Step ratio - Revision history

ArrowHead294 at 00:44, 24 January 2026

2026-01-24T00:44:32Z

← Older revision		Revision as of 00:44, 24 January 2026
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	The '''step ratio''' of a [[scale]] is the [[Wikipedia:ratio\|ratio]] between the [[interval size measure\|size]]s of its [[step]]s. The step ratio of a [[binary scale]] is also known as '''hardness''', alluding to the terms ''hard'' and ''soft'' used to name step ratios in [[TAMNAMS]], or as '''Blackwood's R''', after [[Easley Blackwood]] who described it for [[5L 2s\|diatonic]] scales in ''The Structure of Recognizable Diatonic Tunings'' and referred to this ratio as ''R''.		The '''step ratio''' of a [[scale]] is the [[Wikipedia:ratio\|ratio]] between the [[interval size measure\|size]]s of its [[step]]s. The step ratio of a [[binary scale]] is also known as '''hardness''', alluding to the terms ''hard'' and ''soft'' used to name step ratios in [[TAMNAMS]], or as '''Blackwood's R''', after [[Easley Blackwood]] who described it for [[5L 2s\|diatonic]] scales in ''The Structure of Recognizable Diatonic Tunings'' and referred to this ratio as ''R''.

	For binary scales, including [[MOS scale\|moment-of-symmetry]] scales, the step ratio is usually written in the form ''x'':''y'', where ''x'' and ''y'' represent the sizes of the large and small steps respectively (''x'' > ''y''). For example, in a scale with a step ratio of 2:1, each large step has twice the size of a small step. In general, for ''n''-ary scales, the step ratio is usually written in the form ''x''<sub>1</sub>:''x''<sub>2</sub>:...:''x''<sub>''n''</sub>, where ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub> represent the size of each step in decreasing order of size.		For binary scales, including [[MOS scale\|moment-of-symmetry]] scales, the step ratio is usually written in the form ''x'':''y'', where ''x'' and ''y'' represent the sizes of the large and small steps respectively ({{nowrap\|''x'' > ''y''}}). For example, in a scale with a step ratio of 2:1, each large step has twice the size of a small step. In general, for ''n''-ary scales, the step ratio is usually written in the form ''x''<sub>1</sub>:''x''<sub>2</sub>:...:''x''<sub>''n''</sub>, where ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub> represent the size of each step in decreasing order of size.

	The step ratio of a scale is mostly associated with its melodic shape. Scales whose steps are very similar in size may sound melodically smoother, softer, or more mellow. In contrast, scales with steps of very different sizes may sound jagged, dramatic, or sparkly.		The step ratio of a scale is mostly associated with its melodic shape. Scales whose steps are very similar in size may sound melodically smoother, softer, or more mellow. In contrast, scales with steps of very different sizes may sound jagged, dramatic, or sparkly.

	A binary scale becomes "softer" as its step ratio approaches 1:1 and "harder" when approaching ∞:1 (or 1:0). At the extremes, either the large and small steps become equal, or the small step "collapses" to zero. In both cases, it ~~[[Wikipedia:~~degeneracy (mathematics)\|~~degenerate]]s~~ into a unary scale (by omitting the zero-sized intervals if necessary), with a step ratio trivially equal to 1.		A binary scale becomes "softer" as its step ratio approaches 1:1 and "harder" when approaching ∞:1 (or 1:0). At the extremes, either the large and small steps become equal, or the small step "collapses" to zero. In both cases, it {{w\|degeneracy (mathematics)\|degenerates}} into a unary scale (by omitting the zero-sized intervals if necessary), with a step ratio trivially equal to 1.

	== Relative interval sizes ==		== Relative interval sizes ==
	{{todo\|clarify\|inline=1\|comment=This section relies on multiple assumptions which are not made clear to the reader (including the knowledge of advanced MOS concepts, which should minimally be linked to, or ideally avoided whenever possible).}}		{{todo\|clarify\|inline=1\|comment=This section relies on multiple assumptions which are not made clear to the reader (including the knowledge of advanced MOS concepts, which should minimally be linked to, or ideally avoided whenever possible).}}
	Part of this perception stems from the fact that, as these ''x'':''y'' 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.)		Part of this perception stems from the fact that, as these ''x'':''y'' ratios change and pass certain critical rational values, the ''next'' MOS in the sequence changes structure entirely. For instance, when we have {{nowrap\|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 {{nowrap\|L/s < 2}}, the next MOS will be "7L 5s", and if we have {{nowrap\|L/s > 2}}, the next MOS will be "5L 7s". (When {{nowrap\|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.		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 {{nowrap\|3:2 < L:s < 2:1}}, the next two MOS's have 19 and 31 notes, whereas if we have {{nowrap\|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.		Another way to look at this is using [[Rothenberg propriety]]: it so happens that, with one small exception, if a MOS has {{nowrap\|L:s < 2:1}}, it is "strictly proper", if it has {{nowrap\|L:s > 2:1}}, it is "improper", and if it has {{nowrap\|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 {{nowrap\|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.		The special ratio {{nowrap\|L:s {{=}} {{w\|golden ratio\|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 ==		== TAMNAMS naming system for step ratios ==

Fredg999: Major rework of the lead section, todo:clarify middle section, add summary of TAMNAMS step ratio names

2023-07-05T05:08:20Z

Major rework of the lead section, todo:clarify middle section, add summary of TAMNAMS step ratio names

← Older revision		Revision as of 05:08, 5 July 2023
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	~~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 '''step ratio''' of a [[scale]] is the [[Wikipedia:ratio\|ratio]] between the [[interval size measure\|size]]s of its [[step]]s. The step ratio of a [[binary scale]] is also known as '''hardness''', alluding to the terms ''hard'' and ''soft'' used to name step ratios in [[TAMNAMS]], or as '''Blackwood's R''', after [[Easley Blackwood]] who described it for [[5L 2s\|diatonic]] scales in ''The Structure of Recognizable Diatonic Tunings'' 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~~.		For binary scales, including [[MOS scale\|moment-of-symmetry]] scales, the step ratio is usually written in the form ''x'':''y'', where ''x'' and ''y'' represent the sizes of the large and small steps respectively (''x'' > ''y''). For example, in a scale with a step ratio of 2:1, each large step has twice the size of a small step. In general, for ''n''-ary scales, the step ratio is usually written in the form ''x''<sub>1</sub>:''x''<sub>2</sub>:...:''x''<sub>''n''</sub>, where ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub> represent the size of each step in decreasing order of size.

	~~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.		The step ratio of a scale is mostly associated with its melodic shape. Scales whose steps are very similar in size may sound melodically smoother, softer, or more mellow. In contrast, scales with steps of very different sizes may sound jagged, dramatic, or sparkly.

			A binary scale becomes "softer" as its step ratio approaches 1:1 and "harder" when approaching ∞:1 (or 1:0). At the extremes, either the large and small steps become equal, or the small step "collapses" to zero. In both cases, it [[Wikipedia:degeneracy (mathematics)\|degenerate]]s into a unary scale (by omitting the zero-sized intervals if necessary), with a step ratio trivially equal to 1.

	== Relative interval sizes ==		== Relative interval sizes ==
			{{todo\|clarify\|inline=1\|comment=This section relies on multiple assumptions which are not made clear to the reader (including the knowledge of advanced MOS concepts, which should minimally be linked to, or ideally avoided whenever possible).}}
	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.)		Part of this perception stems from the fact that, as these ''x'':''y'' 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.		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.
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	== TAMNAMS naming system for step ratios ==		== TAMNAMS naming system for step ratios ==
	{{~~main~~\| TAMNAMS #Step ratio spectrum }}		{{Main\| TAMNAMS #Step ratio spectrum }}
			In [[TAMNAMS]], a step ratio of 2:1 is named ''basic''. Step ratios between 1:1 and 2:1 are named ''soft-of-basic'', with 3:2 being ''soft'', while step ratios between 2:1 and ∞:1 are named ''hard-of-basic'', with 3:1 being ''hard''. Other names are given to several other common ratios, as well as to ranges between these ratios.

			It is also proposed to use pairwise naming for step ratios of ternary scales. For example, 3:2:1 would be named ''soft-basic'', because 3:2 is soft and 2:1 is basic.

	[[Category:Scale]]		[[Category:Scale]]
	[[Category:MOS scale]]		[[Category:MOS scale]]

Ganaram inukshuk: Better wording for lead section

2023-07-05T04:02:02Z

Better wording for lead section

← Older revision		Revision as of 04:02, 5 July 2023
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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.		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 ==		== Relative interval sizes ==

Ganaram inukshuk: Rewritten due to 5L 2s's lead section linking to here

2023-07-04T22:53:48Z

Rewritten due to 5L 2s's lead section linking to here

← Older revision		Revision as of 22:53, 4 July 2023
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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 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~~.		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.

			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.

	== Relative interval sizes ==		== Relative interval sizes ==

BudjarnLambeth: Moved from MOS scales to MOS scale

2023-04-28T22:08:12Z

Moved from MOS scales to MOS scale

← Older revision		Revision as of 22:08, 28 April 2023
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	[[Category:Scale]]		[[Category:Scale]]
	[[Category:MOS ~~scales~~]]		[[Category:MOS scale]]

Fredg999 category edits: Moving from Category:Scale theory to Category:Scale using Cat-a-lot

2022-02-26T16:32:52Z

Moving from Category:Scale theory to Category:Scale using Cat-a-lot

← Older revision		Revision as of 16:32, 26 February 2022
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	{{main\| TAMNAMS #Step ratio spectrum }}		{{main\| TAMNAMS #Step ratio spectrum }}

	[[Category:Scale ~~theory~~]]		[[Category:Scale]]
	[[Category:MOS scales]]		[[Category:MOS scales]]

FloraC: Style

2021-09-17T08:44:52Z

Style

← Older revision		Revision as of 08:44, 17 September 2021
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	== Relative interval sizes ==		== 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 "~~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.)		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 ~~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.		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 ~~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.		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 = ~~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.		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 ==		== TAMNAMS naming system for step ratios ==
	:{{main\|TAMNAMS#Step ratio spectrum}}		{{main\| TAMNAMS #Step ratio spectrum }}

			[[Category:Scale theory]]
			[[Category:MOS scales]]

Godtone: made wording less prescriptive

2021-09-17T05:53:35Z

made wording less prescriptive

← Older revision		Revision as of 05:53, 17 September 2021
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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''' 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.		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 ==		== Relative interval sizes ==

Inthar at 03:59, 8 August 2021

2021-08-08T03:59:29Z

← Older revision		Revision as of 03:59, 8 August 2021
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	\|ja =		\|ja =
	}}		}}
	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''' or ~~the~~ '''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.		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''' 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 ==		== Relative interval sizes ==

Inthar: +interwiki

2021-08-05T02:42:57Z

+interwiki

← Older revision		Revision as of 02:42, 5 August 2021
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			{{interwiki
			\|de = Härte
			\|en = Step ratio
			\|es =
			\|ja =
			}}
	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''' or the '''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.		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''' or the '''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 ==		== Relative interval sizes ==