Hobbled scale - Revision history

Pailiaq: removed the mention of ternary scales in the introduction as it seemed to cause needless confusion

2026-04-12T20:38:09Z

removed the mention of ternary scales in the introduction as it seemed to cause needless confusion

← Older revision		Revision as of 20:38, 12 April 2026
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	A '''hobbled scale''' is a [[scale]] created by reducing exactly one step of an existing scale pattern by a step size, ~~typically~~ resulting in a ~~[[ternary]]~~ scale that approximates the original pattern but fits into a different [[edo]]. The term ''hobbled'' derives from the metaphor of "hobbling" one of the step "legs" to be shorter than the other, analogous to how hobbling an animal restricts its movement by shortening one leg. This concept was explored and refined as an effort of TOTYW2025 in the Xenharmonic Alliance Discord.		A '''hobbled scale''' is a [[scale]] created by either reducing or increasing exactly one step of an existing scale pattern by some step size, resulting in a scale that approximates the original pattern but fits into a different [[edo]]. The term ''hobbled'' derives from the metaphor of "hobbling" one of the step "legs" to be shorter than the other, analogous to how hobbling an animal restricts its movement by shortening one leg. This concept was explored and refined as an effort of TOTYW2025 in the Xenharmonic Alliance Discord.

	== Definition / algorithm ==		== Definition / algorithm ==

Overthink: /* Definition / algorithm */ Period

2026-02-06T05:16:09Z

Definition / algorithm: Period

← Older revision		Revision as of 05:16, 6 February 2026
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	# Reducing that step by the calculated difference		# Reducing that step by the calculated difference

	This results in a new pattern that fits into the target edo with one step shorter than in the original		This results in a new pattern that fits into the target edo with one step shorter than in the original.

	== Examples ==		== Examples ==

Zhenlige: /* 18edo hobbled Lydian */ it cannot be truly just since it is irrational

2026-02-05T18:35:29Z

18edo hobbled Lydian: it cannot be truly just since it is irrational

← Older revision		Revision as of 18:35, 5 February 2026
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	[[18edo]] provides an interesting case study for hobbled scales, particularly with lydian patterns. The scale 3–3–3–2–3–3–1 creates an effectively hobbled lydian where one of the short steps has been reduced. This scale exploits the fact that 18edo shares the same wholetone (200{{c}}) as 12edo, since both are supersets of 6edo.		[[18edo]] provides an interesting case study for hobbled scales, particularly with lydian patterns. The scale 3–3–3–2–3–3–1 creates an effectively hobbled lydian where one of the short steps has been reduced. This scale exploits the fact that 18edo shares the same wholetone (200{{c}}) as 12edo, since both are supersets of 6edo.

	The first half of this hobbled Lydian scale is identical to 12edo Lydian, preserving the quintessential dreamy wholetone character. However, the second half becomes distinctly alien with a sharp 733{{c}} fifth, a just 12/7 sixth (933{{c}}), and a smaller leading tone. This creates a scale that starts familiar but ventures into bright, colorful territory that regular lydian cannot access.		The first half of this hobbled Lydian scale is identical to 12edo Lydian, preserving the quintessential dreamy wholetone character. However, the second half becomes distinctly alien with a sharp 733{{c}} fifth, a near-just 12/7 sixth (933{{c}}), and a smaller leading tone. This creates a scale that starts familiar but ventures into bright, colorful territory that regular lydian cannot access.

	This pattern can also be viewed as a hobbled [[17edo]] or [[19edo]] diatonic, demonstrating how hobbling can bridge between different edos and give a useful lens to understand scales.		This pattern can also be viewed as a hobbled [[17edo]] or [[19edo]] diatonic, demonstrating how hobbling can bridge between different edos and give a useful lens to understand scales.

	[[Category:Scale]]		[[Category:Scale]]

FloraC: + category

2025-12-03T07:25:21Z

+ category

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	This pattern can also be viewed as a hobbled [[17edo]] or [[19edo]] diatonic, demonstrating how hobbling can bridge between different edos and give a useful lens to understand scales.		This pattern can also be viewed as a hobbled [[17edo]] or [[19edo]] diatonic, demonstrating how hobbling can bridge between different edos and give a useful lens to understand scales.

			[[Category:Scale]]

FloraC: Linking and style

2025-12-03T07:23:53Z

Linking and style

← Older revision		Revision as of 07:23, 3 December 2025
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	~~== Hobbled Scales ==~~		A '''hobbled scale''' is a [[scale]] created by reducing exactly one step of an existing scale pattern by a step size, typically resulting in a [[ternary]] scale that approximates the original pattern but fits into a different [[edo]]. The term ''hobbled'' derives from the metaphor of "hobbling" one of the step "legs" to be shorter than the other, analogous to how hobbling an animal restricts its movement by shortening one leg. This concept was explored and refined as an effort of TOTYW2025 in the Xenharmonic Alliance Discord.
	A hobbled scale is a scale created by reducing exactly one step of an existing scale pattern by a step size, typically resulting in a ternary scale that approximates the original pattern but fits into a different ~~EDO~~. The term "hobbled" derives from the metaphor of "hobbling" one of the step "legs" to be shorter than the other, analogous to how hobbling an animal restricts its movement by shortening one leg. This concept was explored and refined as an effort of TOTYW2025 in the Xenharmonic Alliance Discord.

	== Definition / ~~Algorithm~~ ==		== Definition / algorithm ==
	Given a scale with a repeating step pattern in some ~~EDO~~ and a target ~~EDO~~ that we want to fit the scale into, a hobbled version is created by:		Given a scale with a repeating step pattern in some edo and a target edo that we want to fit the scale into, a hobbled version is created by:
			# Calculating the difference between the source edo and target edo
			# Selecting any single occurrence of any step size in the pattern
			# Reducing that step by the calculated difference

	~~1. Calculating the difference between the source EDO and target EDO~~		This results in a new pattern that fits into the target edo with one step shorter than in the original

	~~2. Selecting any single occurrence of any step size in the pattern~~

	~~3. Reducing that step by the calculated difference~~

	This results in a new pattern that fits into the target ~~EDO~~ with one step shorter than in the original

	== Examples ==		== Examples ==
	By taking the standard diatonic pattern from ~~12-EDO~~ (in this case we~~'ll~~ upscale it to ~~24-EDO~~) or nearby systems, you can create a hobbled scale in an adjacent ~~EDO~~ that may not support that scale, like ~~23-EDO~~:		By taking the standard diatonic pattern from [[12edo]] (in this case we will upscale it to [[24edo]]) or nearby systems, you can create a hobbled scale in an adjacent edo that may not support that scale, like [[23edo]]:

	'''~~24-EDO~~ diatonic:''' ~~4-4-2-4-4-4-2~~		'''24edo diatonic:''' 4–4–2–4–4–4–2

	'''~~23-EDO~~ hobbled diatonic''': ~~4-4-2-4-4-4-1~~		'''23edo hobbled diatonic''': 4–4–2–4–4–4–1

	This creates a scale that sounds largely diatonic but with one altered interval, providing a "normal" scale with familiar structure yet xenharmonic character. In this example alone you have 7 different options to choose from, as you could hobble a large step as well, creating a ~~4-4-2-~~(3)~~-4-4-2~~ scale for instance.		This creates a scale that sounds largely diatonic but with one altered interval, providing a "normal" scale with familiar structure yet xenharmonic character. In this example alone you have 7 different options to choose from, as you could hobble a large step as well, creating a 4–4–2–(3)–4–4–2 scale for instance.

	From this you have a rank-3 scale with a large variety of ~~chords~~. By climbing the 'circle of fifths' you alternate between a sharp and a flat fifth (as 23edo is a dual-fifth system). By choosing which note to hobble, you not only nudge the melodic movement (for instance, choosing to have a smaller leading tone by hobbling the last step) but also change harmonic qualities of chords throughout your scale. If you want your tonic chord to have a flat fifth, you would choose to hobble a note that occurs below the fifth, and you would choose a note above if you wanted a sharper fifth.		From this you have a [[rank-3 scale]] with a large variety of [[chord]]s. By climbing the "[[circle of fifths]]" you alternate between a sharp and a flat fifth (as 23edo is a [[dual-fifth]] system). By choosing which note to hobble, you not only nudge the melodic movement (for instance, choosing to have a smaller leading tone by hobbling the last step) but also change harmonic qualities of chords throughout your scale. If you want your tonic chord to have a flat fifth, you would choose to hobble a note that occurs below the fifth, and you would choose a note above if you wanted a sharper fifth.

	Furthermore, 23edo is sandwiched between two diatonic-containing ~~EDOs~~: 24edo with its basic diatonic, and 22edo with its ~~709c~~ hard diatonic. If we instead choose to hobble the 22edo diatonic by ''increasing'' an edo step, you create a "superpyth hobbled diatonic" scale:		Furthermore, 23edo is sandwiched between two diatonic-containing edos: 24edo with its basic diatonic, and [[22edo]] with its 709{{c}} hard diatonic. If we instead choose to hobble the 22edo diatonic by ''increasing'' an edo step, you create a "superpyth hobbled diatonic" scale:

	'''~~22-EDO~~ diatonic:''' ~~4-4-1-4-4-4-1~~		'''22edo diatonic:''' 4–4–1–4–4–4–1

	'''~~23-EDO~~ hobbled diatonic''': ~~5-4-1-4-4-4-1~~		'''23edo hobbled diatonic''': 5–4–1–4–4–4–1

	While there are 7 options to choose when hobbling by ''increasing'' step size, if you were to increase one of the small steps, you would get a repeated scale from before (by reducing a 24edo diatonic's small step). Thus in this example, there are 12 options to choose from. (5 from increasing a 22edo ~~5L2s L~~ step, 5 from decreasing a 24edo ~~5L2s L~~ step, and 2 from increasing/decreasing either scale's s step.)		While there are 7 options to choose when hobbling by ''increasing'' step size, if you were to increase one of the small steps, you would get a repeated scale from before (by reducing a 24edo diatonic's small step). Thus in this example, there are 12 options to choose from. (5 from increasing a 22edo [[5L 2s]] large step, 5 from decreasing a 24edo 5L 2s large step, and 2 from increasing/decreasing either scale's small step.)

	Given there are 7 modes in the ~~5L2s~~ scale, there are now ~~7x12~~ = 84 combinations of hobbled scales and modes to choose from. Certain combinations of hobbling will could exaggerate or enhance properties of other modes.		Given there are 7 modes in the 5L 2s scale, there are now 7 × 12 = 84 combinations of hobbled scales and modes to choose from. Certain combinations of hobbling will could exaggerate or enhance properties of other modes.

	== Musical ~~Applications~~ ==		== Musical applications ==
	Hobbled scales serve several compositional purposes:		Hobbled scales serve several compositional purposes:

	=== Finding ~~Familiar Scales~~ ===		=== Finding familiar scales ===
	You can create surprisingly normal sounding music in very 'weird' tuning systems that are 'sandwiched' between two diatonic tunings like 18edo or 23edo by hobbling familiar scales, which widens the available options for composers wanting to write in a diatonic framework.		You can create surprisingly normal sounding music in very weird tuning systems that are sandwiched between two diatonic tunings like 18edo or 23edo by hobbling familiar scales, which widens the available options for composers wanting to write in a diatonic framework.

	~~You can of course fit any scale into other edos by hobbling. For instance, 22edo's pajara can be fit into 23 (in which case will now have 10 modes instead of 5 due to losing symmetry!)~~

	~~=== Modulation Pathways ===~~		You can of course fit any scale into other edos by hobbling. For instance, 22edo's pajara can be fit into 23 (in which case will now have 10 modes instead of 5 due to losing symmetry.)
	~~Hobbled scales~~ can ~~facilitate modulation between different MOS patterns or EDO systems, as the altered intervals may serve as pivot points or transitional harmonies~~. For ~~example~~, ~~you could start in 24edo, hobble one small leg~~ into 23 ~~for a brief passage, then hobble it again~~ to ~~balance the legs out into 22edo so that it temporarily is 'beaten' into shape~~.

	=== ~~Dual Fifth Systems~~ ===		=== Modulation pathways ===
	~~It lends particular well for dual fifth~~ systems, as a ~~hobbled scale will have two different interval types for every scale step~~, ~~and thus sound less 'wrong' when hearing inconsistency in interval quality~~.		Hobbled scales can facilitate modulation between different [[mos]] patterns or edo systems, as the altered intervals may serve as pivot points or transitional harmonies. For example, you could start in 24edo, hobble one small leg into 23 for a brief passage, then hobble it again to balance the legs out into 22edo so that it temporarily is "beaten" into shape.

	== ~~Examples and Discoveries~~ ==		=== Dual-fifth systems ===
			It lends particular well for dual-fifth systems, as a hobbled scale will have two different interval types for every scale step, and thus sound less "wrong" when hearing inconsistency in interval quality.

	=== ~~18-EDO Hobbled~~ Lydian ===		== Examples and discoveries ==
	~~18-EDO~~ provides an interesting case study for hobbled scales, particularly with lydian patterns. The scale ~~3-3-3-2-3-3-1~~ creates an effectively hobbled lydian where one of the short steps has been reduced. This scale exploits the fact that ~~18-EDO~~ shares the same wholetone (~~200¢~~) as ~~12-EDO~~, since both are supersets of ~~6-EDO~~.		=== 18edo hobbled Lydian ===
			[[18edo]] provides an interesting case study for hobbled scales, particularly with lydian patterns. The scale 3–3–3–2–3–3–1 creates an effectively hobbled lydian where one of the short steps has been reduced. This scale exploits the fact that 18edo shares the same wholetone (200{{c}}) as 12edo, since both are supersets of 6edo.

	The first half of this hobbled ~~lydian~~ scale is identical to ~~12-EDO lydian~~, preserving the quintessential dreamy wholetone character. However, the second half becomes distinctly alien with a sharp ~~733¢~~ fifth, a just 12/7 sixth (~~933¢~~), and a smaller leading tone. This creates a scale that starts familiar but ventures into bright, colorful territory that regular lydian cannot access.		The first half of this hobbled Lydian scale is identical to 12edo Lydian, preserving the quintessential dreamy wholetone character. However, the second half becomes distinctly alien with a sharp 733{{c}} fifth, a just 12/7 sixth (933{{c}}), and a smaller leading tone. This creates a scale that starts familiar but ventures into bright, colorful territory that regular lydian cannot access.

	This pattern can also be viewed as a hobbled ~~17-EDO~~ or ~~19-EDO~~ diatonic, demonstrating how hobbling can bridge between different ~~EDOs~~ and give a useful lens to understand scales.		This pattern can also be viewed as a hobbled [[17edo]] or [[19edo]] diatonic, demonstrating how hobbling can bridge between different edos and give a useful lens to understand scales.

FloraC: FloraC moved page Hobbled Scales to Hobbled scale: WP: NCCAPS, WP:PLURAL

2025-12-03T07:10:41Z

FloraC moved page Hobbled Scales to Hobbled scale: WP: NCCAPS, WP:PLURAL

← Older revision	Revision as of 07:10, 3 December 2025
(No difference)

Pailiaq: /* Finding Familiar Scales */ typo

2025-12-03T06:55:11Z

Finding Familiar Scales: typo

← Older revision		Revision as of 06:55, 3 December 2025
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	You can create surprisingly normal sounding music in very 'weird' tuning systems that are 'sandwiched' between two diatonic tunings like 18edo or 23edo by hobbling familiar scales, which widens the available options for composers wanting to write in a diatonic framework.		You can create surprisingly normal sounding music in very 'weird' tuning systems that are 'sandwiched' between two diatonic tunings like 18edo or 23edo by hobbling familiar scales, which widens the available options for composers wanting to write in a diatonic framework.

	You can of course fit any scale into other edos by hobbling. For instance, 22edo's pajara can be fit into 23 (in which case will now have 8 modes instead of 4 due to losing symmetry!)		You can of course fit any scale into other edos by hobbling. For instance, 22edo's pajara can be fit into 23 (in which case will now have 10 modes instead of 5 due to losing symmetry!)

	=== Modulation Pathways ===		=== Modulation Pathways ===

Pailiaq: Pailiaq moved page Xenharmonic Wiki:Hobbled Scales to Hobbled Scales

2025-11-03T04:45:06Z

Pailiaq moved page Xenharmonic Wiki:Hobbled Scales to Hobbled Scales

← Older revision	Revision as of 04:45, 3 November 2025
(No difference)

Pailiaq: Pailiaq moved page User:Pailiaq to Xenharmonic Wiki:Hobbled Scales

2025-11-03T04:44:51Z

Pailiaq moved page User:Pailiaq to Xenharmonic Wiki:Hobbled Scales

← Older revision	Revision as of 04:44, 3 November 2025
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Pailiaq: /* Definition / Algorithm */

2025-08-21T03:33:52Z

Definition / Algorithm

← Older revision		Revision as of 03:33, 21 August 2025
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	This results in a new pattern that fits into the target EDO with one step shorter than in the original		This results in a new pattern that fits into the target EDO with one step shorter than in the original

	The concept originated from the specific case of "hobbling" one of the small steps in a 5L 2s MOS pattern, making it even smaller and creating an asymmetric 5L 1m 1s pattern. However, the technique has been since explored and refined further and can be applied to any scale pattern, not just MOS scales.

	== Examples ==		== Examples ==