Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

$n$	$Tn$	$Kn$

2	1	1
3	1	5
4	2	13
5	1	41
6	3	110
7	1	341
8	6	1035
9	4	3298
10	6	10550
11	1	34781
12	23	117455
13	1	397529
14	13	1.370798
15	25	4.780715
16	49	16788150
17	1	59451809
18	91	212.178317
19	1	761.456429
20	149	2749.100993
21	121	9973.716835
22	99	36347.760182
23	1	133022.502005
24	794	488685.427750
25	126	1.801445.810166
26	322	6.662133.496934
27	766	24.711213.822232
28	1301	91.910318.016551
29	1	342.723412.096889
30	3952	1281.025524.753966
31	1	4798.840870.353221
32	4641	18014.401038.596400
33	5409	67756.652509.423763
34	3864	255318.257892.932894
35	2713	963748.277489.391403
36	31651	3.643801.587330.857840
37	1	13.798002.875101.582409
38	13807	52.325390.403899.973926
39	40937	198.705759.014912.561995
40	64989	755.578639.350274.265100

Table 2:

Numbers of non-isomorphic tiling canons (second column) and canons (third column) in $Zn$ .

The construction described above yields a complete list of all rhythmic canons, whence also the number of rhythmic tiling canons in $Zn$ , indicated by $Tn$ , given in the second column of table 2.

5 Some Results on Regular Complementary Canons of Maximal Category

In Vuza (1991, 1992b,a, 1993) the author showed for which $n$ there exist regular complementary canons of maximal category. Moreover, he described a method how to construct regular complementary canons of maximal category for those $Zn$