User:Frostburn/Fourth-equivalent Interval Classes

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These tables list interval classes under 4/3-equivalence ordered by complexity analogous to odd-limit.

The tables only list new entries. The limits contain all previous limits.

Note that every fourth table is empty (no new entries).

1-(4/3-odd)-limit

Representative Subunison Inbounds Above or at 4/3
1 3/4 1 4/3

2-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
2 27/32 9/8 3/2
1/2 8/9 32/27 128/81

3-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
1/3 64/81 256/243 1024/729
3 243/256 81/64 27/16

5-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
5/2 405/512 135/128 45/32
4/5 4/5 16/15 64/45
1/5 1024/1215 4096/3645 16384/10935
5 3645/4096 1215/1024 405/256
5/3 15/16 5/4 5/3
2/5 128/135 512/405 2048/1215

6-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
6 6561/8192 2187/2048 729/512
5/6 5/6 10/9 40/27
6/5 9/10 6/5 8/5
1/6 2048/2187 8192/6561 32768/19683

7-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
4/7 16/21 64/63 256/189
7/5 63/80 21/20 7/5
1/7 4096/5103 16384/15309 65536/45927
7/2 1701/2048 567/512 189/128
6/7 6/7 8/7 32/21
7/6 7/8 7/6 14/9
2/7 512/567 2048/1701 8192/5103
7 15309/16384 5103/4096 1701/1024
5/7 20/21 80/63 320/189
7/3 63/64 21/16 7/4

9-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
9/5 243/320 81/80 27/20
7/9 7/9 28/27 112/81
1/9 16384/19683 65536/59049 262144/177147
9 59049/65536 19683/16384 6561/4096
9/7 27/28 9/7 12/7
5/9 80/81 320/243 1280/729

10-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
10 98415/131072 32805/32768 10935/8192
10/7 45/56 15/14 10/7
7/10 14/15 56/45 224/135
1/10 32768/32805 131072/98415 524288/295245

11-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
2/11 2048/2673 8192/8019 32768/24057
11/6 99/128 33/32 11/8
5/11 80/99 320/297 1280/891
9/11 9/11 12/11 16/11
11/10 33/40 11/10 22/15
11 216513/262144 72171/65536 24057/16384
7/11 28/33 112/99 448/297
4/11 256/297 1024/891 4096/2673
11/3 891/1024 297/256 99/64
11/7 99/112 33/28 11/7
1/11 65536/72171 262144/216513 1048576/649539
10/11 10/11 40/33 160/99
11/9 11/12 11/9 44/27
11/5 297/320 99/80 33/20
8/11 32/33 128/99 512/297
11/2 8019/8192 2673/2048 891/512

13-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
1/13 65536/85293 262144/255879 1048576/767637
10/13 10/13 40/39 160/117
13/3 3159/4096 1053/1024 351/256
13/7 351/448 117/112 39/28
13/9 13/16 13/12 13/9
8/13 32/39 128/117 512/351
13/5 1053/1280 351/320 117/80
11/13 11/13 44/39 176/117
2/13 8192/9477 32768/28431 131072/85293
13/2 28431/32768 9477/8192 3159/2048
13/11 39/44 13/11 52/33
5/13 320/351 1280/1053 5120/3159
13/6 117/128 39/32 13/8
12/13 12/13 16/13 64/39
7/13 112/117 448/351 1792/1053
4/13 1024/1053 4096/3159 16384/9477
13/10 39/40 13/10 26/15
13 255879/262144 85293/65536 28431/16384

14-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
11/14 11/14 22/21 88/63
14 413343/524288 137781/131072 45927/32768
14/13 21/26 14/13 56/39
5/14 160/189 640/567 2560/1701
14/5 567/640 189/160 63/40
13/14 13/14 26/21 104/63
1/14 131072/137781 524288/413343 2097152/1240029
14/11 21/22 14/11 56/33

15-(4/3-odd)-limit

Representative Subunison Inbounds Above 4/3
15/11 135/176 45/44 15/11
7/15 112/135 448/405 1792/1215
15 885735/1048576 295245/262144 98415/65536
15/13 45/52 15/13 20/13
13/15 13/15 52/45 208/135
1/15 262144/295245 1048576/885735 4194304/2657205
15/7 405/448 135/112 45/28
11/15 44/45 176/135 704/405
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