# Step ratio

The melodic sound of a MOS is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with L more similar to s can sound smoother/softer/more mellow. MOSes with L much larger than s can sound jagged/dramatic/sparkly. For extreme tunings, the step pattern of the MOS will become increasingly ambiguous; this is as much a feature as a bug - it depends on your intent. The **step ratio** or **hardness**, the ratio between the sizes of L and s, is thus important to the sound of the scale. The step ratio has also been called **Blackwood's R**, after Easley Blackwood who described it for diatonic mosses and referred to this ratio as R.

## 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 "*x*L *y*s" to "*y*L *x*s". 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 *x*L 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.

## TAMNAMS naming system for step ratios

*Main article: TAMNAMS #Step ratio spectrum*