Omnitetrachordality: Difference between revisions

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A [[scale]] is '''weakly omnitetrachordal''' if any [[mode]] of the scale (that is, any particular octave span of the ~~infinite~~ scale) can be expressed as two identical sequences of steps ("tetrachords") each spanning [[4/3]], plus a [[9/8]] that may or may not be divided into smaller steps (a "disjunction"). The definition can of course be generalized to intervals of quasi-equivalence other than 4/3, but the original version is with 4/3.

An [[period|octave-repeating]] [[scale]] is '''weakly omnitetrachordal''' if any [[mode]] of the scale (that is, any particular octave span of the scale) can be expressed as two identical sequences of steps ("tetrachords") each spanning [[4/3]], plus a [[9/8]] that may or may not be divided into smaller steps (a "disjunction"). Although the property is called ''omnitetrachordality'', it does not require exactly four notes (three steps) in the sequence. The definition can of course be generalized to intervals of quasi-equivalence other than 4/3, but the original version is with 4/3.

If, for each mode of the scale, the entire pattern of scale steps within the disjunction also occurs within the tetrachord, the scale is '''strongly omnitetrachordal''' ([[Paul Erlich]]'s original definition of omnitetrachordal). For example, the scale "abc abc ac" is weakly omnitetrachordal but not strongly omnitetrachordal, because the disjunction "ac" does not occur in the tetrachords "abc".

Revision as of 11:42, 29 January 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,211 edits m Style and formatting improvements ← Older edit		Revision as of 11:52, 29 January 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,211 edits Clarify that this doesn't require four-note segments Newer edit →
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	A [[scale]] is '''weakly omnitetrachordal''' if any [[mode]] of the scale (that is, any particular octave span of the ~~infinite~~ scale) can be expressed as two identical sequences of steps ("tetrachords") each spanning [[4/3]], plus a [[9/8]] that may or may not be divided into smaller steps (a "disjunction"). The definition can of course be generalized to intervals of quasi-equivalence other than 4/3, but the original version is with 4/3.		An [[period\|octave-repeating]] [[scale]] is '''weakly omnitetrachordal''' if any [[mode]] of the scale (that is, any particular octave span of the scale) can be expressed as two identical sequences of steps ("tetrachords") each spanning [[4/3]], plus a [[9/8]] that may or may not be divided into smaller steps (a "disjunction"). Although the property is called ''omnitetrachordality'', it does not require exactly four notes (three steps) in the sequence. The definition can of course be generalized to intervals of quasi-equivalence other than 4/3, but the original version is with 4/3.

	If, for each mode of the scale, the entire pattern of scale steps within the disjunction also occurs within the tetrachord, the scale is '''strongly omnitetrachordal''' ([[Paul Erlich]]'s original definition of omnitetrachordal). For example, the scale "abc abc ac" is weakly omnitetrachordal but not strongly omnitetrachordal, because the disjunction "ac" does not occur in the tetrachords "abc".		If, for each mode of the scale, the entire pattern of scale steps within the disjunction also occurs within the tetrachord, the scale is '''strongly omnitetrachordal''' ([[Paul Erlich]]'s original definition of omnitetrachordal). For example, the scale "abc abc ac" is weakly omnitetrachordal but not strongly omnitetrachordal, because the disjunction "ac" does not occur in the tetrachords "abc".