Harrison's comma: Difference between revisions
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'''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. | '''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- | 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:Quartertone]] | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
Revision as of 17:08, 6 May 2024
| Interval information |
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)10 = 7 ⋅ 59049/57344. It factors into simpler commas as (81/80)2(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.