31st-octave temperaments: Difference between revisions

Revision as of 16:26, 22 February 2022 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 25,499 edits m "Edos" doesn't sound right as we're not listing numbers of edos ← Older edit		Revision as of 13:01, 24 February 2022 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 25,499 edits m Intro Newer edit →
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	~~All~~ temperaments ~~on this page have~~ a period that is 1/~~31th~~ of an octave.		This page collects rank-2 temperaments with a period that is 1/31 of an octave.

	By the ''31-3-comma'' is meant 617673396283947/562949953421312 = {{monzo\| -49 31 }}, the amount (160.605 [[cent]]s) by which 31 just perfect fifths ([[3/2]]) exceed 18 [[octave]]s. This may not seem like much of a comma, but since [[31edo]] is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense. This approach leads to the prajapati temperament and the gallium temperament.		By the ''31-3-comma'' is meant 617673396283947/562949953421312 = {{monzo\| -49 31 }}, the amount (160.605 [[cent]]s) by which 31 just perfect fifths ([[3/2]]) exceed 18 [[octave]]s. This may not seem like much of a comma, but since [[31edo]] is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense. This approach leads to the prajapati temperament and the gallium temperament.