Harrison's comma: Difference between revisions

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59049/57344~~, or~~ Harrison's ~~[[Comma~~|~~comma]], is the amount by which ten 3/2s exceed 7/4 (all octave-reduced). In other words~~, ~~(3/2)^10 = 7 * 59049/57344. It is tempered out in [[Meantone_family~~|~~septimal meantone]], where ten generators is mapped to 7/4.~~

{{Infobox Interval

| Ratio = 59049/57344

| Name = Harrison's comma

| Color name = Lr-2, Laru comma

| Comma = yes

}}

~~Its~~ [[~~monzo|monzo~~]] ~~is |~~ -13 10 ~~0 -1 >~~

'''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 [[comma]]s as ([[81/80]])2([[225/224]]), that is, two syntonic commas and a marvel comma.

~~Its value is 50.72410 cents~~.~~~~

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]]

~~{| class="wikitable"~~

[[Category:Commas named after individuals]]

|-

~~| | 59049/57344~~

|}

~~~~

[[Category:~~Medium comma~~]]

[[Category:~~Todo:improve layout~~]]

@@ Line 1: / Line 1: @@
-/57344, or Harrison's [[Comma|comma]], is the amount by which ten 3/2s exceed 7/4 <span style="line-height: 1.5;">(all octave-reduced). In other words, (3/2)^10 = 7 * 59049/57344. It is tempered out in [[Meantone_family|septimal meantone]]</span>, where ten generators is mapped to 7/4<span style="line-height: 1.5;">.</span>
+{{Infobox Interval
+| Ratio = 59049/57344
+| Name = Harrison's comma
+| Color name = Lr-2, Laru comma
+| Comma = yes
+}}
-Its [[monzo|monzo]] is | -13 10 0 -1 &gt;
+'''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.
-<span style="line-height: 1.5;">Its value is </span><span style="text-align: -webkit-right;">50.72410 cents.</span>
+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]].
-<span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 25px; width: 1px;">
+[[Category:Quartertone]]
+[[Category:Meantone]]
-{| class="wikitable"
+[[Category:Commas named after individuals]]
-|-
+{{todo|add etymology|comment=Who was Harrison?}}
-| | 59049/57344
-|}
-</span>
-[[Category:Medium comma]]
-[[Category:Todo:improve layout]]