Muddle - Revision history

Sintel: style

2025-07-30T18:56:50Z

style

← Older revision		Revision as of 18:56, 30 July 2025
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	''~~Muddling~~'' ~~refers to~~ a ~~process of~~ mapping one [[periodic scale]] onto another one~~; the scale thus produced is~~ a ''~~'muddle'~~''~~. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else)~~. There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target ~~scale~~ is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].		A '''muddle''' is a scale that results from mapping one [[periodic scale]] onto another one by a process called ''muddling''. There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].

	The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but ~~it should be remembered that~~ this process can be generalized to arbitrary sequences of steps.		The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but this process can be generalized to arbitrary sequences of steps.

	== Construction ==		== Construction ==

OffsuitKnave: /* Comments */

2025-07-01T08:01:46Z

Comments

← Older revision		Revision as of 08:01, 1 July 2025
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	Parent scales that are close to equal (eg. [[Maximal_evenness\|maximally even]] scales) will produce muddles that are melodically closer to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller one.		Parent scales that are close to equal (eg. [[Maximal_evenness\|maximally even]] scales) will produce muddles that are melodically closer to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller one.

	As every note in the muddle is also in the parent scale it will have share any temperament properties and therefore the harmonic relationships of the parent scale, however depending on the choice of the target specific low generator intervals can be absent from the scale.		As every note in the muddle is also in the parent scale it will have share any temperament properties and therefore the harmonic relationships of the parent scale, however depending on the choice of the target, specific low generator intervals can be absent from the scale.

	== History ==		== History ==

OffsuitKnave: /* Comments */ clarification on properties of mos muddles.

2025-07-01T08:01:12Z

Comments: clarification on properties of mos muddles.

← Older revision		Revision as of 08:01, 1 July 2025
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	== Comments ==		== Comments ==
	With the exception of trivial muddles, mos muddles always have more than two sizes of step -- either three or four sizes. Whereas MOS scales have two varieties of interval for each interval class (eg. a "large step" and a "small step"), ~~muddles~~ have ~~potentially~~ two varieties ~~within~~ each ~~variety~~ (eg. ~~two sizes of~~ "~~small step~~" and ~~two sizes of~~ "large step"). Parent scales that are close to equal (eg. [[Maximal_evenness\|maximally even]] scales) will produce muddles that are closer ~~in sound~~ to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller ~~ones~~.		With the exception of trivial muddles, mos muddles always have more than two sizes of step -- either three or four sizes. Whereas MOS scales have two varieties of interval for each interval class (eg. a large step "L" and a small step "s"), a secondary scale can have two varieties for each size step of the target scale (eg. the targets "s" and "L" steps become "s", "S", "l" and "L"). It is very common for a large small step (S) to be smaller than a small large step (l) but this isn't necessarily the case if the parent scale is less even than the target scale, if the parent MOS scale is generated from an equal temperament it is even possible for S and l to be the same size.

			Parent scales that are close to equal (eg. [[Maximal_evenness\|maximally even]] scales) will produce muddles that are melodically closer to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller one.

			As every note in the muddle is also in the parent scale it will have share any temperament properties and therefore the harmonic relationships of the parent scale, however depending on the choice of the target specific low generator intervals can be absent from the scale.

	== History ==		== History ==

FloraC: Cleanup on the intro, mark with todo

2024-08-10T06:54:44Z

Cleanup on the intro, mark with todo

← Older revision		Revision as of 06:54, 10 August 2024
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	''Muddling'' refers to a process of mapping one [[~~Periodic_scale\|~~periodic scale]] onto another one; the scale thus produced is a ''muddle''. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a '''parent scale''' and a '''target shape''', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale -- it's the outline or ''shape'' of a scale -- and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[~~EDO\|EDO~~]].		''Muddling'' refers to a process of mapping one [[periodic scale]] onto another one; the scale thus produced is a '''muddle'''. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].

	The simplest sort of muddle is a ~~MOS Muddle~~, which is a sort of second-order [[~~MOSScales\|MOS Scale~~]] and is useful for generating usable subsets of larger ~~MOS~~ scales and for navigating [[~~Regular_Temperaments\|Regular Temperaments~~]]. This article will mostly deal with ~~MOS~~ muddles, but it should be remembered that this process can be generalized to arbitrary sequences of steps.		The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but it should be remembered that this process can be generalized to arbitrary sequences of steps.

	== Construction ==		== Construction ==
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	[[Category:Muddles\| ]] <!-- Main article -->		[[Category:Muddles\| ]] <!-- Main article -->
			{{Todo\| cleanup }}

ArrowHead294 at 15:20, 29 May 2024

2024-05-29T15:20:43Z

Show changes

Fredg999: Categories

2023-04-23T19:50:12Z

Ganaram inukshuk: Minor edits, mainly "target shape" rather than "target scale"

2022-07-28T20:29:16Z

Minor edits, mainly "target shape" rather than "target scale"

← Older revision		Revision as of 20:29, 28 July 2022
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	== Construction ==		== Construction ==
	Let the target ~~scale~~ T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.		Let the target shape T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.

	The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.		The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.

	===MOS muddles===		===MOS muddles===
	In the case of a mos muddle, both the target and parent ~~scale~~ describe some sort of mos. ~~Ideally~~, the parent scale is large enough from which a subset of its notes is musically useful. As a running example, let's use 22222223 (1L 7s) as a parent scale and 12122 (3L 2s) as a target ~~scale~~.		In the case of a mos muddle, both the target and parent describe some sort of mos. Typically, the parent scale is large enough from which a subset of its notes is musically useful, whereas the target describes a grouping of steps from the parent rather than an edo. As a running example, let's use 22222223 (1L 7s, step ratio 3:2) as a parent scale and 12122 (3L 2s) as a target shape.

	Applying the construction rules to our example results in the parent's steps being grouped as such: (2)(22)(2)(22)(23). This results in a muddle scale with a step pattern of 24245 -- not a mos since it has more than two step sizes. This new scale has melodic properties similar to that of the target ~~scale~~, but has other properties that fall outside the target ~~scale~~; when viewed under regular temperament theory, for example, both the target and muddle fall under different temperament families.		Applying the construction rules to our example results in the parent's steps being grouped as such: (2)(22)(2)(22)(23). This results in a muddle scale with a step pattern of 24245 -- not a mos since it has more than two step sizes. This new scale has melodic properties similar to that of the target, but has other properties that fall outside the target; when viewed under regular temperament theory, for example, both the target and muddle fall under different temperament families.

	Another way to conceptualize a muddle is to consider that the parent scale already describes a subset of an edo (17edo in our example), and the target describes finding a subset of that subset.		Another way to conceptualize a muddle is to consider that the parent scale already describes a subset of an edo (17edo in our example), and the target describes finding a subset of that subset.
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	=== Trivial muddles ===		=== Trivial muddles ===
	If every step size in the parent scale is the same size k, then the muddle scale is similar to the target, only with k times as many divisions. If every step size in the parent scale is 1, then the muddle scale is identical to the target ~~scale~~. Using our running example, this is like having a parent scale of 22222222 or 11111111; applying our target ~~scale~~ on either results in 24244 (the same as the target but with twice as many divisions) and 12122 (the same as the target) respectively.		If every step size in the parent scale is the same size k, then the muddle scale is similar to the target, only with k times as many divisions. If every step size in the parent scale is 1, then the muddle scale is identical to the target. Using our running example, this is like having a parent scale of 22222222 or 11111111; applying our target on either results in 24244 (the same as the target but with twice as many divisions) and 12122 (the same as the target) respectively.

	It is also possible for muddling to result in a mos, even if both the parent and target ~~scales~~ are mosses; see the examples below.		It is also possible for muddling to result in a mos, even if both the parent and target are mosses; see the examples below.

	==Examples==		==Examples==
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	=== A muddle that's itself a mos ===		=== A muddle that's itself a mos ===
	Consider a parent ~~scale~~ of 2212221 (or 12edo diatonic) and a target ~~scale~~ of 11212 (or 2L 3s). Given the construction rules previously described, the resulting mos muddle has a step pattern of (2)(2)(12)(2)(2)(21), or 22323, which itself another mos (~~specifically~~ the same as the target but with different step sizes).		Consider a parent of 2212221 (or 12edo diatonic) and a target of 11212 (or 2L 3s). Given the construction rules previously described, the resulting mos muddle has a step pattern of (2)(2)(12)(2)(2)(21), or 22323, which itself another mos (the same as the target but with different step sizes).

	Rotating either scale can result in a muddle scale that is not a mos, in that it has more than two step sizes. For example, rotating the target to 12121 instead results in a mos muddle with a step pattern of 23241.		Rotating either scale can result in a muddle scale that is not a mos, in that it has more than two step sizes. For example, rotating the target to 12121 instead results in a mos muddle with a step pattern of 23241.

Ganaram inukshuk: /* Construction */ Forgot some words

2022-07-28T07:39:38Z

Construction: Forgot some words

← Older revision		Revision as of 07:39, 28 July 2022
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	If every step size in the parent scale is the same size k, then the muddle scale is similar to the target, only with k times as many divisions. If every step size in the parent scale is 1, then the muddle scale is identical to the target scale. Using our running example, this is like having a parent scale of 22222222 or 11111111; applying our target scale on either results in 24244 (the same as the target but with twice as many divisions) and 12122 (the same as the target) respectively.		If every step size in the parent scale is the same size k, then the muddle scale is similar to the target, only with k times as many divisions. If every step size in the parent scale is 1, then the muddle scale is identical to the target scale. Using our running example, this is like having a parent scale of 22222222 or 11111111; applying our target scale on either results in 24244 (the same as the target but with twice as many divisions) and 12122 (the same as the target) respectively.

	It is also possible muddling to result in a mos, even if both the parent and target scales are mosses; see the examples below.		It is also possible for muddling to result in a mos, even if both the parent and target scales are mosses; see the examples below.

	==Examples==		==Examples==

Ganaram inukshuk: /* Construction */ Reworded the running example (a lot) and also found out that muddling can also create mosses, so I had to amend a few sections

2022-07-28T07:36:20Z

Construction: Reworded the running example (a lot) and also found out that muddling can also create mosses, so I had to amend a few sections

Show changes

Ganaram inukshuk: Minor rewording and some minor heading changes

2022-07-28T05:55:03Z

Minor rewording and some minor heading changes

← Older revision		Revision as of 05:55, 28 July 2022
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	Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.		Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.

	The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 be the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 be the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.		The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.

	=MOS Muddles=		==MOS Muddles==

	In the case of a MOS muddle, the parent scale is any MOS scale large enough that taking subsets of it would be musically useful. The target scale is something like 12122. This could be the form of an actual scale (an MOS subset of [[8edo\|8edo]], in this example), but as a target scale, we are interested in its general ''shape'', which suggests a way of bunching intervals of the parent scale. If we apply the target to an equal-step scale, we arrive at a standard MOS. Eg. If our parent scale is [[8edo\|8edo]] -- with steps 11111111 -- and our target scale is 12122, then the resulting scale is (1)(11)(1)(11)(11) = 12122 -- the same as our target scale. But if our parent scale is some other MOS scale, say 22222223 (a subset of [[17edo\|17edo]]), applying the 12122 target scale generates (2)(22)(2)(22)(23) = 24245 -- not an MOS scale. The latter scale, which we can call a ''muddle'', has some melodic similarity to the target scale of 12122, but belongs to a different temperament family entirely. Choosing a different mode (rotation) of either the parent scale or the target scale may produce a different muddle.		In the case of a MOS muddle, the parent scale is any MOS scale large enough that taking subsets of it would be musically useful. The target scale is something like 12122. This could be the form of an actual scale (an MOS subset of [[8edo\|8edo]], in this example), but as a target scale, we are interested in its general ''shape'', which suggests a way of bunching intervals of the parent scale. If we apply the target to an equal-step scale, we arrive at a standard MOS. Eg. If our parent scale is [[8edo\|8edo]] -- with steps 11111111 -- and our target scale is 12122, then the resulting scale is (1)(11)(1)(11)(11) = 12122 -- the same as our target scale. But if our parent scale is some other MOS scale, say 22222223 (a subset of [[17edo\|17edo]]), applying the 12122 target scale generates (2)(22)(2)(22)(23) = 24245 -- not an MOS scale. The latter scale, which we can call a ''muddle'', has some melodic similarity to the target scale of 12122, but belongs to a different temperament family entirely. Choosing a different mode (rotation) of either the parent scale or the target scale may produce a different muddle.

	=Examples=		==Examples==

	===1.===		===1.===
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	[[File:sensi_pentatonics.png\|alt=sensi_pentatonics.png\|sensi_pentatonics.png]]		[[File:sensi_pentatonics.png\|alt=sensi_pentatonics.png\|sensi_pentatonics.png]]

	=Comments=		==Comments==

	MOS Muddles always have more than two sizes of step -- either three or four sizes. Whereas MOS scales have two varieties of interval for each interval class (eg. a "large step" and a "small step"), muddles have potentially two varieties within each variety (eg. two sizes of "small step" and two sizes of "large step"). Parent scales that are close to equal (eg. [[Maximal_evenness\|maximally even]] scales) will produce muddles that are closer in sound to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller ones.		MOS Muddles always have more than two sizes of step -- either three or four sizes. Whereas MOS scales have two varieties of interval for each interval class (eg. a "large step" and a "small step"), muddles have potentially two varieties within each variety (eg. two sizes of "small step" and two sizes of "large step"). Parent scales that are close to equal (eg. [[Maximal_evenness\|maximally even]] scales) will produce muddles that are closer in sound to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller ones.

	=History=		==History==

	MOS muddles seem to be as old as MOS, although the name "muddle" is new. Page six of [[Erv_Wilson\|Erv Wilson]]'s [http://www.anaphoria.com/mos.PDF seminal article on MOS scales] shows a 17-tone MOS subset of [[41edo\|41edo]] as "parent scale" and a 7-tone MOS pattern as "target scale shape". They are also present in the work of [[Kraig_Grady\|Kraig Grady]], who prefers the term "bi-level" (see [https://anaphoriasouth.blogspot.com/2011/05/pentatonic-family-pt-1.html this blog entry] and [https://anaphoriasouth.blogspot.com/2012/01/pentatonic-family-pt2.html this one]). The word "muddle" comes from [[Gene_Ward_Smith\|Gene Ward Smith]].		MOS muddles seem to be as old as MOS, although the name "muddle" is new. Page six of [[Erv_Wilson\|Erv Wilson]]'s [http://www.anaphoria.com/mos.PDF seminal article on MOS scales] shows a 17-tone MOS subset of [[41edo\|41edo]] as "parent scale" and a 7-tone MOS pattern as "target scale shape". They are also present in the work of [[Kraig_Grady\|Kraig Grady]], who prefers the term "bi-level" (see [https://anaphoriasouth.blogspot.com/2011/05/pentatonic-family-pt-1.html this blog entry] and [https://anaphoriasouth.blogspot.com/2012/01/pentatonic-family-pt2.html this one]). The word "muddle" comes from [[Gene_Ward_Smith\|Gene Ward Smith]].

	=Non-MOS Muddles=		==Non-MOS Muddles==

	As mentioned at the beginning, in a muddle, the parent scale can be any kind of periodic scale at all, including but not limited to [[MODMOS_Scales\|MODMOS scales]], [[MOS_Cradle\|MOS Cradle scales]], other muddles, scales of [[Regular_Temperaments\|temperaments]] with rank higher than 2, [[Just_intonation\|Just Intonation]] scales, etc. The target scale is a little less flexible, but it could be at least a MODMOS scale, a MOS Cradle scale or any other MOS subset or subset of a periodic equal-step scale. It's just important that the total number of "units" in the target scale (eg. the MOS Cradle 23132 has 2+3+1+3+2=11 units) be the same as the number of tones in the parent scale (thus the 23132 target scale must be applied to a scale of 11 tones).		As mentioned at the beginning, in a muddle, the parent scale can be any kind of periodic scale at all, including but not limited to [[MODMOS_Scales\|MODMOS scales]], [[MOS_Cradle\|MOS Cradle scales]], other muddles, scales of [[Regular_Temperaments\|temperaments]] with rank higher than 2, [[Just_intonation\|Just Intonation]] scales, etc. The target scale is a little less flexible, but it could be at least a MODMOS scale, a MOS Cradle scale or any other MOS subset or subset of a periodic equal-step scale. It's just important that the total number of "units" in the target scale (eg. the MOS Cradle 23132 has 2+3+1+3+2=11 units) be the same as the number of tones in the parent scale (thus the 23132 target scale must be applied to a scale of 11 tones).

	<span style="">As one example of a muddle with a non-MOS parent</span><span style="">, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span>		<span style="">As one example of a muddle with a non-MOS parent</span><span style="">, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span>

← Older revision		Revision as of 19:50, 23 April 2023
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	<span style="">As one example of a muddle with a non-MOS parent</span><span style="">, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span>		<span style="">As one example of a muddle with a non-MOS parent</span><span style="">, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span>

			[[Category:Muddles\| ]] <!-- main article -->