ABACABADABACABA JI scales - Revision history

Lériendil: Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

2025-06-24T00:34:22Z

Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:34, 24 June 2025
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	[[Category:Step-nested scales]]		[[Category:Step-nested scales]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
			[[Category:Pages with mostly numerical content]]

Lhearne: edited first sentence to highlight equivalence of Fraenkel words to power SNS

2024-02-19T02:39:44Z

edited first sentence to highlight equivalence of Fraenkel words to power SNS

← Older revision		Revision as of 02:39, 19 February 2024
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	ABACABADABACABA is the quaternary [[Fraenkel word]] ~~and~~ the (8,4,2,1) [[SNS]] pattern ~~(the rank-4 power SNS)~~. When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent [[ABACABA JI scales\|ABACABA scales]] and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.		ABACABADABACABA is the quaternary [[Fraenkel word]] or the rank-4 power [[SNS]], i.e., the (8,4,2,1) [[SNS]] pattern. When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent [[ABACABA JI scales\|ABACABA scales]] and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.

	== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==		== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==

Inthar at 16:35, 15 February 2024

2024-02-15T16:35:15Z

← Older revision		Revision as of 16:35, 15 February 2024
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	ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent [[ABACABA JI scales\|ABACABA scales]] and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.		ABACABADABACABA is the quaternary [[Fraenkel word]] and the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent [[ABACABA JI scales\|ABACABA scales]] and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.

	== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==		== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==

Fredg999: Categories

2023-04-23T21:56:45Z

BudjarnLambeth: Categorised this uncategorised page

2023-04-23T20:51:39Z

Categorised this uncategorised page

← Older revision		Revision as of 20:51, 23 April 2023
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	\|}		\|}
	Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).		Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).
			[[Category:Just intonation scales]]
			[[Category:Scales by family]]

Lhearne at 13:48, 2 April 2023

2023-04-02T13:48:13Z

← Older revision		Revision as of 13:48, 2 April 2023
Line 1:		Line 1:
	ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent ABACABA scales and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.		ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent [[ABACABA JI scales\|ABACABA scales]] and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.

	== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==		== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==

Lhearne at 13:44, 2 April 2023

2023-04-02T13:44:55Z

← Older revision		Revision as of 13:44, 2 April 2023
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	\|256/245 (~76.03c)		\|256/245 (~76.03c)
	\|1/1 33/32 35/33 35/32 8/7 33/28 40/33 5/4 8/5 33/20 48/33 7/4 64/35 66/35 64/33 2/1		\|1/1 33/32 35/33 35/32 8/7 33/28 40/33 5/4 8/5 33/20 48/33 7/4 64/35 66/35 64/33 2/1
	\|~~1125~~		\|1225
	\|22		\|22
	\|-		\|-
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	\|256/245 (~76.03c)		\|256/245 (~76.03c)
	\|1/1 35/34 17/16 35/32 8/7 20/17 17/14 5/4 8/5 28/17 17/10 7/4 64/35 32/17 35/17 2/1		\|1/1 35/34 17/16 35/32 8/7 20/17 17/14 5/4 8/5 28/17 17/10 7/4 64/35 32/17 35/17 2/1
	\|~~1125~~		\|1225
	\|22		\|22
	\|}		\|}
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	\|250/243 (~49.17c)		\|250/243 (~49.17c)
	\|1/1 36/35 21/20 27/25 10/9 8/7 7/6 6/5 5/3 12/7 7/4 9/5 50/27 40/21 35/18 2/1		\|1/1 36/35 21/20 27/25 10/9 8/7 7/6 6/5 5/3 12/7 7/4 9/5 50/27 40/21 35/18 2/1
	\|~~1125~~		\|1225
	\|26/27		\|26/27
	\|}		\|}
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	\|250/243 (~49.17c)		\|250/243 (~49.17c)
	\|1/1 36/35 21/20 27/25 10/9 8/7 7/6 6/5 5/4 9/7 21/16 27/20 25/18 10/7 35/24 3/2		\|1/1 36/35 21/20 27/25 10/9 8/7 7/6 6/5 5/4 9/7 21/16 27/20 25/18 10/7 35/24 3/2
	\|~~1125~~		\|1225
	\|}		\|}
	Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).		Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).

Lhearne at 13:43, 2 April 2023

2023-04-02T13:43:06Z

← Older revision		Revision as of 13:43, 2 April 2023
Line 1:		Line 1:
	ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent ABACABA scales and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not pairwise-~~well~~ formed, and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.		ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent ABACABA scales and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not [[Rank-3 scale#Pairwise well-formed scales\|pairwise well-formed]], and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.

	== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==		== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==

Lhearne at 13:41, 2 April 2023

2023-04-02T13:41:39Z

← Older revision		Revision as of 13:41, 2 April 2023
Line 1:		Line 1:
	ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two ABACABA scales ~~separated by an interval~~ D, akin to how ABACABA scales can be conceived of as two ABA tetrachords ~~separated by an interval~~ C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, H is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not pairwise-well formed, and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.		ABACABADABACABA is the (8,4,2,1) [[SNS]] pattern (the rank-4 power SNS). When covering a period of 2/1, such scales are known as Cantor-3 scales. ABACABADABACABA scales can be conceived of as two equivalent ABACABA scales and a remaining step D, akin to how ABACABA scales can be conceived of as two equivalent ABA tetrachords and a remaining step C. We will classify ABACABADABACABA scales on this page as such, grouping them by the interval subtended by ABACABA, which we will call an octochord. As [[step-nested scales]], ABACABADABACABA scales can be described of as SNS (P, P/O, O/T, A), or equivalently as SNS (P, O, T, A) etc. where P is the period, O is the interval subtended by ABACABA, the octochord, and T is the interval subtended by ABA, the tetrachord. ABACABADABACABA scales, unlike ABA and ABACABA scales, are not pairwise-well formed, and thus their mean variety is above 4. ABACABADABACABA scales have v4454654 4564544, with mean variety ~ 4.57.

	== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==		== 729-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==

Lhearne: /* 1225-limit ABACABADABACABA JI scales with period 3/2, with steps > 20c */

2023-04-02T13:25:17Z

1225-limit ABACABADABACABA JI scales with period 3/2, with steps > 20c

← Older revision		Revision as of 13:25, 2 April 2023
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	\|1125		\|1125
	\|}		\|}
			Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).

← Older revision		Revision as of 21:56, 23 April 2023
Line 248:		Line 248:
	\|}		\|}
	Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).		Noticing that A and C are almost exactly the same size, we temper them together without much loss of accuracy, tempering out [[4375/4374]], the [[Ragisma]]. The tempered scale then has a scale pattern of ABAAABACABAAABA (relabeling so the most frequent step is A and the least frequent is C).

			[[Category:Step-nested scales]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	~~[[Category:Scales by family]]~~