Uniform map: Difference between revisions

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Every [[edo]] has a finite number of possible uniform maps within a given prime limit, but an infinite number of uniform maps if no prime limit is given.

To find a uniform map for some ''n''-edo, choose any multiplier that rounds to ''n'' (anywhere from {{nowrap|''n'' − 0.5}} to {{nowrap|''n'' + 0.5}}). For example, 16.9 rounds to 17, so we could use that to find another example for 17edo. Uniformly multiplying 16.9 · {{map| log22 log23 log25 }} = {{map| 16.9 26.786 39.241 }}, which rounds to {{map| 17 27 39 }}.

To find a uniform map for some ''n''-edo, choose any multiplier that rounds to ''n'' (anywhere from {{nowrap|''n'' − 0.5}} to {{nowrap|''n'' + 0.5}}). For example, 16.9 rounds to 17, so we could use that to find another example for 17edo. Uniformly multiplying {{nowrap|16.9{{dot}}{{map| log22 log23 log25 }} {{=}} {{map| 16.9 26.786 39.241 }}}}, which rounds to {{map| 17 27 39 }}.

Subgroup uniform maps are also possible. For example, a uniform map on the 2.5.9/7 subgroup would be found by uniformly multiplying {{map|log22 log25 log2(9/7)}}.

== Integer uniform map, or simple map ==

A uniform map whose multiplier is an integer is called an '''integer uniform map'''. For example, we could use the integer 17 itself directly. So {{nowrap|17{{dot}}{{map| log22 log23 log25 }} {{=}} {{map| 17 26.944 39.473 }}}}, which also rounds to {{map| 17 27 39 }}. Every edo has one integer uniform map.

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 Every [[edo]] has a finite number of possible uniform maps within a given prime limit, but an infinite number of uniform maps if no prime limit is given.
-To find a uniform map for some ''n''-edo, choose any multiplier that rounds to ''n'' (anywhere from {{nowrap|''n'' − 0.5}} to {{nowrap|''n'' + 0.5}}). For example, 16.9 rounds to 17, so we could use that to find another example for 17edo. Uniformly multiplying 16.9 · {{map| log<sub>2</sub>2 log<sub>2</sub>3 log<sub>2</sub>5 }} = {{map| 16.9 26.786 39.241 }}, which rounds to {{map| 17 27 39 }}.
+To find a uniform map for some ''n''-edo, choose any multiplier that rounds to ''n'' (anywhere from {{nowrap|''n'' − 0.5}} to {{nowrap|''n'' + 0.5}}). For example, 16.9 rounds to 17, so we could use that to find another example for 17edo. Uniformly multiplying {{nowrap|16.9{{dot}}{{map| log<sub>2</sub>2 log<sub>2</sub>3 log<sub>2</sub>5 }} {{=}} {{map| 16.9 26.786 39.241 }}}}, which rounds to {{map| 17 27 39 }}.
 Subgroup uniform maps are also possible. For example, a uniform map on the 2.5.9/7 subgroup would be found by uniformly multiplying {{map|log<sub>2</sub>2 log<sub>2</sub>5 log<sub>2</sub>(9/7)}}.
 == Integer uniform map, or simple map ==
-{{Main| patent val }}
+{{Main| Patent val }}
 A uniform map whose multiplier is an integer is called an '''integer uniform map'''. For example, we could use the integer 17 itself directly. So {{nowrap|17{{dot}}{{map| log<sub>2</sub>2 log<sub>2</sub>3 log<sub>2</sub>5 }} {{=}} {{map| 17 26.944 39.473 }}}}, which also rounds to {{map| 17 27 39 }}. Every edo has one integer uniform map.