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 <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]]

Latest revision as of 02:47, 4 November 2024

Interval information
Ratio 59049/57344
Factorization 2-13 × 310 × 7-1
Monzo [-13 10 0 -1⟩
Size in cents 50.7241¢
Name Harrison's comma
Color name Lr-2, Laru comma
FJS name [math]\displaystyle{ \text{d}{-2}_{7} }[/math]
Special properties reduced
Tenney height (log2 nd) 31.657
Weil height (log2 max(n, d)) 31.6993
Wilson height (sopfr(nd)) 63
Comma size medium
Open this interval in xen-calc

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.

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