from page 116 of Etienne-Jules Marey, “Du Mouvement dans les Fonctions de la Vie: Leçons faites au Collège de France”, Baillière, Paris, 1878.

Here Marey discusses a modification by M.Koenig of the method of visualizing curves by Lissajous; these patterns are produced by a vertical oscillation, a horizontal oscillation, and the horizontal translation of the surface these oscillations are recorded onto. The ratios for the curves above are: 1:1, 1:2, almost 1:2, 5:6, and 15:16. The 5:6 is amazing.