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57edo: Difference between revisions

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m →Intervals: Fix a couple of places where the visual edit botched the formatting
→Intervals: don't add the 19edo interpretation of 9 if you don't intend to add the corresponding 3
Line 14: Line 14:


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2 center-3 center-4"
{| class="wikitable center-1 right-2 center-4 center-5"
|-
|-
! #
! #
! [[Cent]]s
! [[Cent]]s
!Approximate<br>ratios (in ''italics''<br>if inconsistent)
! Approximate ratios*
! [[Ups and downs notation|Ups and downs notation]]<br>(Flat Fifth 11\19)
! [[Kite's ups and downs notation|Ups and downs notation]]<br>(Flat fifth 11\19)
! [[Ups and downs notation|Ups and downs notation]]<br>(Sharp Fifth 34\57)
! [[Kite's ups and downs notation|Ups and downs notation]]<br>(Sharp fifth 34\57)
|-
|-
| 0
| 0
| 0.00
| 0.00
|[[1/1]]
| [[1/1]]
| {{UDnote|step=0}}
| {{UDnote|step=0}}
| {{UDnote|fifth=34|step=0}}
| {{UDnote|fifth=34|step=0}}
Line 42: Line 42:
| 3
| 3
| 63.16
| 63.16
|[[29/28]]
| [[29/28]]
| {{UDnote|step=3}}
| {{UDnote|step=3}}
| {{UDnote|fifth=34|step=3}}
| {{UDnote|fifth=34|step=3}}
Line 48: Line 48:
| 4
| 4
| 84.21
| 84.21
|[[20/19]], [[21/20]], [[22/21]]
| [[20/19]], [[21/20]], [[22/21]]
| {{UDnote|step=4}}
| {{UDnote|step=4}}
| {{UDnote|fifth=34|step=4}}
| {{UDnote|fifth=34|step=4}}
Line 54: Line 54:
| 5
| 5
| 105.26
| 105.26
|[[17/16]], [[33/31]]
| [[17/16]], [[33/31]]
| {{UDnote|step=5}}
| {{UDnote|step=5}}
| {{UDnote|fifth=34|step=5}}
| {{UDnote|fifth=34|step=5}}
Line 60: Line 60:
| 6
| 6
| 126.32
| 126.32
|[[14/13]], ''[[16/15]]''
| [[14/13]]
| {{UDnote|step=6}}
| {{UDnote|step=6}}
| {{UDnote|fifth=34|step=6}}
| {{UDnote|fifth=34|step=6}}
Line 66: Line 66:
| 7
| 7
| 147.37
| 147.37
|[[12/11]]
| [[12/11]]
| {{UDnote|step=7}}
| {{UDnote|step=7}}
| {{UDnote|fifth=34|step=7}}
| {{UDnote|fifth=34|step=7}}
Line 72: Line 72:
| 8
| 8
| 168.42
| 168.42
|[[11/10]], [[32/29]]
| [[11/10]], [[32/29]]
| {{UDnote|step=8}}
| {{UDnote|step=8}}
| {{UDnote|fifth=34|step=8}}
| {{UDnote|fifth=34|step=8}}
Line 78: Line 78:
| 9
| 9
| 189.47
| 189.47
|''[[9/8]]'', [[10/9]],<br>[[19/17]], [[29/26]]
| [[19/17]], [[29/26]]
| {{UDnote|step=9}}
| {{UDnote|step=9}}
| {{UDnote|fifth=34|step=9}}
| {{UDnote|fifth=34|step=9}}
Line 84: Line 84:
| 10
| 10
| 210.53
| 210.53
|[[26/23]]
| [[26/23]]
| {{UDnote|step=10}}
| {{UDnote|step=10}}
| {{UDnote|fifth=34|step=10}}
| {{UDnote|fifth=34|step=10}}
Line 90: Line 90:
| 11
| 11
| 231.58
| 231.58
|[[8/7]]
| [[8/7]]
| {{UDnote|step=11}}
| {{UDnote|step=11}}
| {{UDnote|fifth=34|step=11}}
| {{UDnote|fifth=34|step=11}}
Line 96: Line 96:
| 12
| 12
| 252.63
| 252.63
|[[22/19]]
| [[22/19]]
| {{UDnote|step=12}}
| {{UDnote|step=12}}
| {{UDnote|fifth=34|step=12}}
| {{UDnote|fifth=34|step=12}}
Line 102: Line 102:
| 13
| 13
| 273.68
| 273.68
|[[7/6]], [[34/29]]
| [[7/6]], [[34/29]]
| {{UDnote|step=13}}
| {{UDnote|step=13}}
| {{UDnote|fifth=34|step=13}}
| {{UDnote|fifth=34|step=13}}
Line 108: Line 108:
| 14
| 14
| 294.74
| 294.74
|[[19/16]]
| [[19/16]]
| {{UDnote|step=14}}
| {{UDnote|step=14}}
| {{UDnote|fifth=34|step=14}}
| {{UDnote|fifth=34|step=14}}
Line 114: Line 114:
| 15
| 15
| 315.79
| 315.79
|[[6/5]]
| [[6/5]]
| {{UDnote|step=15}}
| {{UDnote|step=15}}
| {{UDnote|fifth=34|step=15}}
| {{UDnote|fifth=34|step=15}}
Line 120: Line 120:
| 16
| 16
| 336.84
| 336.84
|[[17/14]], [[28/23]]
| [[17/14]], [[28/23]]
| {{UDnote|step=16}}
| {{UDnote|step=16}}
| {{UDnote|fifth=34|step=16}}
| {{UDnote|fifth=34|step=16}}
Line 126: Line 126:
| 17
| 17
| 357.89
| 357.89
|[[16/13]]
| [[16/13]]
| {{UDnote|step=17}}
| {{UDnote|step=17}}
| {{UDnote|fifth=34|step=17}}
| {{UDnote|fifth=34|step=17}}
Line 132: Line 132:
| 18
| 18
| 378.95
| 378.95
|[[5/4]]
| [[5/4]]
| {{UDnote|step=18}}
| {{UDnote|step=18}}
| {{UDnote|fifth=34|step=18}}
| {{UDnote|fifth=34|step=18}}
Line 138: Line 138:
| 19
| 19
| 400.00
| 400.00
|[[24/19]], [[29/23]]
| [[24/19]], [[29/23]]
| {{UDnote|step=19}}
| {{UDnote|step=19}}
| {{UDnote|fifth=34|step=19}}
| {{UDnote|fifth=34|step=19}}
Line 144: Line 144:
| 20
| 20
| 421.05
| 421.05
|''[[9/7]]'', [[14/11]]
| ''[[9/7]]'', [[14/11]]
| {{UDnote|step=20}}
| {{UDnote|step=20}}
| {{UDnote|fifth=34|step=20}}
| {{UDnote|fifth=34|step=20}}
Line 150: Line 150:
| 21
| 21
| 442.11
| 442.11
|[[22/17]], [[31/24]]
| [[22/17]], [[31/24]]
| {{UDnote|step=21}}
| {{UDnote|step=21}}
| {{UDnote|fifth=34|step=21}}
| {{UDnote|fifth=34|step=21}}
Line 156: Line 156:
| 22
| 22
| 463.16
| 463.16
|[[17/13]], [[21/16]], [[38/29]]
| [[17/13]], [[38/29]]
| {{UDnote|step=22}}
| {{UDnote|step=22}}
| {{UDnote|fifth=34|step=22}}
| {{UDnote|fifth=34|step=22}}
Line 162: Line 162:
| 23
| 23
| 484.21
| 484.21
|[[33/25]]
| [[33/25]]
| {{UDnote|step=23}}
| {{UDnote|step=23}}
| {{UDnote|fifth=34|step=23}}
| {{UDnote|fifth=34|step=23}}
Line 174: Line 174:
| 25
| 25
| 526.32
| 526.32
|[[19/14]], [[23/17]]
| [[19/14]], [[23/17]]
| {{UDnote|step=25}}
| {{UDnote|step=25}}
| {{UDnote|fifth=34|step=25}}
| {{UDnote|fifth=34|step=25}}
Line 180: Line 180:
| 26
| 26
| 547.37
| 547.37
|[[11/8]], [[26/19]]
| [[11/8]], [[26/19]]
| {{UDnote|step=26}}
| {{UDnote|step=26}}
| {{UDnote|fifth=34|step=26}}
| {{UDnote|fifth=34|step=26}}
Line 186: Line 186:
| 27
| 27
| 568.42
| 568.42
|[[25/18]], [[32/23]]
| [[25/18]], [[32/23]]
| {{UDnote|step=27}}
| {{UDnote|step=27}}
| {{UDnote|fifth=34|step=27}}
| {{UDnote|fifth=34|step=27}}
Line 192: Line 192:
| 28
| 28
| 589.47
| 589.47
|[[31/22]]
| [[31/22]]
| {{UDnote|step=28}}
| {{UDnote|step=28}}
| {{UDnote|fifth=34|step=28}}
| {{UDnote|fifth=34|step=28}}
Line 204: Line 204:
| 30
| 30
| 631.58
| 631.58
|[[23/16]]
| [[23/16]]
| {{UDnote|step=30}}
| {{UDnote|step=30}}
| {{UDnote|fifth=34|step=30}}
| {{UDnote|fifth=34|step=30}}
Line 210: Line 210:
| 31
| 31
| 652.63
| 652.63
|[[16/11]], [[19/13]]
| [[16/11]], [[19/13]]
| {{UDnote|step=31}}
| {{UDnote|step=31}}
| {{UDnote|fifth=34|step=31}}
| {{UDnote|fifth=34|step=31}}
Line 216: Line 216:
| 32
| 32
| 673.68
| 673.68
|[[28/19]], [[31/21]], [[34/23]]
| [[28/19]], [[31/21]], [[34/23]]
| {{UDnote|step=32}}
| {{UDnote|step=32}}
| {{UDnote|fifth=34|step=32}}
| {{UDnote|fifth=34|step=32}}
Line 234: Line 234:
| 35
| 35
| 736.84
| 736.84
|[[26/17]], [[32/21]] [[29/19]]
| [[26/17]], [[29/19]]
| {{UDnote|step=35}}
| {{UDnote|step=35}}
| {{UDnote|fifth=34|step=35}}
| {{UDnote|fifth=34|step=35}}
Line 240: Line 240:
| 36
| 36
| 757.89
| 757.89
|[[17/11]], [[31/20]]
| [[17/11]], [[31/20]]
| {{UDnote|step=36}}
| {{UDnote|step=36}}
| {{UDnote|fifth=34|step=36}}
| {{UDnote|fifth=34|step=36}}
Line 246: Line 246:
| 37
| 37
| 778.95
| 778.95
|''[[14/9]]'', [[11/7]]
| [[11/7]], ''[[14/9]]''
| {{UDnote|step=37}}
| {{UDnote|step=37}}
| {{UDnote|fifth=34|step=37}}
| {{UDnote|fifth=34|step=37}}
Line 252: Line 252:
| 38
| 38
| 800.00
| 800.00
|[[19/12]]
| [[19/12]]
| {{UDnote|step=38}}
| {{UDnote|step=38}}
| {{UDnote|fifth=34|step=38}}
| {{UDnote|fifth=34|step=38}}
Line 258: Line 258:
| 39
| 39
| 821.05
| 821.05
|[[8/5]]
| [[8/5]]
| {{UDnote|step=39}}
| {{UDnote|step=39}}
| {{UDnote|fifth=34|step=39}}
| {{UDnote|fifth=34|step=39}}
Line 264: Line 264:
| 40
| 40
| 842.11
| 842.11
|[[14/8]]
| [[13/8]]
| {{UDnote|step=40}}
| {{UDnote|step=40}}
| {{UDnote|fifth=34|step=40}}
| {{UDnote|fifth=34|step=40}}
Line 270: Line 270:
| 41
| 41
| 863.16
| 863.16
|[[23/14]], [[28/17]], [[33/20]]
| [[23/14]], [[28/17]], [[33/20]]
| {{UDnote|step=41}}
| {{UDnote|step=41}}
| {{UDnote|fifth=34|step=41}}
| {{UDnote|fifth=34|step=41}}
Line 276: Line 276:
| 42
| 42
| 884.21
| 884.21
|[[5/3]]
| [[5/3]]
| {{UDnote|step=42}}
| {{UDnote|step=42}}
| {{UDnote|fifth=34|step=42}}
| {{UDnote|fifth=34|step=42}}
Line 282: Line 282:
| 43
| 43
| 905.26
| 905.26
|[[32/19]]
| [[32/19]]
| {{UDnote|step=43}}
| {{UDnote|step=43}}
| {{UDnote|fifth=34|step=43}}
| {{UDnote|fifth=34|step=43}}
Line 288: Line 288:
| 44
| 44
| 926.32
| 926.32
|[[12/7]], [[29/17]]
| [[12/7]], [[29/17]]
| {{UDnote|step=44}}
| {{UDnote|step=44}}
| {{UDnote|fifth=34|step=44}}
| {{UDnote|fifth=34|step=44}}
Line 294: Line 294:
| 45
| 45
| 947.37
| 947.37
|[[19/11]]
| [[19/11]]
| {{UDnote|step=45}}
| {{UDnote|step=45}}
| {{UDnote|fifth=34|step=45}}
| {{UDnote|fifth=34|step=45}}
Line 300: Line 300:
| 46
| 46
| 968.42
| 968.42
|[[7/4]]
| [[7/4]]
| {{UDnote|step=46}}
| {{UDnote|step=46}}
| {{UDnote|fifth=34|step=46}}
| {{UDnote|fifth=34|step=46}}
Line 306: Line 306:
| 47
| 47
| 989.47
| 989.47
|[[23/13]]
| [[23/13]]
| {{UDnote|step=47}}
| {{UDnote|step=47}}
| {{UDnote|fifth=34|step=47}}
| {{UDnote|fifth=34|step=47}}
Line 312: Line 312:
| 48
| 48
| 1010.53
| 1010.53
|''[[16/9]]'', [[9/5]],<br>[[34/19]], [[52/29]]
| [[34/19]], [[52/29]]
| {{UDnote|step=48}}
| {{UDnote|step=48}}
| {{UDnote|fifth=34|step=48}}
| {{UDnote|fifth=34|step=48}}
Line 318: Line 318:
| 49
| 49
| 1031.58
| 1031.58
|[[20/11]], [[29/16]]
| [[20/11]], [[29/16]]
| {{UDnote|step=49}}
| {{UDnote|step=49}}
| {{UDnote|fifth=34|step=49}}
| {{UDnote|fifth=34|step=49}}
Line 324: Line 324:
| 50
| 50
| 1052.63
| 1052.63
|[[11/6]]
| [[11/6]]
| {{UDnote|step=50}}
| {{UDnote|step=50}}
| {{UDnote|fifth=34|step=50}}
| {{UDnote|fifth=34|step=50}}
Line 330: Line 330:
| 51
| 51
| 1073.68
| 1073.68
|[[13/7]], ''[[15/8]]''
| [[13/7]]
| {{UDnote|step=51}}
| {{UDnote|step=51}}
| {{UDnote|fifth=34|step=51}}
| {{UDnote|fifth=34|step=51}}
Line 336: Line 336:
| 52
| 52
| 1094.74
| 1094.74
|[[32/17]]
| [[32/17]]
| {{UDnote|step=52}}
| {{UDnote|step=52}}
| {{UDnote|fifth=34|step=52}}
| {{UDnote|fifth=34|step=52}}
Line 342: Line 342:
| 53
| 53
| 1115.79
| 1115.79
|[[19/10]], [[21/11]]
| [[19/10]], [[21/11]]
| {{UDnote|step=53}}
| {{UDnote|step=53}}
| {{UDnote|fifth=34|step=53}}
| {{UDnote|fifth=34|step=53}}
Line 366: Line 366:
| 57
| 57
| 1200.00
| 1200.00
|[[2/1]]
| [[2/1]]
| {{UDnote|step=57}}
| {{UDnote|step=57}}
| {{UDnote|fifth=34|step=57}}
| {{UDnote|fifth=34|step=57}}
|}
|}
<nowiki>*</nowiki> As a 2.5/3.7.11.13.17.19.23.29.31/3-subgroup temperament, in ''italics'' if inconsistent


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/57edo"