Harrison's comma: Difference between revisions

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-'''59049/57344''', or Harrison's [[Comma|comma]], is the amount by which ten [[3/2]]s exceed [[7/4]] (all octave-reduced). In other words, (3/2)<sup>10</sup> = 7 ⋅ 59049/57344. It is tempered out in [[Meantone family|septimal meantone]], where ten generators is mapped to 7/4.
+'''59049/57344''', or '''Harrison's comma''', is the amount by which ten [[3/2]]'s exceed [[7/4]] (all octave-reduced). In other words, (3/2)<sup>10</sup> = 7 ⋅ 59049/57344. It factors into simpler [[comma]]s as ([[81/80]])<sup>2</sup>([[225/224]]), that is, two syntonic commas and a marvel comma.
+Tempering out this comma will map the 7/4 to the augmented sixth (e.g. C-A♯), and the only notable 7-limit temperament that does that is [[septimal meantone]].
 [[Category:Quartertone]]
+[[Category:Meantone]]
+[[Category:Commas named after individuals]]
+{{todo|add etymology|comment=Who was Harrison?}}