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== Intervals ==
== Intervals ==
{{Interval table}}
 
{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
|-
! Steps
! Cents
! Approximate ratios
! [[Ups and downs notation]]
|-
| 0
| 0
| [[1/1]]
| D
|-
| 1
| 6.63
|
| ^D, ^<sup>6</sup>E♭♭
|-
| 2
| 13.26
|
| ^^D, ^<sup>7</sup>E♭♭
|-
| 3
| 19.89
|
| ^<sup>3</sup>D, ^<sup>8</sup>E♭♭
|-
| 4
| 26.52
| [[63/62]], [[64/63]], [[65/64]]
| ^<sup>4</sup>D, v<sup>9</sup>E♭
|-
| 5
| 33.15
| [[52/51]]
| ^<sup>5</sup>D, v<sup>8</sup>E♭
|-
| 6
| 39.78
| [[43/42]], [[44/43]], [[45/44]]
| ^<sup>6</sup>D, v<sup>7</sup>E♭
|-
| 7
| 46.41
| [[37/36]], [[38/37]]
| ^<sup>7</sup>D, v<sup>6</sup>E♭
|-
| 8
| 53.04
| [[33/32]], [[65/63]]
| ^<sup>8</sup>D, v<sup>5</sup>E♭
|-
| 9
| 59.67
| [[29/28]], [[30/29]]
| ^<sup>9</sup>D, v<sup>4</sup>E♭
|-
| 10
| 66.3
| [[27/26]]
| v<sup>8</sup>D♯, v<sup>3</sup>E♭
|-
| 11
| 72.93
| [[24/23]], [[49/47]]
| v<sup>7</sup>D♯, vvE♭
|-
| 12
| 79.56
| [[22/21]], [[45/43]]
| v<sup>6</sup>D♯, vE♭
|-
| 13
| 86.19
| [[41/39]]
| v<sup>5</sup>D♯, E♭
|-
| 14
| 92.82
| [[19/18]], [[58/55]]
| v<sup>4</sup>D♯, ^E♭
|-
| 15
| 99.45
| [[18/17]]
| v<sup>3</sup>D♯, ^^E♭
|-
| 16
| 106.08
| [[17/16]], [[50/47]]
| vvD♯, ^<sup>3</sup>E♭
|-
| 17
| 112.71
| [[16/15]]
| vD♯, ^<sup>4</sup>E♭
|-
| 18
| 119.34
| [[15/14]]
| D♯, ^<sup>5</sup>E♭
|-
| 19
| 125.97
| [[43/40]]
| ^D♯, ^<sup>6</sup>E♭
|-
| 20
| 132.6
| [[41/38]]
| ^^D♯, ^<sup>7</sup>E♭
|-
| 21
| 139.23
| [[13/12]]
| ^<sup>3</sup>D♯, ^<sup>8</sup>E♭
|-
| 22
| 145.86
| [[37/34]], [[62/57]]
| ^<sup>4</sup>D♯, v<sup>9</sup>E
|-
| 23
| 152.49
|
| ^<sup>5</sup>D♯, v<sup>8</sup>E
|-
| 24
| 159.12
| [[34/31]], [[57/52]]
| ^<sup>6</sup>D♯, v<sup>7</sup>E
|-
| 25
| 165.75
| [[11/10]]
| ^<sup>7</sup>D♯, v<sup>6</sup>E
|-
| 26
| 172.38
| [[21/19]]
| ^<sup>8</sup>D♯, v<sup>5</sup>E
|-
| 27
| 179.01
| [[51/46]]
| ^<sup>9</sup>D♯, v<sup>4</sup>E
|-
| 28
| 185.64
| [[49/44]]
| v<sup>8</sup>D𝄪, v<sup>3</sup>E
|-
| 29
| 192.27
| [[19/17]]
| v<sup>7</sup>D𝄪, vvE
|-
| 30
| 198.9
| [[37/33]], [[46/41]], [[55/49]]
| v<sup>6</sup>D𝄪, vE
|-
| 31
| 205.52
|
| E
|-
| 32
| 212.15
| [[26/23]]
| ^E, ^<sup>6</sup>F♭
|-
| 33
| 218.78
| [[42/37]]
| ^^E, ^<sup>7</sup>F♭
|-
| 34
| 225.41
| [[41/36]], [[49/43]]
| ^<sup>3</sup>E, ^<sup>8</sup>F♭
|-
| 35
| 232.04
| [[8/7]]
| ^<sup>4</sup>E, v<sup>9</sup>F
|-
| 36
| 238.67
| [[31/27]], [[39/34]]
| ^<sup>5</sup>E, v<sup>8</sup>F
|-
| 37
| 245.3
| [[38/33]]
| ^<sup>6</sup>E, v<sup>7</sup>F
|-
| 38
| 251.93
| [[37/32]]
| ^<sup>7</sup>E, v<sup>6</sup>F
|-
| 39
| 258.56
| [[36/31]], [[65/56]]
| ^<sup>8</sup>E, v<sup>5</sup>F
|-
| 40
| 265.19
|
| ^<sup>9</sup>E, v<sup>4</sup>F
|-
| 41
| 271.82
| [[48/41]], [[55/47]]
| v<sup>8</sup>E♯, v<sup>3</sup>F
|-
| 42
| 278.45
| [[27/23]], [[47/40]]
| v<sup>7</sup>E♯, vvF
|-
| 43
| 285.08
| [[33/28]], [[46/39]]
| v<sup>6</sup>E♯, vF
|-
| 44
| 291.71
| [[45/38]], [[58/49]]
| F
|-
| 45
| 298.34
| [[19/16]]
| ^F, ^<sup>6</sup>G♭♭
|-
| 46
| 304.97
| [[31/26]]
| ^^F, ^<sup>7</sup>G♭♭
|-
| 47
| 311.6
|
| ^<sup>3</sup>F, ^<sup>8</sup>G♭♭
|-
| 48
| 318.23
|
| ^<sup>4</sup>F, v<sup>9</sup>G♭
|-
| 49
| 324.86
| [[35/29]], [[41/34]]
| ^<sup>5</sup>F, v<sup>8</sup>G♭
|-
| 50
| 331.49
| [[23/19]], [[63/52]]
| ^<sup>6</sup>F, v<sup>7</sup>G♭
|-
| 51
| 338.12
| [[45/37]], [[62/51]]
| ^<sup>7</sup>F, v<sup>6</sup>G♭
|-
| 52
| 344.75
|
| ^<sup>8</sup>F, v<sup>5</sup>G♭
|-
| 53
| 351.38
| [[38/31]], [[49/40]], [[60/49]]
| ^<sup>9</sup>F, v<sup>4</sup>G♭
|-
| 54
| 358.01
|
| v<sup>8</sup>F♯, v<sup>3</sup>G♭
|-
| 55
| 364.64
| [[21/17]], [[58/47]]
| v<sup>7</sup>F♯, vvG♭
|-
| 56
| 371.27
| [[57/46]]
| v<sup>6</sup>F♯, vG♭
|-
| 57
| 377.9
| [[46/37]], [[51/41]], [[56/45]]
| v<sup>5</sup>F♯, G♭
|-
| 58
| 384.53
|
| v<sup>4</sup>F♯, ^G♭
|-
| 59
| 391.16
|
| v<sup>3</sup>F♯, ^^G♭
|-
| 60
| 397.79
| [[39/31]]
| vvF♯, ^<sup>3</sup>G♭
|-
| 61
| 404.42
| [[24/19]]
| vF♯, ^<sup>4</sup>G♭
|-
| 62
| 411.05
| [[52/41]]
| F♯, ^<sup>5</sup>G♭
|-
| 63
| 417.68
| [[14/11]]
| ^F♯, ^<sup>6</sup>G♭
|-
| 64
| 424.31
| [[23/18]]
| ^^F♯, ^<sup>7</sup>G♭
|-
| 65
| 430.94
|
| ^<sup>3</sup>F♯, ^<sup>8</sup>G♭
|-
| 66
| 437.57
|
| ^<sup>4</sup>F♯, v<sup>9</sup>G
|-
| 67
| 444.2
| [[31/24]]
| ^<sup>5</sup>F♯, v<sup>8</sup>G
|-
| 68
| 450.83
| [[48/37]]
| ^<sup>6</sup>F♯, v<sup>7</sup>G
|-
| 69
| 457.46
| [[43/33]], [[56/43]]
| ^<sup>7</sup>F♯, v<sup>6</sup>G
|-
| 70
| 464.09
| [[17/13]]
| ^<sup>8</sup>F♯, v<sup>5</sup>G
|-
| 71
| 470.72
| [[21/16]]
| ^<sup>9</sup>F♯, v<sup>4</sup>G
|-
| 72
| 477.35
| [[29/22]], [[54/41]]
| v<sup>8</sup>F𝄪, v<sup>3</sup>G
|-
| 73
| 483.98
| [[41/31]]
| v<sup>7</sup>F𝄪, vvG
|-
| 74
| 490.61
|
| v<sup>6</sup>F𝄪, vG
|-
| 75
| 497.24
| [[4/3]]
| G
|-
| 76
| 503.87
|
| ^G, ^<sup>6</sup>A♭♭
|-
| 77
| 510.5
| [[43/32]], [[47/35]], [[51/38]]
| ^^G, ^<sup>7</sup>A♭♭
|-
| 78
| 517.13
| [[31/23]], [[58/43]]
| ^<sup>3</sup>G, ^<sup>8</sup>A♭♭
|-
| 79
| 523.76
| [[23/17]], [[65/48]]
| ^<sup>4</sup>G, v<sup>9</sup>A♭
|-
| 80
| 530.39
|
| ^<sup>5</sup>G, v<sup>8</sup>A♭
|-
| 81
| 537.02
| [[15/11]]
| ^<sup>6</sup>G, v<sup>7</sup>A♭
|-
| 82
| 543.65
| [[26/19]], [[63/46]]
| ^<sup>7</sup>G, v<sup>6</sup>A♭
|-
| 83
| 550.28
| [[11/8]]
| ^<sup>8</sup>G, v<sup>5</sup>A♭
|-
| 84
| 556.91
| [[40/29]]
| ^<sup>9</sup>G, v<sup>4</sup>A♭
|-
| 85
| 563.54
| [[18/13]]
| v<sup>8</sup>G♯, v<sup>3</sup>A♭
|-
| 86
| 570.17
| [[57/41]]
| v<sup>7</sup>G♯, vvA♭
|-
| 87
| 576.8
| [[60/43]]
| v<sup>6</sup>G♯, vA♭
|-
| 88
| 583.43
| [[7/5]]
| v<sup>5</sup>G♯, A♭
|-
| 89
| 590.06
| [[45/32]], [[52/37]]
| v<sup>4</sup>G♯, ^A♭
|-
| 90
| 596.69
| [[24/17]]
| v<sup>3</sup>G♯, ^^A♭
|-
| 91
| 603.31
| [[17/12]]
| vvG♯, ^<sup>3</sup>A♭
|-
| 92
| 609.94
| [[37/26]], [[64/45]]
| vG♯, ^<sup>4</sup>A♭
|-
| 93
| 616.57
| [[10/7]]
| G♯, ^<sup>5</sup>A♭
|-
| 94
| 623.2
| [[43/30]]
| ^G♯, ^<sup>6</sup>A♭
|-
| 95
| 629.83
|
| ^^G♯, ^<sup>7</sup>A♭
|-
| 96
| 636.46
| [[13/9]]
| ^<sup>3</sup>G♯, ^<sup>8</sup>A♭
|-
| 97
| 643.09
| [[29/20]]
| ^<sup>4</sup>G♯, v<sup>9</sup>A
|-
| 98
| 649.72
| [[16/11]]
| ^<sup>5</sup>G♯, v<sup>8</sup>A
|-
| 99
| 656.35
| [[19/13]]
| ^<sup>6</sup>G♯, v<sup>7</sup>A
|-
| 100
| 662.98
| [[22/15]]
| ^<sup>7</sup>G♯, v<sup>6</sup>A
|-
| 101
| 669.61
|
| ^<sup>8</sup>G♯, v<sup>5</sup>A
|-
| 102
| 676.24
| [[34/23]], [[65/44]]
| ^<sup>9</sup>G♯, v<sup>4</sup>A
|-
| 103
| 682.87
| [[43/29]], [[46/31]]
| v<sup>8</sup>G𝄪, v<sup>3</sup>A
|-
| 104
| 689.5
| [[64/43]]
| v<sup>7</sup>G𝄪, vvA
|-
| 105
| 696.13
|
| v<sup>6</sup>G𝄪, vA
|-
| 106
| 702.76
| [[3/2]]
| A
|-
| 107
| 709.39
|
| ^A, ^<sup>6</sup>B♭♭
|-
| 108
| 716.02
| [[62/41]], [[65/43]]
| ^^A, ^<sup>7</sup>B♭♭
|-
| 109
| 722.65
| [[41/27]], [[44/29]]
| ^<sup>3</sup>A, ^<sup>8</sup>B♭♭
|-
| 110
| 729.28
| [[32/21]]
| ^<sup>4</sup>A, v<sup>9</sup>B♭
|-
| 111
| 735.91
| [[26/17]]
| ^<sup>5</sup>A, v<sup>8</sup>B♭
|-
| 112
| 742.54
| [[43/28]], [[63/41]]
| ^<sup>6</sup>A, v<sup>7</sup>B♭
|-
| 113
| 749.17
| [[37/24]], [[57/37]]
| ^<sup>7</sup>A, v<sup>6</sup>B♭
|-
| 114
| 755.8
| [[48/31]], [[65/42]]
| ^<sup>8</sup>A, v<sup>5</sup>B♭
|-
| 115
| 762.43
|
| ^<sup>9</sup>A, v<sup>4</sup>B♭
|-
| 116
| 769.06
|
| v<sup>8</sup>A♯, v<sup>3</sup>B♭
|-
| 117
| 775.69
| [[36/23]]
| v<sup>7</sup>A♯, vvB♭
|-
| 118
| 782.32
| [[11/7]]
| v<sup>6</sup>A♯, vB♭
|-
| 119
| 788.95
| [[41/26]]
| v<sup>5</sup>A♯, B♭
|-
| 120
| 795.58
| [[19/12]]
| v<sup>4</sup>A♯, ^B♭
|-
| 121
| 802.21
| [[62/39]]
| v<sup>3</sup>A♯, ^^B♭
|-
| 122
| 808.84
|
| vvA♯, ^<sup>3</sup>B♭
|-
| 123
| 815.47
|
| vA♯, ^<sup>4</sup>B♭
|-
| 124
| 822.1
| [[37/23]], [[45/28]]
| A♯, ^<sup>5</sup>B♭
|-
| 125
| 828.73
|
| ^A♯, ^<sup>6</sup>B♭
|-
| 126
| 835.36
| [[34/21]], [[47/29]]
| ^^A♯, ^<sup>7</sup>B♭
|-
| 127
| 841.99
|
| ^<sup>3</sup>A♯, ^<sup>8</sup>B♭
|-
| 128
| 848.62
| [[31/19]], [[49/30]]
| ^<sup>4</sup>A♯, v<sup>9</sup>B
|-
| 129
| 855.25
|
| ^<sup>5</sup>A♯, v<sup>8</sup>B
|-
| 130
| 861.88
| [[51/31]]
| ^<sup>6</sup>A♯, v<sup>7</sup>B
|-
| 131
| 868.51
| [[38/23]]
| ^<sup>7</sup>A♯, v<sup>6</sup>B
|-
| 132
| 875.14
| [[58/35]], [[63/38]]
| ^<sup>8</sup>A♯, v<sup>5</sup>B
|-
| 133
| 881.77
|
| ^<sup>9</sup>A♯, v<sup>4</sup>B
|-
| 134
| 888.4
|
| v<sup>8</sup>A𝄪, v<sup>3</sup>B
|-
| 135
| 895.03
| [[52/31]], [[57/34]]
| v<sup>7</sup>A𝄪, vvB
|-
| 136
| 901.66
| [[32/19]]
| v<sup>6</sup>A𝄪, vB
|-
| 137
| 908.29
| [[49/29]]
| B
|-
| 138
| 914.92
| [[39/23]], [[56/33]]
| ^B, ^<sup>6</sup>C♭
|-
| 139
| 921.55
| [[46/27]], [[63/37]]
| ^^B, ^<sup>7</sup>C♭
|-
| 140
| 928.18
| [[41/24]], [[65/38]]
| ^<sup>3</sup>B, ^<sup>8</sup>C♭
|-
| 141
| 934.81
|
| ^<sup>4</sup>B, v<sup>9</sup>C
|-
| 142
| 941.44
| [[31/18]]
| ^<sup>5</sup>B, v<sup>8</sup>C
|-
| 143
| 948.07
| [[64/37]]
| ^<sup>6</sup>B, v<sup>7</sup>C
|-
| 144
| 954.7
| [[33/19]]
| ^<sup>7</sup>B, v<sup>6</sup>C
|-
| 145
| 961.33
| [[54/31]]
| ^<sup>8</sup>B, v<sup>5</sup>C
|-
| 146
| 967.96
| [[7/4]]
| ^<sup>9</sup>B, v<sup>4</sup>C
|-
| 147
| 974.59
| [[65/37]]
| v<sup>8</sup>B♯, v<sup>3</sup>C
|-
| 148
| 981.22
| [[37/21]]
| v<sup>7</sup>B♯, vvC
|-
| 149
| 987.85
| [[23/13]]
| v<sup>6</sup>B♯, vC
|-
| 150
| 994.48
|
| C
|-
| 151
| 1001.1
| [[41/23]]
| ^C, ^<sup>6</sup>D♭♭
|-
| 152
| 1007.73
| [[34/19]]
| ^^C, ^<sup>7</sup>D♭♭
|-
| 153
| 1014.36
|
| ^<sup>3</sup>C, ^<sup>8</sup>D♭♭
|-
| 154
| 1020.99
|
| ^<sup>4</sup>C, v<sup>9</sup>D♭
|-
| 155
| 1027.62
| [[38/21]]
| ^<sup>5</sup>C, v<sup>8</sup>D♭
|-
| 156
| 1034.25
| [[20/11]]
| ^<sup>6</sup>C, v<sup>7</sup>D♭
|-
| 157
| 1040.88
| [[31/17]]
| ^<sup>7</sup>C, v<sup>6</sup>D♭
|-
| 158
| 1047.51
|
| ^<sup>8</sup>C, v<sup>5</sup>D♭
|-
| 159
| 1054.14
| [[57/31]]
| ^<sup>9</sup>C, v<sup>4</sup>D♭
|-
| 160
| 1060.77
| [[24/13]]
| v<sup>8</sup>C♯, v<sup>3</sup>D♭
|-
| 161
| 1067.4
| [[63/34]]
| v<sup>7</sup>C♯, vvD♭
|-
| 162
| 1074.03
|
| v<sup>6</sup>C♯, vD♭
|-
| 163
| 1080.66
| [[28/15]]
| v<sup>5</sup>C♯, D♭
|-
| 164
| 1087.29
| [[15/8]]
| v<sup>4</sup>C♯, ^D♭
|-
| 165
| 1093.92
| [[32/17]], [[47/25]]
| v<sup>3</sup>C♯, ^^D♭
|-
| 166
| 1100.55
| [[17/9]]
| vvC♯, ^<sup>3</sup>D♭
|-
| 167
| 1107.18
| [[36/19]], [[55/29]]
| vC♯, ^<sup>4</sup>D♭
|-
| 168
| 1113.81
|
| C♯, ^<sup>5</sup>D♭
|-
| 169
| 1120.44
| [[21/11]]
| ^C♯, ^<sup>6</sup>D♭
|-
| 170
| 1127.07
| [[23/12]]
| ^^C♯, ^<sup>7</sup>D♭
|-
| 171
| 1133.7
| [[52/27]]
| ^<sup>3</sup>C♯, ^<sup>8</sup>D♭
|-
| 172
| 1140.33
| [[29/15]], [[56/29]]
| ^<sup>4</sup>C♯, v<sup>9</sup>D
|-
| 173
| 1146.96
| [[64/33]]
| ^<sup>5</sup>C♯, v<sup>8</sup>D
|-
| 174
| 1153.59
| [[37/19]]
| ^<sup>6</sup>C♯, v<sup>7</sup>D
|-
| 175
| 1160.22
| [[43/22]]
| ^<sup>7</sup>C♯, v<sup>6</sup>D
|-
| 176
| 1166.85
| [[51/26]]
| ^<sup>8</sup>C♯, v<sup>5</sup>D
|-
| 177
| 1173.48
| [[63/32]], [[65/33]]
| ^<sup>9</sup>C♯, v<sup>4</sup>D
|-
| 178
| 1180.11
|
| v<sup>8</sup>C𝄪, v<sup>3</sup>D
|-
| 179
| 1186.74
|
| v<sup>7</sup>C𝄪, vvD
|-
| 180
| 1193.37
|
| v<sup>6</sup>C𝄪, vD
|-
| 181
| 1200
| [[2/1]]
| D
|}{{Todo|replace auto-generated table of intervals with manually curated table}}


== Regular temperament properties ==
== Regular temperament properties ==
Retrieved from "https://en.xen.wiki/w/181edo"