,
line cap=butt,
]
\strand [dotted,double, double distance=2pt] (-1 ,1)
to [out=up , in=down ] (0 ,2) ;
\end{knot}
\begin{knot}[
clip width=5 ,
scale =3,
clip radius=8pt,
]
\strand [red,dashed,double, double distance=2pt] (0,1.5)
to [out=up , in=down ] (-1 ,1);
\end{knot}
\end{tikzpicture}
\end{document}
double dotted/.style={preaction={dotted},postaction={white}}. Same trick applies if you want triple dotted with phases. – Symbol 1 Aug 24 '15 at 04:47