User:Overthink/The 7-limit in 171edo: Difference between revisions

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m substitute again (idk the right way)
Overthink (talk | contribs)
autopatrolled
2,790 edits
clean up table
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{{Harmonics in equal|171|columns=4|prec=5}}
{{Harmonics in equal|171|columns=4|prec=5}}
{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
|+7-limit intervals in 171edo
|-
|-
! Steps
! Steps
! Cents
! Cents
! Approximate ratios
! Approximate ratios
! [[Ups and downs notation]]
|-
|-
| 0
| 0
| 0
| 0
| [[1/1]]
| [[1/1]]
| D
|-
|-
| 1
| 1
| 7.02
| 7.02
|  
|
| ^D, ^<sup>4</sup>E♭♭
|-
|-
| 2
| 2
| 14.04
| 14.04
|  
|
| ^^D, ^<sup>5</sup>E♭♭
|-
|-
| 3
| 3
| 21.05
| 21.05
|  
|
| ^<sup>3</sup>D, ^<sup>6</sup>E♭♭
|-
|-
| 4
| 4
| 28.07
| 28.07
|  
|
| ^<sup>4</sup>D, ^<sup>7</sup>E♭♭
|-
|-
| 5
| 5
| 35.09
| 35.09
| [[49/48]], [[50/49]], [[51/50]]
|
| ^<sup>5</sup>D, v<sup>8</sup>E♭
|-
|-
| 6
| 6
| 42.11
| 42.11
| [[41/40]], [[42/41]]
|
| ^<sup>6</sup>D, v<sup>7</sup>E♭
|-
|-
| 7
| 7
| 49.12
| 49.12
| [[35/34]], [[36/35]]
|
| ^<sup>7</sup>D, v<sup>6</sup>E♭
|-
|-
| 8
| 8
| 56.14
| 56.14
| [[31/30]], [[32/31]]
|
| ^<sup>8</sup>D, v<sup>5</sup>E♭
|-
|-
| 9
| 9
| 63.16
| 63.16
| [[28/27]]
|
| v<sup>7</sup>D♯, v<sup>4</sup>E♭
|-
|-
| 10
| 10
| 70.18
| 70.18
| [[25/24]], [[51/49]]
|
| v<sup>6</sup>D♯, v<sup>3</sup>E♭
|-
|-
| 11
| 11
| 77.19
| 77.19
| [[23/22]]
|
| v<sup>5</sup>D♯, vvE♭
|-
|-
| 12
| 12
| 84.21
| 84.21
| [[21/20]]
|
| v<sup>4</sup>D♯, vE♭
|-
|-
| 13
| 13
| 91.23
| 91.23
| [[39/37]], [[58/55]]
|
| v<sup>3</sup>D♯, E♭
|-
|-
| 14
| 14
| 98.25
| 98.25
| [[18/17]], [[55/52]]
|
| vvD♯, ^E♭
|-
|-
| 15
| 15
| 105.26
| 105.26
| [[17/16]]
|
| vD♯, ^^E♭
|-
|-
| 16
| 16
| 112.28
| 112.28
| [[16/15]]
|
| D♯, ^<sup>3</sup>E♭
|-
|-
| 17
| 17
| 119.3
| 119.3
| [[15/14]]
|
| ^D♯, ^<sup>4</sup>E♭
|-
|-
| 18
| 18
| 126.32
| 126.32
| [[43/40]]
|
| ^^D♯, ^<sup>5</sup>E♭
|-
|-
| 19
| 19
| 133.33
| 133.33
| [[27/25]]
|
| ^<sup>3</sup>D♯, ^<sup>6</sup>E♭
|-
|-
| 20
| 20
| 140.35
| 140.35
| [[51/47]]
|
| ^<sup>4</sup>D♯, ^<sup>7</sup>E♭
|-
|-
| 21
| 21
| 147.37
| 147.37
| [[37/34]], [[49/45]]
|
| ^<sup>5</sup>D♯, v<sup>8</sup>E
|-
|-
| 22
| 22
| 154.39
| 154.39
| [[35/32]], [[47/43]]
|
| ^<sup>6</sup>D♯, v<sup>7</sup>E
|-
|-
| 23
| 23
| 161.4
| 161.4
| [[45/41]], [[56/51]]
|
| ^<sup>7</sup>D♯, v<sup>6</sup>E
|-
|-
| 24
| 24
| 168.42
| 168.42
| [[43/39]], [[54/49]]
|
| ^<sup>8</sup>D♯, v<sup>5</sup>E
|-
|-
| 25
| 25
| 175.44
| 175.44
| [[31/28]], [[52/47]]
|
| v<sup>7</sup>D𝄪, v<sup>4</sup>E
|-
|-
| 26
| 26
| 182.46
| 182.46
| [[10/9]]
|
| v<sup>6</sup>D𝄪, v<sup>3</sup>E
|-
|-
| 27
| 27
| 189.47
| 189.47
| [[29/26]], [[48/43]]
|
| v<sup>5</sup>D𝄪, vvE
|-
|-
| 28
| 28
| 196.49
| 196.49
| [[28/25]]
|
| v<sup>4</sup>D𝄪, vE
|-
|-
| 29
| 29
| 203.51
| 203.51
| [[9/8]]
|
| E
|-
|-
| 30
| 30
| 210.53
| 210.53
| [[35/31]]
|
| ^E, ^<sup>4</sup>F♭
|-
|-
| 31
| 31
| 217.54
| 217.54
| [[17/15]]
|
| ^^E, ^<sup>5</sup>F♭
|-
|-
| 32
| 32
| 224.56
| 224.56
| [[33/29]], [[41/36]]
|
| ^<sup>3</sup>E, ^<sup>6</sup>F♭
|-
|-
| 33
| 33
| 231.58
| 231.58
| [[8/7]]
|
| ^<sup>4</sup>E, ^<sup>7</sup>F♭
|-
|-
| 34
| 34
| 238.6
| 238.6
| [[31/27]], [[39/34]]
|
| ^<sup>5</sup>E, v<sup>8</sup>F
|-
|-
| 35
| 35
| 245.61
| 245.61
|  
|
| ^<sup>6</sup>E, v<sup>7</sup>F
|-
|-
| 36
| 36
| 252.63
| 252.63
| [[37/32]]
|
| ^<sup>7</sup>E, v<sup>6</sup>F
|-
|-
| 37
| 37
| 259.65
| 259.65
| [[36/31]], [[43/37]]
|
| ^<sup>8</sup>E, v<sup>5</sup>F
|-
|-
| 38
| 38
| 266.67
| 266.67
| [[7/6]]
|
| v<sup>7</sup>E♯, v<sup>4</sup>F
|-
|-
| 39
| 39
| 273.68
| 273.68
| [[41/35]], [[48/41]]
|
| v<sup>6</sup>E♯, v<sup>3</sup>F
|-
|-
| 40
| 40
| 280.7
| 280.7
| [[20/17]]
|
| v<sup>5</sup>E♯, vvF
|-
|-
| 41
| 41
| 287.72
| 287.72
|  
|
| v<sup>4</sup>E♯, vF
|-
|-
| 42
| 42
| 294.74
| 294.74
| [[32/27]], [[51/43]]
|
| F
|-
|-
| 43
| 43
| 301.75
| 301.75
| [[25/21]]
|
| ^F, ^<sup>4</sup>G♭♭
|-
|-
| 44
| 44
| 308.77
| 308.77
| [[43/36]], [[49/41]], [[55/46]]
|
| ^^F, ^<sup>5</sup>G♭♭
|-
|-
| 45
| 45
| 315.79
| 315.79
| [[6/5]]
|
| ^<sup>3</sup>F, ^<sup>6</sup>G♭♭
|-
|-
| 46
| 46
| 322.81
| 322.81
| [[41/34]], [[47/39]]
|
| ^<sup>4</sup>F, ^<sup>7</sup>G♭♭
|-
|-
| 47
| 47
| 329.82
| 329.82
| [[52/43]]
|
| ^<sup>5</sup>F, v<sup>8</sup>G♭
|-
|-
| 48
| 48
| 336.84
| 336.84
| [[17/14]], [[62/51]]
|
| ^<sup>6</sup>F, v<sup>7</sup>G♭
|-
|-
| 49
| 49
| 343.86
| 343.86
| [[50/41]]
|
| ^<sup>7</sup>F, v<sup>6</sup>G♭
|-
|-
| 50
| 50
| 350.88
| 350.88
| [[49/40]], [[60/49]]
|
| ^<sup>8</sup>F, v<sup>5</sup>G♭
|-
|-
| 51
| 51
| 357.89
| 357.89
|  
|
| v<sup>7</sup>F♯, v<sup>4</sup>G♭
|-
|-
| 52
| 52
| 364.91
| 364.91
| [[21/17]], [[58/47]]
|
| v<sup>6</sup>F♯, v<sup>3</sup>G♭
|-
|-
| 53
| 53
| 371.93
| 371.93
| [[31/25]]
|
| v<sup>5</sup>F♯, vvG♭
|-
|-
| 54
| 54
| 378.95
| 378.95
| [[51/41]], [[56/45]]
|
| v<sup>4</sup>F♯, vG♭
|-
|-
| 55
| 55
| 385.96
| 385.96
| [[5/4]]
|
| v<sup>3</sup>F♯, G♭
|-
|-
| 56
| 56
| 392.98
| 392.98
|  
|
| vvF♯, ^G♭
|-
|-
| 57
| 57
| 400
| 400
| [[29/23]], [[34/27]]
|
| vF♯, ^^G♭
|-
|-
| 58
| 58
| 407.02
| 407.02
| [[43/34]], [[62/49]]
|
| F♯, ^<sup>3</sup>G♭
|-
|-
| 59
| 59
| 414.04
| 414.04
| [[33/26]], [[47/37]]
|
| ^F♯, ^<sup>4</sup>G♭
|-
|-
| 60
| 60
| 421.05
| 421.05
| [[37/29]], [[51/40]]
|
| ^^F♯, ^<sup>5</sup>G♭
|-
|-
| 61
| 61
| 428.07
| 428.07
| [[32/25]], [[41/32]]
|
| ^<sup>3</sup>F♯, ^<sup>6</sup>G♭
|-
|-
| 62
| 62
| 435.09
| 435.09
| [[9/7]]
|
| ^<sup>4</sup>F♯, ^<sup>7</sup>G♭
|-
|-
| 63
| 63
| 442.11
| 442.11
| [[31/24]], [[40/31]]
|
| ^<sup>5</sup>F♯, v<sup>8</sup>G
|-
|-
| 64
| 64
| 449.12
| 449.12
| [[35/27]]
|
| ^<sup>6</sup>F♯, v<sup>7</sup>G
|-
|-
| 65
| 65
| 456.14
| 456.14
| [[56/43]]
|
| ^<sup>7</sup>F♯, v<sup>6</sup>G
|-
|-
| 66
| 66
| 463.16
| 463.16
| [[17/13]]
|
| ^<sup>8</sup>F♯, v<sup>5</sup>G
|-
|-
| 67
| 67
| 470.18
| 470.18
| [[21/16]]
|
| v<sup>7</sup>F𝄪, v<sup>4</sup>G
|-
|-
| 68
| 68
| 477.19
| 477.19
| [[29/22]], [[54/41]]
|
| v<sup>6</sup>F𝄪, v<sup>3</sup>G
|-
|-
| 69
| 69
| 484.21
| 484.21
| [[41/31]], [[45/34]]
|
| v<sup>5</sup>F𝄪, vvG
|-
|-
| 70
| 70
| 491.23
| 491.23
|  
|
| v<sup>4</sup>F𝄪, vG
|-
|-
| 71
| 71
| 498.25
| 498.25
| [[4/3]]
|
| G
|-
|-
| 72
| 72
| 505.26
| 505.26
|  
|
| ^G, ^<sup>4</sup>A♭♭
|-
|-
| 73
| 73
| 512.28
| 512.28
| [[39/29]], [[43/32]]
|
| ^^G, ^<sup>5</sup>A♭♭
|-
|-
| 74
| 74
| 519.3
| 519.3
| [[27/20]], [[58/43]]
|
| ^<sup>3</sup>G, ^<sup>6</sup>A♭♭
|-
|-
| 75
| 75
| 526.32
| 526.32
| [[42/31]]
|
| ^<sup>4</sup>G, ^<sup>7</sup>A♭♭
|-
|-
| 76
| 76
| 533.33
| 533.33
| [[34/25]], [[49/36]]
|
| ^<sup>5</sup>G, v<sup>8</sup>A♭
|-
|-
| 77
| 77
| 540.35
| 540.35
| [[41/30]], [[56/41]]
|
| ^<sup>6</sup>G, v<sup>7</sup>A♭
|-
|-
| 78
| 78
| 547.37
| 547.37
| [[48/35]]
|
| ^<sup>7</sup>G, v<sup>6</sup>A♭
|-
|-
| 79
| 79
| 554.39
| 554.39
| [[51/37]], [[62/45]]
|
| ^<sup>8</sup>G, v<sup>5</sup>A♭
|-
|-
| 80
| 80
| 561.4
| 561.4
| [[47/34]]
|
| v<sup>7</sup>G♯, v<sup>4</sup>A♭
|-
|-
| 81
| 81
| 568.42
| 568.42
| [[25/18]]
|
| v<sup>6</sup>G♯, v<sup>3</sup>A♭
|-
|-
| 82
| 82
| 575.44
| 575.44
| [[46/33]], [[60/43]]
|
| v<sup>5</sup>G♯, vvA♭
|-
|-
| 83
| 83
| 582.46
| 582.46
| [[7/5]]
|
| v<sup>4</sup>G♯, vA♭
|-
|-
| 84
| 84
| 589.47
| 589.47
| [[45/32]], [[52/37]]
|
| v<sup>3</sup>G♯, A♭
|-
|-
| 85
| 85
| 596.49
| 596.49
| [[24/17]]
|
| vvG♯, ^A♭
|-
|-
| 86
| 86
| 603.51
| 603.51
| [[17/12]]
|
| vG♯, ^^A♭
|-
|-
| 87
| 87
| 610.53
| 610.53
| [[37/26]]
|
| G♯, ^<sup>3</sup>A♭
|-
|-
| 88
| 88
| 617.54
| 617.54
| [[10/7]]
|
| ^G♯, ^<sup>4</sup>A♭
|-
|-
| 89
| 89
| 624.56
| 624.56
| [[33/23]], [[43/30]]
|
| ^^G♯, ^<sup>5</sup>A♭
|-
|-
| 90
| 90
| 631.58
| 631.58
| [[36/25]], [[49/34]]
|
| ^<sup>3</sup>G♯, ^<sup>6</sup>A♭
|-
|-
| 91
| 91
| 638.6
| 638.6
|  
|
| ^<sup>4</sup>G♯, ^<sup>7</sup>A♭
|-
|-
| 92
| 92
| 645.61
| 645.61
| [[45/31]]
|
| ^<sup>5</sup>G♯, v<sup>8</sup>A
|-
|-
| 93
| 93
| 652.63
| 652.63
| [[35/24]], [[51/35]]
|
| ^<sup>6</sup>G♯, v<sup>7</sup>A
|-
|-
| 94
| 94
| 659.65
| 659.65
| [[41/28]], [[60/41]]
|
| ^<sup>7</sup>G♯, v<sup>6</sup>A
|-
|-
| 95
| 95
| 666.67
| 666.67
| [[25/17]], [[47/32]]
|
| ^<sup>8</sup>G♯, v<sup>5</sup>A
|-
|-
| 96
| 96
| 673.68
| 673.68
| [[31/21]]
|
| v<sup>7</sup>G𝄪, v<sup>4</sup>A
|-
|-
| 97
| 97
| 680.7
| 680.7
| [[40/27]], [[43/29]]
|
| v<sup>6</sup>G𝄪, v<sup>3</sup>A
|-
|-
| 98
| 98
| 687.72
| 687.72
| [[58/39]]
|
| v<sup>5</sup>G𝄪, vvA
|-
|-
| 99
| 99
| 694.74
| 694.74
|  
|
| v<sup>4</sup>G𝄪, vA
|-
|-
| 100
| 100
| 701.75
| 701.75
| [[3/2]]
|
| A
|-
|-
| 101
| 101
| 708.77
| 708.77
|  
|
| ^A, ^<sup>4</sup>B♭♭
|-
|-
| 102
| 102
| 715.79
| 715.79
| [[62/41]]
|
| ^^A, ^<sup>5</sup>B♭♭
|-
|-
| 103
| 103
| 722.81
| 722.81
| [[41/27]], [[44/29]]
|
| ^<sup>3</sup>A, ^<sup>6</sup>B♭♭
|-
|-
| 104
| 104
| 729.82
| 729.82
| [[32/21]]
|
| ^<sup>4</sup>A, ^<sup>7</sup>B♭♭
|-
|-
| 105
| 105
| 736.84
| 736.84
| [[26/17]], [[49/32]]
|
| ^<sup>5</sup>A, v<sup>8</sup>B♭
|-
|-
| 106
| 106
| 743.86
| 743.86
| [[43/28]]
|
| ^<sup>6</sup>A, v<sup>7</sup>B♭
|-
|-
| 107
| 107
| 750.88
| 750.88
| [[54/35]]
|
| ^<sup>7</sup>A, v<sup>6</sup>B♭
|-
|-
| 108
| 108
| 757.89
| 757.89
| [[31/20]], [[48/31]]
|
| ^<sup>8</sup>A, v<sup>5</sup>B♭
|-
|-
| 109
| 109
| 764.91
| 764.91
| [[14/9]]
|
| v<sup>7</sup>A♯, v<sup>4</sup>B♭
|-
|-
| 110
| 110
| 771.93
| 771.93
| [[25/16]]
|
| v<sup>6</sup>A♯, v<sup>3</sup>B♭
|-
|-
| 111
| 111
| 778.95
| 778.95
| [[58/37]]
|
| v<sup>5</sup>A♯, vvB♭
|-
|-
| 112
| 112
| 785.96
| 785.96
| [[52/33]]
|
| v<sup>4</sup>A♯, vB♭
|-
|-
| 113
| 113
| 792.98
| 792.98
| [[49/31]]
|
| v<sup>3</sup>A♯, B♭
|-
|-
| 114
| 114
| 800
| 800
| [[27/17]], [[46/29]]
|
| vvA♯, ^B♭
|-
|-
| 115
| 115
| 807.02
| 807.02
| [[51/32]]
|
| vA♯, ^^B♭
|-
|-
| 116
| 116
| 814.04
| 814.04
| [[8/5]]
|
| A♯, ^<sup>3</sup>B♭
|-
|-
| 117
| 117
| 821.05
| 821.05
| [[45/28]]
|
| ^A♯, ^<sup>4</sup>B♭
|-
|-
| 118
| 118
| 828.07
| 828.07
| [[50/31]]
|
| ^^A♯, ^<sup>5</sup>B♭
|-
|-
| 119
| 119
| 835.09
| 835.09
| [[34/21]], [[47/29]]
|
| ^<sup>3</sup>A♯, ^<sup>6</sup>B♭
|-
|-
| 120
| 120
| 842.11
| 842.11
|  
|
| ^<sup>4</sup>A♯, ^<sup>7</sup>B♭
|-
|-
| 121
| 121
| 849.12
| 849.12
| [[49/30]]
|
| ^<sup>5</sup>A♯, v<sup>8</sup>B
|-
|-
| 122
| 122
| 856.14
| 856.14
| [[41/25]]
|
| ^<sup>6</sup>A♯, v<sup>7</sup>B
|-
|-
| 123
| 123
| 863.16
| 863.16
| [[28/17]], [[51/31]]
|
| ^<sup>7</sup>A♯, v<sup>6</sup>B
|-
|-
| 124
| 124
| 870.18
| 870.18
| [[43/26]]
|
| ^<sup>8</sup>A♯, v<sup>5</sup>B
|-
|-
| 125
| 125
| 877.19
| 877.19
|  
|
| v<sup>7</sup>A𝄪, v<sup>4</sup>B
|-
|-
| 126
| 126
| 884.21
| 884.21
| [[5/3]]
|
| v<sup>6</sup>A𝄪, v<sup>3</sup>B
|-
|-
| 127
| 127
| 891.23
| 891.23
|  
|
| v<sup>5</sup>A𝄪, vvB
|-
|-
| 128
| 128
| 898.25
| 898.25
| [[42/25]]
|
| v<sup>4</sup>A𝄪, vB
|-
|-
| 129
| 129
| 905.26
| 905.26
| [[27/16]]
|
| B
|-
|-
| 130
| 130
| 912.28
| 912.28
|  
|
| ^B, ^<sup>4</sup>C♭
|-
|-
| 131
| 131
| 919.3
| 919.3
| [[17/10]]
|
| ^^B, ^<sup>5</sup>C♭
|-
|-
| 132
| 132
| 926.32
| 926.32
| [[41/24]]
|
| ^<sup>3</sup>B, ^<sup>6</sup>C♭
|-
|-
| 133
| 133
| 933.33
| 933.33
| [[12/7]]
|
| ^<sup>4</sup>B, ^<sup>7</sup>C♭
|-
|-
| 134
| 134
| 940.35
| 940.35
| [[31/18]]
|
| ^<sup>5</sup>B, v<sup>8</sup>C
|-
|-
| 135
| 135
| 947.37
| 947.37
|  
|
| ^<sup>6</sup>B, v<sup>7</sup>C
|-
|-
| 136
| 136
| 954.39
| 954.39
|  
|
| ^<sup>7</sup>B, v<sup>6</sup>C
|-
|-
| 137
| 137
| 961.4
| 961.4
| [[54/31]]
|
| ^<sup>8</sup>B, v<sup>5</sup>C
|-
|-
| 138
| 138
| 968.42
| 968.42
| [[7/4]]
|
| v<sup>7</sup>B♯, v<sup>4</sup>C
|-
|-
| 139
| 139
| 975.44
| 975.44
| [[58/33]]
|
| v<sup>6</sup>B♯, v<sup>3</sup>C
|-
|-
| 140
| 140
| 982.46
| 982.46
| [[30/17]]
|
| v<sup>5</sup>B♯, vvC
|-
|-
| 141
| 141
| 989.47
| 989.47
| [[62/35]]
|
| v<sup>4</sup>B♯, vC
|-
|-
| 142
| 142
| 996.49
| 996.49
| [[16/9]]
|
| C
|-
|-
| 143
| 143
| 1003.51
| 1003.51
| [[25/14]]
|
| ^C, ^<sup>4</sup>D♭♭
|-
|-
| 144
| 144
| 1010.53
| 1010.53
| [[43/24]], [[52/29]]
|
| ^^C, ^<sup>5</sup>D♭♭
|-
|-
| 145
| 145
| 1017.54
| 1017.54
| [[9/5]]
|
| ^<sup>3</sup>C, ^<sup>6</sup>D♭♭
|-
|-
| 146
| 146
| 1024.56
| 1024.56
| [[47/26]], [[56/31]]
|
| ^<sup>4</sup>C, ^<sup>7</sup>D♭♭
|-
|-
| 147
| 147
| 1031.58
| 1031.58
| [[49/27]]
|
| ^<sup>5</sup>C, v<sup>8</sup>D♭
|-
|-
| 148
| 148
| 1038.6
| 1038.6
| [[51/28]]
|
| ^<sup>6</sup>C, v<sup>7</sup>D♭
|-
|-
| 149
| 149
| 1045.61
| 1045.61
|  
|
| ^<sup>7</sup>C, v<sup>6</sup>D♭
|-
|-
| 150
| 150
| 1052.63
| 1052.63
|  
|
| ^<sup>8</sup>C, v<sup>5</sup>D♭
|-
|-
| 151
| 151
| 1059.65
| 1059.65
|  
|
| v<sup>7</sup>C♯, v<sup>4</sup>D♭
|-
|-
| 152
| 152
| 1066.67
| 1066.67
| [[50/27]]
|
| v<sup>6</sup>C♯, v<sup>3</sup>D♭
|-
|-
| 153
| 153
| 1073.68
| 1073.68
|  
|
| v<sup>5</sup>C♯, vvD♭
|-
|-
| 154
| 154
| 1080.7
| 1080.7
| [[28/15]]
|
| v<sup>4</sup>C♯, vD♭
|-
|-
| 155
| 155
| 1087.72
| 1087.72
| [[15/8]]
|
| v<sup>3</sup>C♯, D♭
|-
|-
| 156
| 156
| 1094.74
| 1094.74
| [[32/17]]
|
| vvC♯, ^D♭
|-
|-
| 157
| 157
| 1101.75
| 1101.75
| [[17/9]]
|
| vC♯, ^^D♭
|-
|-
| 158
| 158
| 1108.77
| 1108.77
| [[55/29]]
|
| C♯, ^<sup>3</sup>D♭
|-
|-
| 159
| 159
| 1115.79
| 1115.79
| [[40/21]]
|
| ^C♯, ^<sup>4</sup>D♭
|-
|-
| 160
| 160
| 1122.81
| 1122.81
| [[44/23]]
|
| ^^C♯, ^<sup>5</sup>D♭
|-
|-
| 161
| 161
| 1129.82
| 1129.82
| [[48/25]]
|
| ^<sup>3</sup>C♯, ^<sup>6</sup>D♭
|-
|-
| 162
| 162
| 1136.84
| 1136.84
| [[27/14]]
|
| ^<sup>4</sup>C♯, ^<sup>7</sup>D♭
|-
|-
| 163
| 163
| 1143.86
| 1143.86
| [[31/16]], [[60/31]]
|
| ^<sup>5</sup>C♯, v<sup>8</sup>D
|-
|-
| 164
| 164
| 1150.88
| 1150.88
| [[35/18]]
|
| ^<sup>6</sup>C♯, v<sup>7</sup>D
|-
|-
| 165
| 165
| 1157.89
| 1157.89
| [[41/21]]
|
| ^<sup>7</sup>C♯, v<sup>6</sup>D
|-
|-
| 166
| 166
| 1164.91
| 1164.91
| [[49/25]]
|
| ^<sup>8</sup>C♯, v<sup>5</sup>D
|-
|-
| 167
| 167
| 1171.93
| 1171.93
|  
|
| v<sup>7</sup>C𝄪, v<sup>4</sup>D
|-
|-
| 168
| 168
| 1178.95
| 1178.95
|  
|
| v<sup>6</sup>C𝄪, v<sup>3</sup>D
|-
|-
| 169
| 169
| 1185.96
| 1185.96
|  
|
| v<sup>5</sup>C𝄪, vvD
|-
|-
| 170
| 170
| 1192.98
| 1192.98
|  
|
| v<sup>4</sup>C𝄪, vD
|-
|-
| 171
| 171
| 1200
| 1200
| [[2/1]]
| [[2/1]]
| D
|}
|}

Revision as of 09:40, 25 December 2025

An excellent system for approximating the 7-limit is 171edo. The 9-odd-limit tonality diamond is approximated with just over 0.4 cents of error, and all 7-limit intervals with odd limit up to 10,000,000 are consistent (first odd to cause inconsistencies is 13671875). 171edo is thus an excellent system for classifying intervals and commas simply and accurately.

Approximation of prime harmonics in 171edo
Harmonic 2 3 5 7
Error Absolute (¢) +0.00000 -0.20061 -0.34880 -0.40485
Relative (%) +0.0 -2.9 -5.0 -5.8
Steps
(reduced) 		171
(0) 		271
(100) 		397
(55) 		480
(138)
7-limit intervals in 171edo
Steps Cents Approximate ratios
0 0 1/1
1 7.02
2 14.04
3 21.05
4 28.07
5 35.09
6 42.11
7 49.12
8 56.14
9 63.16
10 70.18
11 77.19
12 84.21
13 91.23
14 98.25
15 105.26
16 112.28
17 119.3
18 126.32
19 133.33
20 140.35
21 147.37
22 154.39
23 161.4
24 168.42
25 175.44
26 182.46
27 189.47
28 196.49
29 203.51
30 210.53
31 217.54
32 224.56
33 231.58
34 238.6
35 245.61
36 252.63
37 259.65
38 266.67
39 273.68
40 280.7
41 287.72
42 294.74
43 301.75
44 308.77
45 315.79
46 322.81
47 329.82
48 336.84
49 343.86
50 350.88
51 357.89
52 364.91
53 371.93
54 378.95
55 385.96
56 392.98
57 400
58 407.02
59 414.04
60 421.05
61 428.07
62 435.09
63 442.11
64 449.12
65 456.14
66 463.16
67 470.18
68 477.19
69 484.21
70 491.23
71 498.25
72 505.26
73 512.28
74 519.3
75 526.32
76 533.33
77 540.35
78 547.37
79 554.39
80 561.4
81 568.42
82 575.44
83 582.46
84 589.47
85 596.49
86 603.51
87 610.53
88 617.54
89 624.56
90 631.58
91 638.6
92 645.61
93 652.63
94 659.65
95 666.67
96 673.68
97 680.7
98 687.72
99 694.74
100 701.75
101 708.77
102 715.79
103 722.81
104 729.82
105 736.84
106 743.86
107 750.88
108 757.89
109 764.91
110 771.93
111 778.95
112 785.96
113 792.98
114 800
115 807.02
116 814.04
117 821.05
118 828.07
119 835.09
120 842.11
121 849.12
122 856.14
123 863.16
124 870.18
125 877.19
126 884.21
127 891.23
128 898.25
129 905.26
130 912.28
131 919.3
132 926.32
133 933.33
134 940.35
135 947.37
136 954.39
137 961.4
138 968.42
139 975.44
140 982.46
141 989.47
142 996.49
143 1003.51
144 1010.53
145 1017.54
146 1024.56
147 1031.58
148 1038.6
149 1045.61
150 1052.63
151 1059.65
152 1066.67
153 1073.68
154 1080.7
155 1087.72
156 1094.74
157 1101.75
158 1108.77
159 1115.79
160 1122.81
161 1129.82
162 1136.84
163 1143.86
164 1150.88
165 1157.89
166 1164.91
167 1171.93
168 1178.95
169 1185.96
170 1192.98
171 1200 2/1
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