Tour of regular temperaments: Difference between revisions
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These are families defined by a comma that uses a wa or 3-limit comma. If prime 5 is assumed to be part of the subgroup, and no other comma is tempered out, the comma creates a rank-2 temperament. The comma can also stand as parent to a 7-limit or higher family when other commas are tempered out as well, or when prime 7 is assumed to be part of the subgroup. Any temperament in these families can be thought of as consisting of mutiple "copies" of an EDO separated by a small comma. This small comma is represented in the pergen by ^1. | These are families defined by a comma that uses a wa or 3-limit comma. If prime 5 is assumed to be part of the subgroup, and no other comma is tempered out, the comma creates a rank-2 temperament. The comma can also stand as parent to a 7-limit or higher family when other commas are tempered out as well, or when prime 7 is assumed to be part of the subgroup. Any temperament in these families can be thought of as consisting of mutiple "copies" of an EDO separated by a small comma. This small comma is represented in the pergen by ^1. | ||
; [[ | ; [[Limma family|Limma or Sawa family]] (P8/5, ^1) | ||
: This family tempers out the limma, {{Monzo|8 -5 0}} = 256/243, which implies [[5edo|5EDO]]. | : This family tempers out the limma, {{Monzo|8 -5 0}} = 256/243, which implies [[5edo|5EDO]]. | ||
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; [[Mercator family|Mercator or Quadbilawa family]] (P8/53, ^1) | ; [[Mercator family|Mercator or Quadbilawa family]] (P8/53, ^1) | ||
: The Mercator family tempers out the [[Mercator's comma]], {{Monzo| -84 53 }}, which implies [[53edo|53EDO]]. | : The Mercator family tempers out the [[Mercator's comma]], {{Monzo| -84 53 }}, which implies [[53edo|53EDO]]. | ||
=== Families defined by a 2.3.5 (ya) comma === | === Families defined by a 2.3.5 (ya) comma === | ||