Frostburn: Created page with "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 limit..."

2024-06-10T08:43:23Z

Created page with "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 limit..."

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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 ==
{| class="wikitable"
|+
|-
! Representative !! Subunison !! Inbounds !! Above or at 4/3
|-
| 1 || 3/4 || 1 || 4/3
|}
== 2-(4/3-odd)-limit ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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 ==
{| class="wikitable"
|+
|-
! 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
|}

User:Frostburn/Fourth-equivalent Interval Classes - Revision history

Frostburn: Created page with "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 limit..."