Template:Odd-limit intro: Difference between revisions

Latest revision as of 21:27, 3 August 2025

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This template invokes the following functions: get_term from Sequence.

This template should not be substituted.

This template generates an intro (lead section) for odd limit pages.

Provide the number of the odd limit as an unnamed argument, e.g. {{odd-limit intro|5}} for an intro to the 5-odd-limit page.

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-<includeonly>The '''{{{1|}}}-odd-limit''' is the set of all [[rational interval]]s for which neither the numerator nor the denominator of the [[frequency ratio]] exceeds {{{1|}}}, once all powers of 2 are removed. {{#ifexpr: {{{1|}}} > 1|To the [[{{#expr: {{{1|}}}-2}}-odd-limit]], it adds {{#invoke: Sequence | get_term
+<includeonly>The '''{{{1|}}}-odd-limit''' is the set of all [[rational interval]]s which can be written as 2<sup>''k''</sup>(''a''/''b'') where ''a'', ''b'' ≤ {{{1|}}} and ''k'' is an integer. {{#ifexpr: {{{1|}}} > 1|To the [[{{#expr: {{{1|}}}-2}}-odd-limit]], it adds {{#invoke: Sequence | get_term
 | odd_limit_diff
 | {{#expr: ({{{1|}}} + 1) / 2}}
-}} interval pair{{#ifexpr: {{{1|}}} > 3|s|}} involving {{{1|}}}.|}}
+}} pairs of [[octave-reduced]] interval{{#ifexpr: {{{1|}}} > 3|s|}} involving {{{1|}}}.|}}
-Below is a list of all [[octave-reduced]] intervals in the {{{1|}}}-odd-limit.</includeonly><noinclude>
+Below is a list of all octave-reduced intervals in the {{{1|}}}-odd-limit.</includeonly><noinclude>
 {{documentation}}
 [[Category:Intro templates]]
 </noinclude>