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| 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 sound smoother and more mellow. MOSes with L much larger than s sound jagged and dramatic. The '''step ratio''', 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.
| | #redirect [[Step ratio]] |
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| == Relative interval sizes ==
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| 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 "xLys" to "yLxs." As an example, with the "5L2s" diatonic MOS, if we have L/s < 2, the next MOS will be "7L5s," and if we have L/s > 2, the next MOS will be "5L7s." (At the point L/s = 2, we have that the next MOS is an equal temperament.)
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| 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 5L2s 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.
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| 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 xL1s), 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.
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| The special ratio L:s = phi 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.
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| == TAMNAMS naming system for step ratios ==
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| :{{main|TAMNAMS#Step ratio spectrum}}
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