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|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.


[[Category:Medium comma]]
[[Category:Medium commas]]
[[Category:Quartertone]]
[[Category:Quartertone]]

Revision as of 21:53, 20 March 2022

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 norm (log2 nd) 31.657
Weil norm (log2 max(n, d)) 31.6993
Wilson norm (sopfr(nd)) 63
Open this interval in xen-calc

59049/57344, or Harrison's 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 septimal meantone, where ten generators is mapped to 7/4.