Template:Odd-limit intro: Difference between revisions

Revision as of 21:21, 3 August 2025

Template documentation[view] [edit] [history] [purge]

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.

@@ Line 1: / Line 1: @@
-<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 $2^k\frac{a}{b}$ where $a, b \leq {{{1|}}}$ 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 [[octavew-reduced]] interval{{#ifexpr: {{{1|}}} > 3|s|}} involving {{{1|}}}.|}}
 Below is a list of all [[octave-reduced]] intervals in the {{{1|}}}-odd-limit.</includeonly><noinclude>