Word: Difference between revisions

Line 1:

A '''word''', in mathematical terminology, is a sequence of letters from some finite alphabet, such as "aabaaab" or "LLsLLLs." In music theory, they are often used to represent an abstract scale template with some specified pattern of step sizes, such as when working with [[MOS]] scales.

A '''word''', in mathematical terminology, is a sequence of letters from some finite alphabet, such as "aabaaab" or "LLsLLLs." In music theory, they are often used to represent an abstract scale template with some specified pattern of step sizes, such as when working with [[MOS]] scales. Two words that are rotations of one another, such as "aabaaab" and "abaaaba", are termed ''conjugate'', and equivalence classes of a word under conjugacy is dubbed a '''circular word''' or a '''necklace'''.

For example, the word "aabaaab" can be thought of as representing a '''scale template''' where "a" represents one kind of step, and "b" represents a different kind of step. It is often useful to specify the relative sizes of the steps as well, leading to the two related words "LLsLLLs" and "ssLsssL," where L means "large" and s means "small." Of these, LLsLLLs basically corresponds to the diatonic scale, and ssLsssL the anti-diatonic scale; aabaaab can be thought of a more generic word incorporating both into a single template.

Revision as of 00:54, 27 April 2023 view source BudjarnLambeth (talk \| contribs) autopatrolled, emailconfirmed 21,295 edits m Categorised this uncategorised page Tag: Visual edit ← Older edit		Revision as of 16:34, 20 December 2023 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,674 edits No edit summary Newer edit →
Line 1:		Line 1:
	A '''word''', in mathematical terminology, is a sequence of letters from some finite alphabet, such as "aabaaab" or "LLsLLLs." In music theory, they are often used to represent an abstract scale template with some specified pattern of step sizes, such as when working with [[MOS]] scales.		A '''word''', in mathematical terminology, is a sequence of letters from some finite alphabet, such as "aabaaab" or "LLsLLLs." In music theory, they are often used to represent an abstract scale template with some specified pattern of step sizes, such as when working with [[MOS]] scales. Two words that are rotations of one another, such as "aabaaab" and "abaaaba", are termed ''conjugate'', and equivalence classes of a word under conjugacy is dubbed a '''circular word''' or a '''necklace'''.

	For example, the word "aabaaab" can be thought of as representing a '''scale template''' where "a" represents one kind of step, and "b" represents a different kind of step. It is often useful to specify the relative sizes of the steps as well, leading to the two related words "LLsLLLs" and "ssLsssL," where L means "large" and s means "small." Of these, LLsLLLs basically corresponds to the diatonic scale, and ssLsssL the anti-diatonic scale; aabaaab can be thought of a more generic word incorporating both into a single template.		For example, the word "aabaaab" can be thought of as representing a '''scale template''' where "a" represents one kind of step, and "b" represents a different kind of step. It is often useful to specify the relative sizes of the steps as well, leading to the two related words "LLsLLLs" and "ssLsssL," where L means "large" and s means "small." Of these, LLsLLLs basically corresponds to the diatonic scale, and ssLsssL the anti-diatonic scale; aabaaab can be thought of a more generic word incorporating both into a single template.