Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

geometric complexity

[Gene Ward Smith, Yahoo tuning-math group message]

I gave a definition of geometric complexity using natural logs; Graham suggested log base 2 instead. He also proposed taking the dth root of this, where d is the codimension of the wedgie--that is, the number of commas used to define it.

If G is the Graham geometric complexity under this definition, R is (rms or minimax, etc.) error, and n = pi(p) is the number of primes in the p-limit we are looking at, the formula for geometic badness now becomes: B = R Gn, which is pretty nice. Does anyone have a concern about switching definitions to the Graham version, which looks to me like a good idea?

. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

support level