Xenharmonic Wiki

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

Newer edit →
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,790 edits
create page
 
Overthink (talk | contribs)
autopatrolled
2,790 edits
m substitute again (idk the right way)
Line 1: Line 1:
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
|-
| additional=
! Steps
| max_error=35
! Cents
| debug={{lc:}}
! Approximate ratios
}}
! [[Ups and downs notation]]
|-
| 0
| 0
| [[1/1]]
| D
|-
| 1
| 7.02
|
| ^D, ^<sup>4</sup>E♭♭
|-
| 2
| 14.04
|
| ^^D, ^<sup>5</sup>E♭♭
|-
| 3
| 21.05
|
| ^<sup>3</sup>D, ^<sup>6</sup>E♭♭
|-
| 4
| 28.07
|
| ^<sup>4</sup>D, ^<sup>7</sup>E♭♭
|-
| 5
| 35.09
| [[49/48]], [[50/49]], [[51/50]]
| ^<sup>5</sup>D, v<sup>8</sup>E♭
|-
| 6
| 42.11
| [[41/40]], [[42/41]]
| ^<sup>6</sup>D, v<sup>7</sup>E♭
|-
| 7
| 49.12
| [[35/34]], [[36/35]]
| ^<sup>7</sup>D, v<sup>6</sup>E♭
|-
| 8
| 56.14
| [[31/30]], [[32/31]]
| ^<sup>8</sup>D, v<sup>5</sup>E♭
|-
| 9
| 63.16
| [[28/27]]
| v<sup>7</sup>D♯, v<sup>4</sup>E♭
|-
| 10
| 70.18
| [[25/24]], [[51/49]]
| v<sup>6</sup>D♯, v<sup>3</sup>E♭
|-
| 11
| 77.19
| [[23/22]]
| v<sup>5</sup>D♯, vvE♭
|-
| 12
| 84.21
| [[21/20]]
| v<sup>4</sup>D♯, vE♭
|-
| 13
| 91.23
| [[39/37]], [[58/55]]
| v<sup>3</sup>D♯, E♭
|-
| 14
| 98.25
| [[18/17]], [[55/52]]
| vvD♯, ^E♭
|-
| 15
| 105.26
| [[17/16]]
| vD♯, ^^E♭
|-
| 16
| 112.28
| [[16/15]]
| D♯, ^<sup>3</sup>E♭
|-
| 17
| 119.3
| [[15/14]]
| ^D♯, ^<sup>4</sup>E♭
|-
| 18
| 126.32
| [[43/40]]
| ^^D♯, ^<sup>5</sup>E♭
|-
| 19
| 133.33
| [[27/25]]
| ^<sup>3</sup>D♯, ^<sup>6</sup>E♭
|-
| 20
| 140.35
| [[51/47]]
| ^<sup>4</sup>D♯, ^<sup>7</sup>E♭
|-
| 21
| 147.37
| [[37/34]], [[49/45]]
| ^<sup>5</sup>D♯, v<sup>8</sup>E
|-
| 22
| 154.39
| [[35/32]], [[47/43]]
| ^<sup>6</sup>D♯, v<sup>7</sup>E
|-
| 23
| 161.4
| [[45/41]], [[56/51]]
| ^<sup>7</sup>D♯, v<sup>6</sup>E
|-
| 24
| 168.42
| [[43/39]], [[54/49]]
| ^<sup>8</sup>D♯, v<sup>5</sup>E
|-
| 25
| 175.44
| [[31/28]], [[52/47]]
| v<sup>7</sup>D𝄪, v<sup>4</sup>E
|-
| 26
| 182.46
| [[10/9]]
| v<sup>6</sup>D𝄪, v<sup>3</sup>E
|-
| 27
| 189.47
| [[29/26]], [[48/43]]
| v<sup>5</sup>D𝄪, vvE
|-
| 28
| 196.49
| [[28/25]]
| v<sup>4</sup>D𝄪, vE
|-
| 29
| 203.51
| [[9/8]]
| E
|-
| 30
| 210.53
| [[35/31]]
| ^E, ^<sup>4</sup>F♭
|-
| 31
| 217.54
| [[17/15]]
| ^^E, ^<sup>5</sup>F♭
|-
| 32
| 224.56
| [[33/29]], [[41/36]]
| ^<sup>3</sup>E, ^<sup>6</sup>F♭
|-
| 33
| 231.58
| [[8/7]]
| ^<sup>4</sup>E, ^<sup>7</sup>F♭
|-
| 34
| 238.6
| [[31/27]], [[39/34]]
| ^<sup>5</sup>E, v<sup>8</sup>F
|-
| 35
| 245.61
|
| ^<sup>6</sup>E, v<sup>7</sup>F
|-
| 36
| 252.63
| [[37/32]]
| ^<sup>7</sup>E, v<sup>6</sup>F
|-
| 37
| 259.65
| [[36/31]], [[43/37]]
| ^<sup>8</sup>E, v<sup>5</sup>F
|-
| 38
| 266.67
| [[7/6]]
| v<sup>7</sup>E♯, v<sup>4</sup>F
|-
| 39
| 273.68
| [[41/35]], [[48/41]]
| v<sup>6</sup>E♯, v<sup>3</sup>F
|-
| 40
| 280.7
| [[20/17]]
| v<sup>5</sup>E♯, vvF
|-
| 41
| 287.72
|
| v<sup>4</sup>E♯, vF
|-
| 42
| 294.74
| [[32/27]], [[51/43]]
| F
|-
| 43
| 301.75
| [[25/21]]
| ^F, ^<sup>4</sup>G♭♭
|-
| 44
| 308.77
| [[43/36]], [[49/41]], [[55/46]]
| ^^F, ^<sup>5</sup>G♭♭
|-
| 45
| 315.79
| [[6/5]]
| ^<sup>3</sup>F, ^<sup>6</sup>G♭♭
|-
| 46
| 322.81
| [[41/34]], [[47/39]]
| ^<sup>4</sup>F, ^<sup>7</sup>G♭♭
|-
| 47
| 329.82
| [[52/43]]
| ^<sup>5</sup>F, v<sup>8</sup>G♭
|-
| 48
| 336.84
| [[17/14]], [[62/51]]
| ^<sup>6</sup>F, v<sup>7</sup>G♭
|-
| 49
| 343.86
| [[50/41]]
| ^<sup>7</sup>F, v<sup>6</sup>G♭
|-
| 50
| 350.88
| [[49/40]], [[60/49]]
| ^<sup>8</sup>F, v<sup>5</sup>G♭
|-
| 51
| 357.89
|
| v<sup>7</sup>F♯, v<sup>4</sup>G♭
|-
| 52
| 364.91
| [[21/17]], [[58/47]]
| v<sup>6</sup>F♯, v<sup>3</sup>G♭
|-
| 53
| 371.93
| [[31/25]]
| v<sup>5</sup>F♯, vvG♭
|-
| 54
| 378.95
| [[51/41]], [[56/45]]
| v<sup>4</sup>F♯, vG♭
|-
| 55
| 385.96
| [[5/4]]
| v<sup>3</sup>F♯, G♭
|-
| 56
| 392.98
|
| vvF♯, ^G♭
|-
| 57
| 400
| [[29/23]], [[34/27]]
| vF♯, ^^G♭
|-
| 58
| 407.02
| [[43/34]], [[62/49]]
| F♯, ^<sup>3</sup>G♭
|-
| 59
| 414.04
| [[33/26]], [[47/37]]
| ^F♯, ^<sup>4</sup>G♭
|-
| 60
| 421.05
| [[37/29]], [[51/40]]
| ^^F♯, ^<sup>5</sup>G♭
|-
| 61
| 428.07
| [[32/25]], [[41/32]]
| ^<sup>3</sup>F♯, ^<sup>6</sup>G♭
|-
| 62
| 435.09
| [[9/7]]
| ^<sup>4</sup>F♯, ^<sup>7</sup>G♭
|-
| 63
| 442.11
| [[31/24]], [[40/31]]
| ^<sup>5</sup>F♯, v<sup>8</sup>G
|-
| 64
| 449.12
| [[35/27]]
| ^<sup>6</sup>F♯, v<sup>7</sup>G
|-
| 65
| 456.14
| [[56/43]]
| ^<sup>7</sup>F♯, v<sup>6</sup>G
|-
| 66
| 463.16
| [[17/13]]
| ^<sup>8</sup>F♯, v<sup>5</sup>G
|-
| 67
| 470.18
| [[21/16]]
| v<sup>7</sup>F𝄪, v<sup>4</sup>G
|-
| 68
| 477.19
| [[29/22]], [[54/41]]
| v<sup>6</sup>F𝄪, v<sup>3</sup>G
|-
| 69
| 484.21
| [[41/31]], [[45/34]]
| v<sup>5</sup>F𝄪, vvG
|-
| 70
| 491.23
|
| v<sup>4</sup>F𝄪, vG
|-
| 71
| 498.25
| [[4/3]]
| G
|-
| 72
| 505.26
|
| ^G, ^<sup>4</sup>A♭♭
|-
| 73
| 512.28
| [[39/29]], [[43/32]]
| ^^G, ^<sup>5</sup>A♭♭
|-
| 74
| 519.3
| [[27/20]], [[58/43]]
| ^<sup>3</sup>G, ^<sup>6</sup>A♭♭
|-
| 75
| 526.32
| [[42/31]]
| ^<sup>4</sup>G, ^<sup>7</sup>A♭♭
|-
| 76
| 533.33
| [[34/25]], [[49/36]]
| ^<sup>5</sup>G, v<sup>8</sup>A♭
|-
| 77
| 540.35
| [[41/30]], [[56/41]]
| ^<sup>6</sup>G, v<sup>7</sup>A♭
|-
| 78
| 547.37
| [[48/35]]
| ^<sup>7</sup>G, v<sup>6</sup>A♭
|-
| 79
| 554.39
| [[51/37]], [[62/45]]
| ^<sup>8</sup>G, v<sup>5</sup>A♭
|-
| 80
| 561.4
| [[47/34]]
| v<sup>7</sup>G♯, v<sup>4</sup>A♭
|-
| 81
| 568.42
| [[25/18]]
| v<sup>6</sup>G♯, v<sup>3</sup>A♭
|-
| 82
| 575.44
| [[46/33]], [[60/43]]
| v<sup>5</sup>G♯, vvA♭
|-
| 83
| 582.46
| [[7/5]]
| v<sup>4</sup>G♯, vA♭
|-
| 84
| 589.47
| [[45/32]], [[52/37]]
| v<sup>3</sup>G♯, A♭
|-
| 85
| 596.49
| [[24/17]]
| vvG♯, ^A♭
|-
| 86
| 603.51
| [[17/12]]
| vG♯, ^^A♭
|-
| 87
| 610.53
| [[37/26]]
| G♯, ^<sup>3</sup>A♭
|-
| 88
| 617.54
| [[10/7]]
| ^G♯, ^<sup>4</sup>A♭
|-
| 89
| 624.56
| [[33/23]], [[43/30]]
| ^^G♯, ^<sup>5</sup>A♭
|-
| 90
| 631.58
| [[36/25]], [[49/34]]
| ^<sup>3</sup>G♯, ^<sup>6</sup>A♭
|-
| 91
| 638.6
|
| ^<sup>4</sup>G♯, ^<sup>7</sup>A♭
|-
| 92
| 645.61
| [[45/31]]
| ^<sup>5</sup>G♯, v<sup>8</sup>A
|-
| 93
| 652.63
| [[35/24]], [[51/35]]
| ^<sup>6</sup>G♯, v<sup>7</sup>A
|-
| 94
| 659.65
| [[41/28]], [[60/41]]
| ^<sup>7</sup>G♯, v<sup>6</sup>A
|-
| 95
| 666.67
| [[25/17]], [[47/32]]
| ^<sup>8</sup>G♯, v<sup>5</sup>A
|-
| 96
| 673.68
| [[31/21]]
| v<sup>7</sup>G𝄪, v<sup>4</sup>A
|-
| 97
| 680.7
| [[40/27]], [[43/29]]
| v<sup>6</sup>G𝄪, v<sup>3</sup>A
|-
| 98
| 687.72
| [[58/39]]
| v<sup>5</sup>G𝄪, vvA
|-
| 99
| 694.74
|
| v<sup>4</sup>G𝄪, vA
|-
| 100
| 701.75
| [[3/2]]
| A
|-
| 101
| 708.77
|
| ^A, ^<sup>4</sup>B♭♭
|-
| 102
| 715.79
| [[62/41]]
| ^^A, ^<sup>5</sup>B♭♭
|-
| 103
| 722.81
| [[41/27]], [[44/29]]
| ^<sup>3</sup>A, ^<sup>6</sup>B♭♭
|-
| 104
| 729.82
| [[32/21]]
| ^<sup>4</sup>A, ^<sup>7</sup>B♭♭
|-
| 105
| 736.84
| [[26/17]], [[49/32]]
| ^<sup>5</sup>A, v<sup>8</sup>B♭
|-
| 106
| 743.86
| [[43/28]]
| ^<sup>6</sup>A, v<sup>7</sup>B♭
|-
| 107
| 750.88
| [[54/35]]
| ^<sup>7</sup>A, v<sup>6</sup>B♭
|-
| 108
| 757.89
| [[31/20]], [[48/31]]
| ^<sup>8</sup>A, v<sup>5</sup>B♭
|-
| 109
| 764.91
| [[14/9]]
| v<sup>7</sup>A♯, v<sup>4</sup>B♭
|-
| 110
| 771.93
| [[25/16]]
| v<sup>6</sup>A♯, v<sup>3</sup>B♭
|-
| 111
| 778.95
| [[58/37]]
| v<sup>5</sup>A♯, vvB♭
|-
| 112
| 785.96
| [[52/33]]
| v<sup>4</sup>A♯, vB♭
|-
| 113
| 792.98
| [[49/31]]
| v<sup>3</sup>A♯, B♭
|-
| 114
| 800
| [[27/17]], [[46/29]]
| vvA♯, ^B♭
|-
| 115
| 807.02
| [[51/32]]
| vA♯, ^^B♭
|-
| 116
| 814.04
| [[8/5]]
| A♯, ^<sup>3</sup>B♭
|-
| 117
| 821.05
| [[45/28]]
| ^A♯, ^<sup>4</sup>B♭
|-
| 118
| 828.07
| [[50/31]]
| ^^A♯, ^<sup>5</sup>B♭
|-
| 119
| 835.09
| [[34/21]], [[47/29]]
| ^<sup>3</sup>A♯, ^<sup>6</sup>B♭
|-
| 120
| 842.11
|
| ^<sup>4</sup>A♯, ^<sup>7</sup>B♭
|-
| 121
| 849.12
| [[49/30]]
| ^<sup>5</sup>A♯, v<sup>8</sup>B
|-
| 122
| 856.14
| [[41/25]]
| ^<sup>6</sup>A♯, v<sup>7</sup>B
|-
| 123
| 863.16
| [[28/17]], [[51/31]]
| ^<sup>7</sup>A♯, v<sup>6</sup>B
|-
| 124
| 870.18
| [[43/26]]
| ^<sup>8</sup>A♯, v<sup>5</sup>B
|-
| 125
| 877.19
|
| v<sup>7</sup>A𝄪, v<sup>4</sup>B
|-
| 126
| 884.21
| [[5/3]]
| v<sup>6</sup>A𝄪, v<sup>3</sup>B
|-
| 127
| 891.23
|
| v<sup>5</sup>A𝄪, vvB
|-
| 128
| 898.25
| [[42/25]]
| v<sup>4</sup>A𝄪, vB
|-
| 129
| 905.26
| [[27/16]]
| B
|-
| 130
| 912.28
|
| ^B, ^<sup>4</sup>C♭
|-
| 131
| 919.3
| [[17/10]]
| ^^B, ^<sup>5</sup>C♭
|-
| 132
| 926.32
| [[41/24]]
| ^<sup>3</sup>B, ^<sup>6</sup>C♭
|-
| 133
| 933.33
| [[12/7]]
| ^<sup>4</sup>B, ^<sup>7</sup>C♭
|-
| 134
| 940.35
| [[31/18]]
| ^<sup>5</sup>B, v<sup>8</sup>C
|-
| 135
| 947.37
|
| ^<sup>6</sup>B, v<sup>7</sup>C
|-
| 136
| 954.39
|
| ^<sup>7</sup>B, v<sup>6</sup>C
|-
| 137
| 961.4
| [[54/31]]
| ^<sup>8</sup>B, v<sup>5</sup>C
|-
| 138
| 968.42
| [[7/4]]
| v<sup>7</sup>B♯, v<sup>4</sup>C
|-
| 139
| 975.44
| [[58/33]]
| v<sup>6</sup>B♯, v<sup>3</sup>C
|-
| 140
| 982.46
| [[30/17]]
| v<sup>5</sup>B♯, vvC
|-
| 141
| 989.47
| [[62/35]]
| v<sup>4</sup>B♯, vC
|-
| 142
| 996.49
| [[16/9]]
| C
|-
| 143
| 1003.51
| [[25/14]]
| ^C, ^<sup>4</sup>D♭♭
|-
| 144
| 1010.53
| [[43/24]], [[52/29]]
| ^^C, ^<sup>5</sup>D♭♭
|-
| 145
| 1017.54
| [[9/5]]
| ^<sup>3</sup>C, ^<sup>6</sup>D♭♭
|-
| 146
| 1024.56
| [[47/26]], [[56/31]]
| ^<sup>4</sup>C, ^<sup>7</sup>D♭♭
|-
| 147
| 1031.58
| [[49/27]]
| ^<sup>5</sup>C, v<sup>8</sup>D♭
|-
| 148
| 1038.6
| [[51/28]]
| ^<sup>6</sup>C, v<sup>7</sup>D♭
|-
| 149
| 1045.61
|
| ^<sup>7</sup>C, v<sup>6</sup>D♭
|-
| 150
| 1052.63
|
| ^<sup>8</sup>C, v<sup>5</sup>D♭
|-
| 151
| 1059.65
|
| v<sup>7</sup>C♯, v<sup>4</sup>D♭
|-
| 152
| 1066.67
| [[50/27]]
| v<sup>6</sup>C♯, v<sup>3</sup>D♭
|-
| 153
| 1073.68
|
| v<sup>5</sup>C♯, vvD♭
|-
| 154
| 1080.7
| [[28/15]]
| v<sup>4</sup>C♯, vD♭
|-
| 155
| 1087.72
| [[15/8]]
| v<sup>3</sup>C♯, D♭
|-
| 156
| 1094.74
| [[32/17]]
| vvC♯, ^D♭
|-
| 157
| 1101.75
| [[17/9]]
| vC♯, ^^D♭
|-
| 158
| 1108.77
| [[55/29]]
| C♯, ^<sup>3</sup>D♭
|-
| 159
| 1115.79
| [[40/21]]
| ^C♯, ^<sup>4</sup>D♭
|-
| 160
| 1122.81
| [[44/23]]
| ^^C♯, ^<sup>5</sup>D♭
|-
| 161
| 1129.82
| [[48/25]]
| ^<sup>3</sup>C♯, ^<sup>6</sup>D♭
|-
| 162
| 1136.84
| [[27/14]]
| ^<sup>4</sup>C♯, ^<sup>7</sup>D♭
|-
| 163
| 1143.86
| [[31/16]], [[60/31]]
| ^<sup>5</sup>C♯, v<sup>8</sup>D
|-
| 164
| 1150.88
| [[35/18]]
| ^<sup>6</sup>C♯, v<sup>7</sup>D
|-
| 165
| 1157.89
| [[41/21]]
| ^<sup>7</sup>C♯, v<sup>6</sup>D
|-
| 166
| 1164.91
| [[49/25]]
| ^<sup>8</sup>C♯, v<sup>5</sup>D
|-
| 167
| 1171.93
|
| v<sup>7</sup>C𝄪, v<sup>4</sup>D
|-
| 168
| 1178.95
|
| v<sup>6</sup>C𝄪, v<sup>3</sup>D
|-
| 169
| 1185.96
|
| v<sup>5</sup>C𝄪, vvD
|-
| 170
| 1192.98
|
| v<sup>4</sup>C𝄪, vD
|-
| 171
| 1200
| [[2/1]]
| D
|}
Retrieved from "https://en.xen.wiki/w/User:Overthink/The_7-limit_in_171edo"