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

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Create page. Add first two sets.
 
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Add more tables
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These tables list interval classes under 3/2-equivalence ordered by complexity analogous to [[odd-limit]].
These tables list interval classes under 3/2-equivalence ordered by complexity analogous to [[odd-limit]].


Note that every third set is empty similar to throdd-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 ==
== 1-(3/2-odd)-limit ==
Line 23: Line 25:
|}
|}


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

Revision as of 17:26, 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
1/4 27/32 81/64 243/128
4/1 8/3 4/1 6/1

5-(3/2-odd)-limit

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

7-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
7/4 7/6 7/4 21/8
7/2 7/3 7/2 21/4
5/7 5/7 15/14 45/28
7/1 14/3 7/1 21/2
3/7 27/28 81/56 243/112
7/6 7/9 7/6 7/4
1/7 81/112 243/224 729/448
6/7 6/7 9/7 27/14
7/5 14/15 7/5 21/10
4/7 6/7 9/7 27/14
2/7 27/28 81/56 243/112
7/3 14/9 7/3 7/2

8-(3/2-odd)-limit

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

10-(3/2-odd)-limit

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

11-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
11/8 11/12 11/8 33/16
11/4 11/6 11/4 33/8
11/2 11/3 11/2 33/4
2/11 81/88 243/176 729/352
11/1 22/3 11/1 33/2
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
11/7 22/21 11/7 33/14
10/11 10/11 15/11 45/22
1/11 243/352 729/704 2187/1408
11/10 11/15 11/10 33/20
3/11 81/88 243/176 729/352
11/6 11/9 11/6 11/4
5/11 15/22 45/44 135/88
11/9 22/27 11/9 11/6
7/11 21/22 63/44 189/88
9/11 9/11 27/22 81/44

13-(3/2-odd)-limit

Representative Subunison Inbounds Above 3/2
13/8 13/12 13/8 39/16
13/4 13/6 13/4 39/8
13/2 13/3 13/2 39/4
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
13/7 26/21 13/7 39/14
3/13 81/104 243/208 729/416
4/13 9/13 27/26 81/52
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
13/9 26/27 13/9 13/6
8/13 12/13 18/13 27/13
13/5 26/15 13/5 39/10
13/12 13/18 13/12 13/8
13/3 26/9 13/3 13/2
9/13 9/13 27/26 81/52
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

14-(3/2-odd)-limit

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

16-(3/2-odd)-limit

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