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RE: [tuning] error in Dictionary entry fixed

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

4/19/2000 12:09:38 PM

>Paul Erlich pointed out [TD 605.10] an error in the 'Harmonic
>Distance' entry of my Tuning Dictionary.

>http://www.ixpres.com/interval/dict/harmonicdistance.htm

>It's been fixed. Thanks, Paul!

I wonder why, in this definition, Chalmers refers to the city-block metric
as the "Minkowski metric". The only definitions of the Minkowski metric I've
ever seen are the usual special relativistic space-time distance -- see
http://aci.mta.ca/Courses/Physics/4701/EText/MinkowskiMetric.html
or
http://mathworld.wolfram.com/MinkowskiMetric.html
or
http://www.treasure-troves.com/physics/MinkowskiMetric.html;
and a generalized Euclidean metric where the exponents 2 and 1/2 are
replaced with p and 1/p respectively (p can be infinite, in which case one
takes a limit):
http://www.cs.mcgill.ca/~scottyb/DistTrans/Project.html
or
http://www.ctr.columbia.edu/~jrsmith/html/pubs/acmmm96/node8.html
or
http://zx81.ncsa.uiuc.edu/camilleg/eviolin.html (a MIDI violin controller!)

So what Chalmers really means is, using the second definition, the Minkowski
_first-order_ metric. Subject to Chalmers' approval, I suggest we change
that definition.

It also might help to give an example using a ratio with one even number, to
emphasize that one doesn't ignore factors of 2 in this computation.