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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.
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.
{{Harmonics in equal|171|columns=4|prec=5}}
{{Harmonics in equal|171|columns=4|prec=5}}
{{#invoke: Interval_table | interval_table
{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
| tuning=171edo
|+{{nowrap|7-limit intervals in 171edo}}
| additional=
|-
| max_error=35
! Steps
| debug={{lc:}}
! Cents
}}
! Approximate ratios
!Name
|-
| 0
| 0.00
| 1/1
|Unison
|-
| 1
| 7.02
|225/224, 5120/5103, 15625/15552
|Kleisma
|-
| 2
| 14.04
|126/125, 245/243, 78732/78125
|Semicomma
|-
| 3
| 21.05
|81/80, 875/864, 3125/3087
|
|-
| 4
| 28.07
|64/63, 3125/3072, 20000/19683
|
|-
| 5
| 35.09
|49/48, 50/49
|
|-
| 6
| 42.11
|128/125, 525/512
|
|-
| 7
| 49.12
|36/35, 250/243
|
|-
| 8
| 56.14
|405/392, 1323/1280
|
|-
| 9
| 63.16
|28/27, 648/625
|
|-
| 10
| 70.18
|25/24, 20480/19683
|
|-
| 11
| 77.19
|256/245
|
|-
| 12
| 84.21
|21/20
|
|-
| 13
| 91.23
|135/128, 256/243
|
|-
| 14
| 98.25
|
|
|-
| 15
| 105.26
|
|
|-
| 16
| 112.28
|16/15, 2187/2048
|
|-
| 17
| 119.30
|
|
|-
| 18
| 126.32
|
|
|-
| 19
| 133.33
|
|
|-
| 20
| 140.35
|
|
|-
| 21
| 147.37
|
|
|-
| 22
| 154.39
|
|
|-
| 23
| 161.40
|
|
|-
| 24
| 168.42
|
|
|-
| 25
| 175.44
|
|
|-
| 26
| 182.46
|10/9
|
|-
| 27
| 189.47
|
|
|-
| 28
| 196.49
|
|
|-
| 29
| 203.51
|9/8
|
|-
| 30
| 210.53
|
|
|-
| 31
| 217.54
|
|
|-
| 32
| 224.56
|
|
|-
| 33
| 231.58
|8/7
|
|-
| 34
| 238.60
|
|
|-
| 35
| 245.61
|
|
|-
| 36
| 252.63
|
|
|-
| 37
| 259.65
|
|
|-
| 38
| 266.67
|7/6
|
|-
| 39
| 273.68
|
|
|-
| 40
| 280.70
|
|
|-
| 41
| 287.72
|
|
|-
| 42
| 294.74
|
|
|-
| 43
| 301.75
|
|
|-
| 44
| 308.77
|
|
|-
| 45
| 315.79
|6/5
|
|-
| 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
|5/4
|
|-
| 56
| 392.98
|
|
|-
| 57
| 400.00
|
|
|-
| 58
| 407.02
|
|
|-
| 59
| 414.04
|
|
|-
| 60
| 421.05
|
|
|-
| 61
| 428.07
|
|
|-
| 62
| 435.09
|9/7
|
|-
| 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
|4/3
|
|-
| 72
| 505.26
|
|
|-
| 73
| 512.28
|
|
|-
| 74
| 519.30
|
|
|-
| 75
| 526.32
|
|
|-
| 76
| 533.33
|
|
|-
| 77
| 540.35
|
|
|-
| 78
| 547.37
|
|
|-
| 79
| 554.39
|
|
|-
| 80
| 561.40
|
|
|-
| 81
| 568.42
|
|
|-
| 82
| 575.44
|
|
|-
| 83
| 582.46
|7/5
|
|-
| 84
| 589.47
|
|
|-
| 85
| 596.49
|
|
|-
| 86
| 603.51
|
|
|-
| 87
| 610.53
|
|
|-
| 88
| 617.54
|10/7
|
|-
| 89
| 624.56
|
|
|-
| 90
| 631.58
|
|
|-
| 91
| 638.60
|
|
|-
| 92
| 645.61
|
|
|-
| 93
| 652.63
|
|
|-
| 94
| 659.65
|
|
|-
| 95
| 666.67
|
|
|-
| 96
| 673.68
|
|
|-
| 97
| 680.70
|
|
|-
| 98
| 687.72
|
|
|-
| 99
| 694.74
|
|
|-
| 100
| 701.75
|3/2
|
|-
| 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
|14/9
|
|-
| 110
| 771.93
|
|
|-
| 111
| 778.95
|
|
|-
| 112
| 785.96
|
|
|-
| 113
| 792.98
|
|
|-
| 114
| 800.00
|
|
|-
| 115
| 807.02
|
|
|-
| 116
| 814.04
|8/5
|
|-
| 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
|5/3
|
|-
| 127
| 891.23
|
|
|-
| 128
| 898.25
|
|
|-
| 129
| 905.26
|
|
|-
| 130
| 912.28
|
|
|-
| 131
| 919.30
|
|
|-
| 132
| 926.32
|
|
|-
| 133
| 933.33
|12/7
|
|-
| 134
| 940.35
|
|
|-
| 135
| 947.37
|
|
|-
| 136
| 954.39
|
|
|-
| 137
| 961.40
|
|
|-
| 138
| 968.42
|7/4
|
|-
| 139
| 975.44
|
|
|-
| 140
| 982.46
|
|
|-
| 141
| 989.47
|
|
|-
| 142
| 996.49
|16/9
|
|-
| 143
| 1003.51
|
|
|-
| 144
| 1010.53
|
|
|-
| 145
| 1017.54
|9/5
|
|-
| 146
| 1024.56
|
|
|-
| 147
| 1031.58
|
|
|-
| 148
| 1038.60
|
|
|-
| 149
| 1045.61
|
|
|-
| 150
| 1052.63
|
|
|-
| 151
| 1059.65
|
|
|-
| 152
| 1066.67
|
|
|-
| 153
| 1073.68
|
|
|-
| 154
| 1080.70
|
|
|-
| 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
| 1200.00
| 2/1
|
|}
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