ABACABADABACABA JI scales: Difference between revisions

Line 1:

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 ==

Revision as of 16:35, 15 February 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits No edit summary ← Older edit		Revision as of 02:39, 19 February 2024 view source Lhearne (talk \| contribs) autopatrolled, emailconfirmed 1,510 edits m edited first sentence to highlight equivalence of Fraenkel words to power SNS Tag: Visual edit Newer edit →
Line 1:		Line 1:
	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 ==