User:Frostburn/Fifth-equivalent Interval Classes: Difference between revisions

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Remove duplicates. Sort by inbounds intervals.
 
Line 24: Line 24:
| 2/1 || 8/9 || 4/3 || 2/1
| 2/1 || 8/9 || 4/3 || 2/1
|}
|}
== 4-(3/2-odd)-limit ==
== 4-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
Line 30: Line 29:
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
| 4 || 64/81 || 32/27 || 16/9
|-
|-
| 1/4 || 27/32 || 81/64 || 243/128  
| 1/4 || 27/32 || 81/64 || 243/128  
|-
| 4/1 || 8/3 || 4/1 || 6/1
|}
|}
== 5-(3/2-odd)-limit ==
== 5-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
|-
| 5/4 || 5/6 || 5/4 || 15/8
| 1/5 || 27/40 || 81/80 || 243/160
|-
|-
| 5/2 || 5/3 || 5/2 || 15/4
| 5/2 || 20/27 || 10/9 || 5/3  
|-
| 5/1 || 10/3 || 5/1 || 15/2
|-
|-
| 4/5 || 4/5 || 6/5 || 9/5  
| 4/5 || 4/5 || 6/5 || 9/5  
|-
|-
| 5/3 || 10/9 || 5/3 || 5/2
| 5/4 || 5/6 || 5/4 || 15/8
|-
|-
| 3/5 || 9/10 || 27/20 || 81/40  
| 3/5 || 9/10 || 27/20 || 81/40  
|-
|-
| 2/5 || 9/10 || 27/20 || 81/40  
| 5 || 80/81 || 40/27 || 20/9
|-
| 1/5 || 27/40 || 81/80 || 243/160
|}
|}
== 7-(3/2-odd)-limit ==
== 7-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
| 7/4 || 7/6 || 7/4 || 21/8
|-
|-
| 7/2 || 7/3 || 7/2 || 21/4
| 7/2 || 56/81 || 28/27 || 14/9
|-
|-
| 5/7 || 5/7 || 15/14 || 45/28  
| 5/7 || 5/7 || 15/14 || 45/28  
|-
|-
| 7/1 || 14/3 || 7/1 || 21/2
| 1/7 || 81/112 || 243/224 || 729/448
|-
|-
| 3/7 || 27/28 || 81/56 || 243/112
| 7/4 || 7/9 || 7/6 || 7/4
|-
|-
| 7/6 || 7/9 || 7/6 || 7/4
| 6/7 || 6/7 || 9/7 || 27/14
|-
| 1/7 || 81/112 || 243/224 || 729/448
|-
|-
| 6/7 || 6/7 || 9/7 || 27/14
| 7 || 224/243 || 112/81 || 56/27  
|-
|-
| 7/5 || 14/15 || 7/5 || 21/10  
| 7/5 || 14/15 || 7/5 || 21/10  
|-
|-
| 4/7 || 6/7 || 9/7 || 27/14
| 3/7 || 27/28 || 81/56 || 243/112  
|-
| 2/7 || 27/28 || 81/56 || 243/112  
|-
| 7/3 || 14/9 || 7/3 || 7/2
|}
|}
== 8-(3/2-odd)-limit ==
== 8-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
|-
| 1/8 || 243/256 || 729/512 || 2187/1024
| 8 || 512/729 || 256/243 || 128/81
|-
| 8/5 || 32/45 || 16/15 || 8/5
|-
|-
| 5/8 || 15/16 || 45/32 || 135/64
| 8/7 || 16/21 || 8/7 || 12/7
|-
|-
| 7/8 || 7/8 || 21/16 || 63/32  
| 7/8 || 7/8 || 21/16 || 63/32  
|-
|-
| 8/1 || 16/3 || 8/1 || 12/1
| 5/8 || 15/16 || 45/32 || 135/64
|-
|-
| 8/5 || 16/15 || 8/5 || 12/5
| 1/8 || 243/256 || 729/512 || 2187/1024
|-
| 8/7 || 16/21 || 8/7 || 12/7
|}
|}
== 10-(3/2-odd)-limit ==
== 10-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
|-
| 7/10 || 7/10 || 21/20 || 63/40  
| 7/10 || 7/10 || 21/20 || 63/40  
|-
|-
| 10/1 || 20/3 || 10/1 || 15/1
| 1/10 || 243/320 || 729/640 || 2187/1280
|-
|-
| 1/10 || 243/320 || 729/640 || 2187/1280
| 10 || 640/729 || 320/243 || 160/81
|-
|-
| 10/7 || 20/21 || 10/7 || 15/7  
| 10/7 || 20/21 || 10/7 || 15/7  
|}
|}
== 11-(3/2-odd)-limit ==
== 11-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
| 5/11 || 15/22 || 45/44 || 135/88
|-
|-
| 11/8 || 11/12 || 11/8 || 33/16
| 1/11 || 243/352 || 729/704 || 2187/1408
|-
|-
| 11/4 || 11/6 || 11/4 || 33/8
| 11/7 || 44/63 || 22/21 || 11/7
|-
|-
| 11/2 || 11/3 || 11/2 || 33/4
| 11/2 || 176/243 || 88/81 || 44/27
|-
|-
| 2/11 || 81/88 || 243/176 || 729/352
| 8/11 || 8/11 || 12/11 || 18/11
|-
|-
| 11/1 || 22/3 || 11/1 || 33/2
| 11/10 || 11/15 || 11/10 || 33/20
|-
| 4/11 || 9/11 || 27/22 || 81/44
|-
| 11/5 || 22/15 || 11/5 || 33/10
|-
| 6/11 || 9/11 || 27/22 || 81/44
|-
| 11/3 || 22/9 || 11/3 || 11/2
|-
|-
| 8/11 || 8/11 || 12/11 || 18/11
| 11/4 || 22/27 || 11/9 || 11/6
|-
|-
| 11/7 || 22/21 || 11/7 || 33/14
| 9/11 || 9/11 || 27/22 || 81/44
|-
|-
| 10/11 || 10/11 || 15/11 || 45/22  
| 10/11 || 10/11 || 15/11 || 45/22  
|-
|-
| 1/11 || 243/352 || 729/704 || 2187/1408
| 11/8 || 11/12 || 11/8 || 33/16
|-
| 11/10 || 11/15 || 11/10 || 33/20
|-
|-
| 3/11 || 81/88 || 243/176 || 729/352  
| 3/11 || 81/88 || 243/176 || 729/352  
|-
|-
| 11/6 || 11/9 || 11/6 || 11/4
| 7/11 || 21/22 || 63/44 || 189/88
|-
|-
| 5/11 || 15/22 || 45/44 || 135/88
| 11 || 704/729 || 352/243 || 176/81
|-
|-
| 11/9 || 22/27 || 11/9 || 11/6
| 11/5 || 44/45 || 22/15 || 11/5
|-
| 7/11 || 21/22 || 63/44 || 189/88
|-
| 9/11 || 9/11 || 27/22 || 81/44
|}
|}
== 13-(3/2-odd)-limit ==
== 13-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
| 9/13 || 9/13 || 27/26 || 81/52
|-
|-
| 13/8 || 13/12 || 13/8 || 39/16
| 13/8 || 13/18 || 13/12 || 13/8
|-
|-
| 13/4 || 13/6 || 13/4 || 39/8
| 13 || 1664/2187 || 832/729 || 416/243
|-
|-
| 13/2 || 13/3 || 13/2 || 39/4
| 10/13 || 10/13 || 15/13 || 45/26  
|-
| 1/13 || 729/832 || 2187/1664 || 6561/3328
|-
| 13/11 || 26/33 || 13/11 || 39/22
|-
| 13/1 || 26/3 || 13/1 || 39/2
|-
|-
| 2/13 || 81/104 || 243/208 || 729/416
| 13/5 || 104/135 || 52/45 || 26/15
|-
| 13/7 || 26/21 || 13/7 || 39/14
|-
|-
| 3/13 || 81/104 || 243/208 || 729/416  
| 3/13 || 81/104 || 243/208 || 729/416  
|-
|-
| 4/13 || 9/13 || 27/26 || 81/52
| 13/11 || 26/33 || 13/11 || 39/22
|-
| 13/6 || 13/9 || 13/6 || 13/4
|-
| 5/13 || 45/52 || 135/104 || 405/208
|-
| 6/13 || 9/13 || 27/26 || 81/52
|-
|-
| 7/13 || 21/26 || 63/52 || 189/104  
| 7/13 || 21/26 || 63/52 || 189/104  
|-
|-
| 13/9 || 26/27 || 13/9 || 13/6
| 13/7 || 52/63 || 26/21 || 13/7
|-
|-
| 8/13 || 12/13 || 18/13 || 27/13
| 11/13 || 11/13 || 33/26 || 99/52
|-
|-
| 13/5 || 26/15 || 13/5 || 39/10
| 13/2 || 208/243 || 104/81 || 52/27
|-
|-
| 13/12 || 13/18 || 13/12 || 13/8
| 5/13 || 45/52 || 135/104 || 405/208
|-
|-
| 13/3 || 26/9 || 13/3 || 13/2
| 13/10 || 13/15 || 13/10 || 39/20
|-
|-
| 9/13 || 9/13 || 27/26 || 81/52
| 1/13 || 729/832 || 2187/1664 || 6561/3328
|-
| 10/13 || 10/13 || 15/13 || 45/26
|-
| 13/10 || 13/15 || 13/10 || 39/20
|-
|-
| 11/13 || 11/13 || 33/26 || 99/52
| 12/13 || 12/13 || 18/13 || 27/13
|-
|-
| 12/13 || 12/13 || 18/13 || 27/13
| 13/4 || 26/27 || 13/9 || 13/6
|}
|}
== 14-(3/2-odd)-limit ==
== 14-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
| 14/13 || 28/39 || 14/13 || 21/13
|-
|-
| 14/5 || 28/15 || 14/5 || 21/5
| 11/14 || 11/14 || 33/28 || 99/56
|-
|-
| 13/14 || 13/14 || 39/28 || 117/56
| 5/14 || 45/56 || 135/112 || 405/224
|-
|-
| 14/13 || 28/39 || 14/13 || 21/13
| 1/14 || 729/896 || 2187/1792 || 6561/3584
|-
|-
| 14/1 || 28/3 || 14/1 || 21/1
| 14 || 1792/2187 || 896/729 || 448/243
|-
|-
| 5/14 || 45/56 || 135/112 || 405/224
| 14/5 || 112/135 || 56/45 || 28/15
|-
|-
| 14/11 || 28/33 || 14/11 || 21/11  
| 14/11 || 28/33 || 14/11 || 21/11  
|-
|-
| 1/14 || 729/896 || 2187/1792 || 6561/3584
| 13/14 || 13/14 || 39/28 || 117/56  
|-
| 11/14 || 11/14 || 33/28 || 99/56
|}
|}
== 16-(3/2-odd)-limit ==
== 16-(3/2-odd)-limit ==
{| class="wikitable"
{| class="wikitable"
|+
|+  
|-
|-
! Representative !! Subunison !! Inbounds !! Above 3/2
! Representative !! Subunison !! Inbounds !! Above 3/2
|-
|-
| 16/7 || 128/189 || 64/63 || 32/21
|-
|-
| 1/16 || 729/1024 || 2187/2048 || 6561/4096
| 11/16 || 11/16 || 33/32 || 99/64
|-
|-
| 5/16 || 45/64 || 135/128 || 405/256  
| 5/16 || 45/64 || 135/128 || 405/256  
|-
| 1/16 || 729/1024 || 2187/2048 || 6561/4096
|-
|-
| 13/16 || 13/16 || 39/32 || 117/64  
| 13/16 || 13/16 || 39/32 || 117/64  
|-
|-
| 7/16 || 63/64 || 189/128 || 567/256
| 16/13 || 32/39 || 16/13 || 24/13
|-
| 11/16 || 11/16 || 33/32 || 99/64
|-
|-
| 16/1 || 32/3 || 16/1 || 24/1
| 16 || 2048/2187 || 1024/729 || 512/243
|-
|-
| 16/13 || 32/39 || 16/13 || 24/13
| 16/5 || 128/135 || 64/45 || 32/15
|-
|-
| 16/5 || 32/15 || 16/5 || 24/5
| 16/11 || 32/33 || 16/11 || 24/11
|-
|-
| 16/7 || 32/21 || 16/7 || 24/7
| 7/16 || 63/64 || 189/128 || 567/256
|-
| 16/11 || 32/33 || 16/11 || 24/11
|}
|}

Latest revision as of 17:41, 9 June 2024

These tables list interval classes under 3/2-equivalence ordered by complexity analogous to odd-limit.

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

Note that every third table is empty similar to throdd-limit.

1-(3/2-odd)-limit

Representative Subunison Inbounds Above (or at) 3/2
1/1 2/3 1/1 3/2

2-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
1/2 3/4 9/8 27/16
2/1 8/9 4/3 2/1

4-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
4 64/81 32/27 16/9
1/4 27/32 81/64 243/128

5-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
1/5 27/40 81/80 243/160
5/2 20/27 10/9 5/3
4/5 4/5 6/5 9/5
5/4 5/6 5/4 15/8
3/5 9/10 27/20 81/40
5 80/81 40/27 20/9

7-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
7/2 56/81 28/27 14/9
5/7 5/7 15/14 45/28
1/7 81/112 243/224 729/448
7/4 7/9 7/6 7/4
6/7 6/7 9/7 27/14
7 224/243 112/81 56/27
7/5 14/15 7/5 21/10
3/7 27/28 81/56 243/112

8-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
8 512/729 256/243 128/81
8/5 32/45 16/15 8/5
8/7 16/21 8/7 12/7
7/8 7/8 21/16 63/32
5/8 15/16 45/32 135/64
1/8 243/256 729/512 2187/1024

10-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
7/10 7/10 21/20 63/40
1/10 243/320 729/640 2187/1280
10 640/729 320/243 160/81
10/7 20/21 10/7 15/7

11-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
5/11 15/22 45/44 135/88
1/11 243/352 729/704 2187/1408
11/7 44/63 22/21 11/7
11/2 176/243 88/81 44/27
8/11 8/11 12/11 18/11
11/10 11/15 11/10 33/20
11/4 22/27 11/9 11/6
9/11 9/11 27/22 81/44
10/11 10/11 15/11 45/22
11/8 11/12 11/8 33/16
3/11 81/88 243/176 729/352
7/11 21/22 63/44 189/88
11 704/729 352/243 176/81
11/5 44/45 22/15 11/5

13-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
9/13 9/13 27/26 81/52
13/8 13/18 13/12 13/8
13 1664/2187 832/729 416/243
10/13 10/13 15/13 45/26
13/5 104/135 52/45 26/15
3/13 81/104 243/208 729/416
13/11 26/33 13/11 39/22
7/13 21/26 63/52 189/104
13/7 52/63 26/21 13/7
11/13 11/13 33/26 99/52
13/2 208/243 104/81 52/27
5/13 45/52 135/104 405/208
13/10 13/15 13/10 39/20
1/13 729/832 2187/1664 6561/3328
12/13 12/13 18/13 27/13
13/4 26/27 13/9 13/6

14-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
14/13 28/39 14/13 21/13
11/14 11/14 33/28 99/56
5/14 45/56 135/112 405/224
1/14 729/896 2187/1792 6561/3584
14 1792/2187 896/729 448/243
14/5 112/135 56/45 28/15
14/11 28/33 14/11 21/11
13/14 13/14 39/28 117/56

16-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
16/7 128/189 64/63 32/21
11/16 11/16 33/32 99/64
5/16 45/64 135/128 405/256
1/16 729/1024 2187/2048 6561/4096
13/16 13/16 39/32 117/64
16/13 32/39 16/13 24/13
16 2048/2187 1024/729 512/243
16/5 128/135 64/45 32/15
16/11 32/33 16/11 24/11
7/16 63/64 189/128 567/256
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