Template:Odd-limit intro: Difference between revisions

Latest revision as of 21:27, 3 August 2025

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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|odd_limit_diff|{{#expr:({{{1|}}}+1)/2}}}} interval pair{{#ifexpr: {{{1|}}}>3|s|}} involving {{{1|}}}.|}}
+<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}}
+}} 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>
-This template generates an intro (lead section) for [[odd limit]] pages.
+{{documentation}}
-== Usage ==
-Provide the number of the odd limit as an unnamed argument, e.g. <code><nowiki>{{odd-limit intro|5}}</nowiki></code> for an intro to the [[5-odd-limit]] page.
-== See also ==
-* [[Template:Odd-limit navigation]]
 [[Category:Intro templates]]
 </noinclude>