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The isomorphism type of the Galois group G of finite 3-class field towers ofquadratic number fields with 3-class group of type (9,9) is determined by meansof Artin patterns which contain information on the transfer of 3-classes tounramified abelian 3-extensions. First, as an approximation of the group G, itsmetabelianization M=G/G", which is isomorphic to the Galois group of the secondHilbert 3-class field, is sought by sifting the SmallGroups library with theaid of pattern recognition. In cases with order |M|>3^8, the SmallGroupsdatabase must be extended by means of the p-group generation algorithm, whichreveals new phenomena of groups with harmonically balanced transfer kernels andtrees with periodic trifurcations. Bounds for the relation rank d2(M) of M independence on the signature of the quadratic base field admit the decisionwhether the derived length of G is dl(G)=2 or dl(G)>=3.

Harmonically balanced capitulation over quadratic fields of type (9,9)