Generator: Difference between revisions

Line 9:

g = g1^n1 g2^n2 ... gk^nk

An important example is provided by [[~~Regular_Temperaments|~~regular temperaments]], where if a particular tuning for the temperament is written additively, the generators can be taken as intervals expressed in terms of cents, and if multiplicatively, as intervals given as frequency ratios. Another example is provided by [[~~Just_intonation_subgroups|~~just intonation subgroups]], where the generators are a finite set of positive rational numbers. These two example converge when we seek generators for the [[~~Abstract_regular_temperament~~|abstract temperament]] rather than any particular tuning of it.

== Relation to music ==

[[Category:~~definition~~]]

[[Category:~~math~~]]

An important example is provided by [[regular temperaments]], where if a particular tuning for the temperament is written additively, the generators can be taken as intervals expressed in terms of cents, and if multiplicatively, as intervals given as frequency ratios. Another example is provided by [[just intonation subgroups]], where the generators are a finite set of positive rational numbers. These two example converge when we seek generators for the [[abstract regular temperament|abstract temperament]] rather than any particular tuning of it.

[[Category:todo:~~increase_applicability~~]]

[[Category:Definition]]

[[Category:Math]]

[[Category:todo:increase applicability]]

[[Category:todo:increase focus to lemma]]

@@ Line 9: / Line 9: @@
 g = g1^n1 g2^n2 ... gk^nk
-An important example is provided by [[Regular_Temperaments|regular temperaments]], where if a particular tuning for the temperament is written additively, the generators can be taken as intervals expressed in terms of cents, and if multiplicatively, as intervals given as frequency ratios. Another example is provided by [[Just_intonation_subgroups|just intonation subgroups]], where the generators are a finite set of positive rational numbers. These two example converge when we seek generators for the [[Abstract_regular_temperament|abstract temperament]] rather than any particular tuning of it.
+== Relation to music ==
-[[Category:definition]]
-[[Category:math]]
+An important example is provided by [[regular temperaments]], where if a particular tuning for the temperament is written additively, the generators can be taken as intervals expressed in terms of cents, and if multiplicatively, as intervals given as frequency ratios. Another example is provided by [[just intonation subgroups]], where the generators are a finite set of positive rational numbers. These two example converge when we seek generators for the [[abstract regular temperament|abstract temperament]] rather than any particular tuning of it.
-[[Category:todo:increase_applicability]]
+[[Category:Definition]]
+[[Category:Math]]
+[[Category:todo:increase applicability]]
+[[Category:todo:increase focus to lemma]]