BudjarnLambeth: Categorise uncategorised page

2025-10-01T09:34:03Z

Categorise uncategorised page

← Older revision		Revision as of 09:34, 1 October 2025
Line 490:		Line 490:
	\|}		\|}
	The smallest EDO to be consistent in the 57-odd-limit is [[20567edo]], on which it is also distinctly consistent and ''almost'' purely consistent (harmonic 49 is off by 26.3%).		The smallest EDO to be consistent in the 57-odd-limit is [[20567edo]], on which it is also distinctly consistent and ''almost'' purely consistent (harmonic 49 is off by 26.3%).

			[[Category:Odd limits]]

Eufalesio: added the new navigation system... but I reckon the seven previous odd limit pages would have to be created

2025-09-23T15:40:40Z

added the new navigation system... but I reckon the seven previous odd limit pages would have to be created

← Older revision		Revision as of 15:40, 23 September 2025
Line 1:		Line 1:
	{{Odd-limit navigation}}¨The '''57-odd-limit''' is the set of all [[Rational interval\|rational intervals]] which can be written as 2<sup>''k''</sup>(''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.		{{Odd-limit navigation\|57}}¨The '''57-odd-limit''' is the set of all [[Rational interval\|rational intervals]] which can be written as 2<sup>''k''</sup>(''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.

	Below is a list of all octave-reduced intervals in the 57-odd-limit.		Below is a list of all octave-reduced intervals in the 57-odd-limit.

Eufalesio: rephrased things a bit for 20567edo

2025-09-18T21:41:41Z

rephrased things a bit for 20567edo

← Older revision		Revision as of 21:41, 18 September 2025
Line 489:		Line 489:
	\|twenuno octave		\|twenuno octave
	\|}		\|}
	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~~.		The smallest EDO to be consistent in the 57-odd-limit is [[20567edo]], on which it is also distinctly consistent and ''almost'' purely consistent (harmonic 49 is off by 26.3%).

Eufalesio at 20:48, 18 September 2025

2025-09-18T20:48:59Z

Show changes

Eufalesio: Adding some links

2025-09-18T20:20:56Z

Adding some links

Show changes

Eufalesio: fixed incorrect format, missing links on all intervals, added navigation

2025-09-16T18:34:52Z

fixed incorrect format, missing links on all intervals, added navigation

Show changes

Eufalesio: Birth

2025-09-16T17:42:28Z

Birth

New page

The '''57-odd-limit''' is the set of all [[Rational interval|rational intervals]] which can be written as 2<sup>''k''</sup>(''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.

Below is a list of all octave-reduced intervals in the 57-odd-limit.
{| class="wikitable mw-collapsible mw-collapsed"
|+57-odd-limit intervals
|1
|2
|-
|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
|}
{| class="wikitable"
|Ratio
|'''Size ('''[[Cents|¢]]''')'''
|Color name
|-
|58/57
|30.109
|twenonu unison
|-
|57/56
|30.642
|noru unison
|-
|57/55
|61.836
|nolugu 2nd
|-
|57/53
|125.963
|fithuno 2nd
|-
|62/57
|145.568
|thiwonu unison
|-
|57/52
|158.94
|nothu 2nd
|-
|64/57
|200.532
|inu 2nd
|-
|57/50
|226.841
|nogugu 3rd
|-
|57/49
|261.816
|noruru 2nd
|-
|68/57
|305.487
|nuso 3rd
|-
|57/47
|333.961
|fosuno 3rd
|-
|70/57
|355.672
|nuzoyo 3rd
|-
|57/46
|371.194
|twethuno 3rd
|-
|57/44
|448.15
|nolu 4th
|-
|74/57
|451.876
|thisonu 4th
|-
|57/43
|487.95
|fothuno 4th
|-
|57/41
|570.406
|fowuno 4th
|-
|80/57
|586.846
|nuyo 4th
|-
|57/40
|613.154
|nogu 5th
|-
|82/57
|629.594
|fowunu 4th
|-
|86/57
|712.05
|fothonu 5th
|-
|57/37
|748.124
|thisuno 5th
|-
|88/57
|751.85
|nulo 5th
|-
|92/57
|828.806
|twethonu 6th
|-
|57/35
|844.328
|norugu 6th
|-
|94/57
|866.039
|fosonu 6th
|-
|57/34
|894.513
|nosu 6th
|-
|98/57
|938.184
|nuzozo 7th
|-
|100/57
|973.159
|nuyoyo 6th
|-
|57/32
|999.468
|ino 7th
|-
|104/57
|1041.06
|nutho 7th
|-
|57/31
|1054.432
|thiwuno octave
|-
|106/57
|1074.037
|fithonu 7th
|-
|110/57
|1138.164
|nuloyo 7th
|-
|112/57
|1169.358
|nuzo octave
|-
|57/29
|1169.891
|twenuno octave
|}
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.

57-odd-limit - Revision history

BudjarnLambeth: Categorise uncategorised page

Eufalesio: added the new navigation system... but I reckon the seven previous odd limit pages would have to be created

Eufalesio: rephrased things a bit for 20567edo

Eufalesio at 20:48, 18 September 2025

Eufalesio: Adding some links

Eufalesio: fixed incorrect format, missing links on all intervals, added navigation

Eufalesio: Birth