Step ratio: Difference between revisions

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In the context of scales ~~described using whole-number step sizes~~, a '''step ratio''' is a ratio of a scale's step sizes, ~~where the values are listed in decreasing order of size. For a [[MOS scale|moment-of-symmetry]] scale, this is~~ denoted in the general form of L:s. This is also called '''Blackwood's R''', after Easley Blackwood who described it for diatonic ~~mosses~~ and referred to this ratio as R.

In the context of [[MOS scale|moment-of-symmetry]] scales and [[Binary scale|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, or where the small step "collapses" to zero. 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. ~~The '''step ratio''' or~~ '''hardness''', the ~~ratio between~~ the ~~sizes of L and s~~, is ~~thus~~ important to the sound of the scale.

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 ==

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-In the context of scales described using whole-number step sizes, a '''step ratio''' is a ratio of a scale's step sizes, where the values are listed in decreasing order of size. For a [[MOS scale|moment-of-symmetry]] scale, this is denoted in the general form of L:s. This is also called '''Blackwood's R''', after Easley Blackwood who described it for diatonic mosses and referred to this ratio as R.
+In the context of [[MOS scale|moment-of-symmetry]] scales and [[Binary scale|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, or where the small step "collapses" to zero. 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. The '''step ratio''' or '''hardness''', the ratio between the sizes of L and s, is thus important to the sound of the scale.
+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 ==