57-odd-limit: Difference between revisions

The '''57-odd-limit''' is the set of all [[Rational interval|rational intervals]] which can be written as 2^''k''(''a''/''b'') where ''a'', ''b'' ≤ 57 and ''k'' is an integer. To the 55-odd-limit, it adds 18 pairs of [[octave-reduced]] intervals involving 57.

|1

|58/57

|57/29

|57/56

|112/57

|56/55

|55/28

|55/54

|108/55

|54/53

|53/27

|53/52

|104/53

|52/51

|51/26

|51/50

|100/51

|50/49

|49/25

|49/48

|96/49

|48/47

|47/24

|47/46

|92/47

|46/45

|45/23

|45/44

|88/45

|44/43

|43/22

|43/42

|84/43

|42/41

|41/21

|41/40

|80/41

|40/39

|39/20

|39/38

|76/39

|38/37

|37/19

|37/36

|72/37

|36/35

|35/18

|35/34

|68/35

|34/33

|33/17

|33/32

|64/33

|32/31

|31/16

|31/30

|60/31

|30/29

|29/15

|29/28

|56/29

|57/55

|110/57

|28/27

|27/14

|55/53

|106/55

|27/26

|52/27

|53/51

|102/53

|26/25

|25/13

|51/49

|98/51

|25/24

|48/25

|49/47

|94/49

|24/23

|23/12

|47/45

|90/47

|23/22

|44/23

|45/43

|86/45

|22/21

|21/11

|43/41

|82/43

|21/20

|40/21

|41/39

|78/41

|20/19

|19/10

|39/37

|74/39

|58/55

|55/29

|19/18

|36/19

|56/53

|53/28

|37/35

|70/37

|55/52

|104/55

|18/17

|17/9

|53/50

|100/53

|35/33

|66/35

|52/49

|49/26

|17/16

|32/17

|50/47

|47/25

|33/31

|62/33

|49/46

|92/49

|16/15

|15/8

|47/44

|88/47

|31/29

|58/31

|46/43

|43/23

|15/14

|28/15

|44/41

|41/22

|29/27

|54/29

|43/40

|80/43

|57/53

|106/57

|14/13

|13/7

|55/51

|102/55

|41/38

|76/41

|27/25

|50/27

|40/37

|37/20

|53/49

|98/53

|13/12

|24/13

|51/47

|94/51

|38/35

|35/19

|25/23

|46/25

|62/57

|57/31

|37/34

|68/37

|49/45

|11/6

|12/11

|86/47

|47/43

|64/35

|35/32

|53/29

|58/53

|42/23

|23/21

|104/57

|57/52

|31/17

|34/31

|82/45

|45/41

|51/28

|56/51

|20/11

|11/10

|49/27

|54/49

|78/43

|43/39

|29/16

|32/29

|96/53

|53/48

|38/21

|21/19

|47/26

|52/47

|56/31

|31/28

|74/41

|41/37

|92/51

|51/46

|9/5

|10/9

|88/49

|49/44

|70/39

|39/35

|52/29

|29/26

|43/24

|48/43

|34/19

|19/17

|84/47

|47/42

|25/14

|28/25

|66/37

|37/33

|41/23

|46/41

|98/55

|55/49

|57/32

|64/57

|16/9

|9/8

|55/31

|62/55

|94/53

|53/47

|39/22

|44/39

|62/35

|35/31

|23/13

|26/23

|76/43

|43/38

|53/30

|60/53

|30/17

|17/15

|37/21

|42/37

|44/25

|25/22

|51/29

|58/51

|58/33

|33/29

|72/41

|41/36

|86/49

|49/43

|100/57

|57/50

|7/4

|8/7

|96/55

|55/48

|38/39

|47/41

|82/47

|39/34

|68/39

|31/27

|54/31

|54/47

|47/27

|23/20

|40/23

|38/33

|33/19

|53/46

|92/53

|15/13

|26/15

|52/45

|45/26

|37/32

|64/37

|22/19

|19/11

|51/44

|88/51

|29/25

|50/29

|36/31

|31/18

|43/37

|74/43

|50/43

|43/25

|57/49

|98/57

|64/55

|55/32

|7/6

|12/7

|62/53

|53/31

|55/47

|94/55

|48/41

|41/24

|41/35

|70/41

|34/29

|29/17

|27/23

|46/27

|47/40

|80/47

|20/17

|17/10

|53/45

|90/53

|33/28

|56/33

|46/39

|39/23

|13/11

|22/13

|58/49

|49/29

|45/38

|76/45

|32/27

|27/16

|51/43

|86/51

|19/16

|32/19

|44/37

|37/22

|25/21

|42/25

|56/47

|47/28

|31/26

|52/31

|68/57

|57/34

|37/31

|62/37

|43/36

|72/43

|49/41

|82/49

|55/46

|92/55

|6/5

|5/3

|53/44

|88/53

|47/39

|78/47

|41/34

|68/41

|35/29

|58/35

|64/53

|53/32

|29/24

|48/29

|52/43

|43/26

|23/19

|38/23

|40/33

|33/20

|57/47

|94/57

|17/14

|28/17

|62/51

|51/31

|45/37

|74/45

|28/23

|23/14

|39/32

|64/39

|50/41

|41/25

|11/9

|18/11

|60/49

|49/30

|49/40

|80/49

|38/31

|31/19

|27/22

|44/27

|70/57

|57/35

|43/35

|70/43

|16/13

|13/8

|53/43

|86/53

|37/30

|60/37

|58/47

|47/29

|21/17

|34/21

|68/55

|55/34

|47/38

|76/47

|26/21

|21/13

|57/46

|92/57

|31/25

|50/31

|36/29

|29/18

|41/33

|66/41

|46/37

|37/23

|51/41

|82/51

|56/45

|45/28

|66/53

|53/33

|5/4

|8/5

|64/51

|51/32

|54/43

|43/27

|49/39

|78/49

|44/35

|35/22

|39/31

|62/39

|34/27

|27/17

|29/23

|46/29

|53/42

|84/53

|24/19

|19/12

|43/34

|68/43

|62/49

|49/31

|19/15

|30/19

|52/41

|41/26

|33/26

|52/33

|47/37

|74/47

|14/11

|11/7

|51/40

|80/51

|37/29

|58/37

|60/47

|47/30

|23/18

|36/23

|55/43

|86/55

|32/25

|25/16

|41/32

|64/41

|50/39

|39/25

|68/53

|53/34

|9/7

|14/9

|58/45

|45/29

|49/38

|76/49

|40/31

|31/20

|31/24

|48/31

|53/41

|82/53

|22/17

|17/11

|57/44

|88/57

|35/27

|54/35

|48/37

|37/24

|74/57

|57/37

|13/10

|20/13

|56/43

|43/28

|43/33

|66/43

|30/23

|23/15

|47/36

|72/47

|64/49

|49/32

|17/13

|26/17

|72/55

|55/36

|55/42

|84/55

|38/29

|29/19

|21/16

|32/21

|46/35

|35/23

|25/19

|38/25

|54/41

|41/27

|29/22

|44/29

|62/47

|47/31

|33/25

|50/33

|70/53

|53/35

|37/28

|56/37

|41/31

|62/41

|45/34

|68/45

|49/37

|74/49

|53/40

|80/53

|57/43

|86/57

|4/3

|3/2

|55/41

|82/55

|51/38

|76/51

|47/35

|70/47

|43/32

|64/43

|39/29

|58/39

|74/55

|55/37

|35/26

|52/35

|66/49

|49/33

|31/23

|46/31

|58/43

|43/29

|27/20

|40/27

|50/37

|37/25

|23/17

|34/23

|42/31

|31/21

|19/14

|28/19

|72/53

|53/36

|53/39

|78/53

|34/25

|25/17

|49/36

|72/49

|64/47

|47/32

|15/11

|22/15

|56/41

|41/28

|41/30

|60/41

|26/19

|19/13

|37/27

|54/37

|48/35

|35/24

|70/51

|51/35

|11/8

|16/11

|62/45

|45/31

|51/37

|74/51

|40/29

|29/20

|29/21

|42/29

|76/55

|55/38

|47/34

|68/47

|18/13

|13/9

|43/31

|62/43

|68/49

|49/34

|25/18

|36/25

|57/41

|82/57

|32/23

|23/16

|39/28

|56/39

|46/33

|33/23

|53/38

|76/53

|60/43

|43/30

|74/53

|53/37

|7/5

|10/7

|80/57

|57/40

|66/47

|47/33

|52/37

|37/26

|45/32

|64/45

|38/27

|27/19

|31/22

|44/31

|55/39

|78/55

|24/17

|17/12

|41/29

|58/41

The smallest EDO to be consistent in the 57-odd-limit is [[20567edo]]. It is also distinctly consistent and almost purely consistent in the 57-odd-limit.