Hahn distance: Difference between revisions
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</math> | </math> | ||
where y = signum(x2)ceil | where y = signum(x2){{ceil|{{abs|x2/2}}}}; here "signum" is +1 or −1 depending on the sign of x2 and {{ceil|''x''}} is the ceiling function. Hahn distance for the 9 or 11 limit can also be found from this formula. | ||
It should be noted that this formula defines a {{w|Metric space|metric space distance function}} but not a norm, and hence does not define a normed vector space, making the 9-, 11- or 13-limit pitch classes into a lattice. We can modify it to | It should be noted that this formula defines a {{w|Metric space|metric space distance function}} but not a norm, and hence does not define a normed vector space, making the 9-, 11- or 13-limit pitch classes into a lattice. We can modify it to | ||