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However, the description of the isomorphism classes of canons as pairs For finding the number of rhythmic tiling canons, we make use of still another result concerning regular complementary canons of maximal category. First we realize that |
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However, the description of the isomorphism classes of canons as pairs For finding the number of rhythmic tiling canons, we make use of still another result concerning regular complementary canons of maximal category. First we realize that |
of block-type 
.
consisting of Lyndon words 
and 
-orbits of subsets 
of 
with some additional properties (c.f. Lemma 7) can also be used for the determination of complete sets of representatives of non-isomorphic canons in 
, as was indicated in the last part of 
over 
and all 
-orbit representatives of subsets of 
. For finding rhythmic tiling canons with 
voices (where 
is necessarily a divisor of 
), we can restrict ourselves to Lyndon words 
with exactly 
entries 
and to representatives 
of the 
-orbits of 
-subsets of 
. Then each pair 
must be tested whether it is a regular tiling canon. In this test we only have to test whether the voices described by 
determine a partition on 
, because in this case it is obvious that 
does not satisfy the assumptions of Lemma 7. 
is a tiling canon if and only if 
is the direct sum 
, i.e. 
and 
. In other words, for each element 
there exists exactly one pair 
such that 
.