Step ratio
In the context of moment-of-symmetry scales and binary scales, a step ratio is the ratio of a scale's large and small step sizes, denoted in the general form of L:s. This is also called Blackwood's R, after Easley Blackwood who described it for diatonic MOS scales and referred to this ratio as R.
The melodic sound of a MOS scale is not just affected by the tuning of its intervals, but by the sizes of its steps. Step ratios whose large and small step are close to equal to one another may sound smoother, softer, or more mellow. In contrast, step ratios whose large step is significantly larger than the small step may sound jagged, dramatic, or sparkly.
At the extremes are step ratios whose large and small steps either equal to one another (L:s = 1:1), or where the large step is so large that the small step "collapses" to zero (L:s = 1:0). At this point, the step pattern of the MOS scale will become increasingly ambiguous; this is as much a feature as a bug - it depends on your intent. Thus, the hardness, the value produced by dividing the large step by the small step, is important to the sound of the scale, with hardness values ranging from 1 for a step ratio of 1:1, to infinity for a step ratio of 1:0.
Relative interval sizes
Part of this perception stems from the fact that, as these L:s ratios change and pass certain critical rational values, the next MOS in the sequence changes structure entirely. For instance, when we have L:s > 2, the next MOS changes from "xL ys" to "yL xs". As an example, with the "5L 2s" diatonic MOS, if we have L/s < 2, the next MOS will be "7L 5s", and if we have L/s > 2, the next MOS will be "5L 7s". (At the point L/s = 2, we have that the next MOS is an equal temperament.)
Similar things happen with all of these rational points. As the L:s ratio decreases and passes 3/2, for instance, the MOS that is two steps after the current one changes. Again, as an example, with the familiar 5L 2s diatonic MOS sequence, if we have 3:2 < L:s < 2:1, the next two MOS's have 19 and 31 notes, whereas if we have L:s < 3:2, the next two MOS's have 19 and 26 notes.
Another way to look at this is using Rothenberg propriety: it so happens that, with one small exception, if a MOS has L:s < 2:1, it is "strictly proper", if it has L:s > 2:1, it is "improper", and if it has L:s = 2:1, it is "proper", all using Rothenberg's definition. The one exception is if the MOS has a single small step (e.g. it is of the form xL 1s), at which point it is always "strictly proper". Similarly we pass the L:s = 3:2 boundary, the next MOS changes from strictly proper to improper, and so on.
The special ratio L:s = φ is unique in that it is the only ratio in which the MOS is strictly proper, and all of the following MOS's are also strictly proper.