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List of superparticular intervals: Difference between revisions

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Use actual multiplication sign and +subgroup monzos for 31-limit and beyond; 37 -> tricesimoseptimal, 41 -> quadracesimoprimal, 43 -> quadracesimotertial
Line 5: Line 5:


== List of superparticular intervals ==
== List of superparticular intervals ==
{| class="wikitable"
{| class="wikitable center-6"
|-
|-
! [[Ratio]]
! [[Ratio]]
Line 1,872: Line 1,872:
| [[31/30]]
| [[31/30]]
| 56.767
| 56.767
| 31/(2*3*5)
| 31/(2×3×5)
|  
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| Large tricesimoprimal quartertone
| Large tricesimoprimal quartertone
|
|
Line 1,880: Line 1,880:
| 54.964
| 54.964
| 2<sup>5</sup>/31
| 2<sup>5</sup>/31
|  
| 2.31 {{monzo| 5 -1 }}
| Small tricesimoprimal quartertone, 31st subharmonic
| Small tricesimoprimal quartertone, octave-reduced 31st subharmonic
|
|
|-
|-
| [[63/62]]
| [[63/62]]
| 27.700
| 27.700
| (3<sup>2</sup>*7)/(2*31)
| (3<sup>2</sup>×7)/(2×31)
|  
| 2.3.7.31 {{monzo| -1 2 1 -1 }}
|  
|  
|
|
Line 1,893: Line 1,893:
| [[93/92]]
| [[93/92]]
| 18.716
| 18.716
| (3*31)/(2<sup>2</sup>*23)
| (3×31)/(2<sup>2</sup>×23)
|  
| 2.3.23.31 {{monzo| -2 1 -1 1 }}
|  
|  
|
|
Line 1,900: Line 1,900:
| [[125/124]]
| [[125/124]]
| 13.906
| 13.906
| (5<sup>3</sup>)/(2<sup>2</sup>*31)
| 5<sup>3</sup>/(2<sup>2</sup>×31)
|  
| 2.5.31 {{monzo| -2 3 -1 }}
| Twizzler
| Twizzler
|
|
Line 1,907: Line 1,907:
| [[621/620]]
| [[621/620]]
| 2.7901
| 2.7901
| (3³*23)/(2²*5*31)
| (3<sup>3</sup>×23)/(2<sup>2</sup>×5×31)
|
| 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}
| Owowhatsthisma
| Owowhatsthisma
|
|
Line 1,914: Line 1,914:
| [[3969/3968]]
| [[3969/3968]]
| 0.43624
| 0.43624
| (3<sup>4</sup>*7<sup>2</sup>)/(2<sup>7</sup>*31)
| (3<sup>4</sup>×7<sup>2</sup>)/(2<sup>7</sup>×31)
|  
| 2.3.7.31 {{monzo| -7 4 2 -1 }}
| Yunzee comma
| Yunzee comma
| S63
| S63
Line 1,923: Line 1,923:
| [[37/36]]
| [[37/36]]
| 47.434
| 47.434
| 37/(2<sup>2</sup>*3<sup>2</sup>)
| 37/(2<sup>2</sup>×3<sup>2</sup>)
|  
| 2.3.37 {{monzo| -2 -2 1 }}
| Large 37-limit quartertone, 37th-partial chroma
| Large tricesimoseptimal quartertone, 37th-partial chroma
|
|
|-
|-
| [[38/37]]
| [[38/37]]
| 46.169
| 46.169
| (2*19)/37
| (2×19)/37
|  
| 2.19.37 {{monzo| 1 1 -1 }}
| Small 37-limit quartertone
| Small tricesimoseptimal quartertone
|
|
|-
|-
| [[75/74]]
| [[75/74]]
| 23.238
| 23.238
| (3*5<sup>2</sup>)/(2*37)
| (3×5<sup>2</sup>)/(2×37)
|  
| 2.3.5.37 {{monzo| -1 1 2 -1 }}
|  
|  
|
|
Line 1,946: Line 1,946:
| [[41/40]]
| [[41/40]]
| 42.749
| 42.749
| 41/(2<sup>3</sup>*5)
| 41/(2<sup>3</sup>×5)
|  
| 2.5.41 {{monzo| -3 -1 1 }}
| Large 41-limit fifth-tone
| Large quadracesimoprimal fifth-tone
|
|
|-
|-
| [[42/41]]
| [[42/41]]
| 41.719
| 41.719
| (2*3*7)/41
| (2×3×7)/41
|  
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small 41-limit fifth-tone
| Small quadracesimoprimal fifth-tone
|
|
|-
|-
| [[82/81]]
| [[82/81]]
| 21.242
| 21.242
| (2*41)/3<sup>4</sup>
| (2×41)/3<sup>4</sup>
|  
| 2.3.41 {{monzo| 1 -4 1 }}
| 41st-partial chroma
| 41st-partial chroma
|
|
Line 1,969: Line 1,969:
| [[43/42]]
| [[43/42]]
| 40.737
| 40.737
| 43/(2*3*7)
| 43/(2×3×7)
|  
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large 43-limit fifth-tone
| Large quadracesimotertial fifth-tone
|
|
|-
|-
| [[44/43]]
| [[44/43]]
| 39.800
| 39.800
| (2<sup>2</sup>*11)/43
| (2<sup>2</sup>×11)/43
|  
| 2.11.43 {{monzo| 2 1 -1 }}
| Small 43-limit fifth-tone
| Small quadracesimotertial fifth-tone
|
|
|-
|-
| [[86/85]]
| [[86/85]]
| 20.249
| 20.249
| (2*43)/(5*17)
| (2×43)/(5×17)
|  
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
|  
|  
|
|
Line 1,990: Line 1,990:
| [[87/86]]
| [[87/86]]
| 20.014
| 20.014
| (3*29)/(2*43)
| (3×29)/(2×43)
|  
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
|  
|  
|
|
Line 1,997: Line 1,997:
| [[129/128]]
| [[129/128]]
| 13.473
| 13.473
| (3*43)/2<sup>7
| (3×43)/2<sup>7
|  
| 2.3.43 {{monzo| -7 1 1 }}
| 43rd-partial chroma
| 43rd-partial chroma
|
|
Line 2,006: Line 2,006:
| [[47/46]]
| [[47/46]]
| 37.232
| 37.232
| 47/(2*23)
| 47/(2×23)
|  
| 2.23.47 {{monzo| -1 -1 1 }}
|  
|  
|
|
Line 2,013: Line 2,013:
| [[48/47]]
| [[48/47]]
| 36.448
| 36.448
| (2<sup>4</sup>*3)/47
| (2<sup>4</sup>×3)/47
|  
| 2.3.47 {{monzo| 4 1 -1 }}
|  
|  
|
|
Line 2,020: Line 2,020:
| [[94/93]]
| [[94/93]]
| 18.516
| 18.516
| (2*47)/(3*31)
| (2×47)/(3×31)
|  
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
|  
|  
|
|
Line 2,027: Line 2,027:
| [[95/94]]
| [[95/94]]
| 18.320
| 18.320
| (5*19)/(2*47)
| (5×19)/(2×47)
|  
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
|  
|  
|
|
Line 2,036: Line 2,036:
| [[53/52]]
| [[53/52]]
| 32.977
| 32.977
| 53/(2<sup>2</sup>*13)
| 53/(2<sup>2</sup>×13)
|  
| 2.13.53 {{monzo| -2 -1 1 }}
|  
|  
|
|
Line 2,043: Line 2,043:
| [[54/53]]
| [[54/53]]
| 32.360
| 32.360
| (2*3<sup>3</sup>)/53
| (2×3<sup>3</sup>)/53
|  
| 2.3.53 {{monzo| 1 3 -1 }}
|  
|  
|
|
|-
|-
! colspan="5" | 59-limit (incomplete)
! colspan="6" | 59-limit (incomplete)
!
|-
|-
| [[59/58]]
| [[59/58]]
| 29.594
| 29.594
| 59/(2*29)
| 59/(2×29)
|  
| 2.29.59 {{monzo| -1 -1 1 }}
|  
|  
|
|
Line 2,060: Line 2,059:
| [[60/59]]
| [[60/59]]
| 29.097
| 29.097
| (2<sup>2</sup>*3*5)/59
| (2<sup>2</sup>×3×5)/59
|  
| 2.3.5.59 {{monzo| 2 1 1 -1 }}
|  
|  
|
|
Line 2,069: Line 2,068:
| [[61/60]]
| [[61/60]]
| 28.616
| 28.616
| 61/(2<sup>2</sup>*3*5)
| 61/(2<sup>2</sup>×3×5)
|  
| 2.3.5.61 {{monzo| -2 -1 -1 1 }}
|  
|  
|
|
Line 2,076: Line 2,075:
| [[62/61]]
| [[62/61]]
| 28.151
| 28.151
| (2*31)/61
| (2×31)/61
|  
| 2.31.61 {{monzo| 1 1 -1 }}
|  
|  
|
|
Line 2,085: Line 2,084:
| [[67/66]]
| [[67/66]]
| 26.034
| 26.034
| 67/(2*3*11)
| 67/(2×3×11)
|  
| 2.3.11.67 {{monzo| -1 -1 -1 1 }}
|  
|  
|
|
Line 2,092: Line 2,091:
| [[68/67]]
| [[68/67]]
| 25.648
| 25.648
| (2<sup>2</sup>*17)/67
| (2<sup>2</sup>×17)/67
|  
| 2.17.67 {{monzo| 2 1 -1 }}
|  
|  
|
|
Line 2,101: Line 2,100:
| [[71/70]]
| [[71/70]]
| 24.557
| 24.557
| 71/(2*5*7)
| 71/(2×5×7)
|  
| 2.5.7.71 {{monzo| -1 -1 -1 1 }}
|  
|  
|
|
Line 2,108: Line 2,107:
| [[72/71]]
| [[72/71]]
| 24.213
| 24.213
| (2<sup>3</sup>*3<sup>2</sup>)/71
| (2<sup>3</sup>×3<sup>2</sup>)/71
|  
| 2.3.71 {{monzo| 3 2 -1 }}
|  
|  
|
|
Line 2,117: Line 2,116:
| [[73/72]]
| [[73/72]]
| 23.879
| 23.879
| 73/(2<sup>3</sup>*3<sup>2</sup>)
| 73/(2<sup>3</sup>×3<sup>2</sup>)
|  
| 2.3.73 {{monzo| -3 -2 1 }}
|  
|  
|
|
Line 2,124: Line 2,123:
| [[74/73]]
| [[74/73]]
| 23.555
| 23.555
| (2*37)/73
| (2×37)/73
|  
| 2.37.73 {{monzo| 1 1 -1 }}
|  
|  
|
|
Line 2,133: Line 2,132:
| [[79/78]]
| [[79/78]]
| 22.054
| 22.054
| 79/(2*3*13)
| 79/(2×3×13)
|  
| 2.3.13.79 {{monzo| -1 -1 -1 1 }}
|  
|  
|
|
Line 2,140: Line 2,139:
| [[80/79]]
| [[80/79]]
| 21.777
| 21.777
| (2<sup>4</sup>*5)/79
| (2<sup>4</sup>×5)/79
|  
| 2.5.79 {{monzo| 4 1 -1 }}
|  
|  
|
|
Line 2,149: Line 2,148:
| [[83/82]]
| [[83/82]]
| 20.985
| 20.985
| 83/(2*41)
| 83/(2×41)
|  
| 2.41.83 {{monzo| -1 -1 1 }}
|  
|  
|
|
Line 2,157: Line 2,156:
| 20.734
| 20.734
| (2<sup>2</sup>*3*7)/83
| (2<sup>2</sup>*3*7)/83
|  
| 2.3.7.83 {{monzo| 2 1 1 -1 }}
|  
|  
|
|
Line 2,165: Line 2,164:
| [[89/88]]
| [[89/88]]
| 19.562
| 19.562
| 89/(2<sup>3</sup>*11)
| 89/(2<sup>3</sup>×11)
|  
| 2.11.89 {{monzo| -3 -1 1 }}
|  
|  
|
|
Line 2,172: Line 2,171:
| [[90/89]]
| [[90/89]]
| 19.344
| 19.344
| (2*3<sup>2</sup>*5)/89
| (2×3<sup>2</sup>×5)/89
|  
| 2.3.5.89 {{monzo| 1 2 1 -1 }}
|  
|  
|
|
Line 2,181: Line 2,180:
| [[97/96]]
| [[97/96]]
| 17.940
| 17.940
| 97/(2<sup>5</sup>*3)
| 97/(2<sup>5</sup>×3)
|  
| 2.3.97 {{monzo| -5 -1 1 }}
|  
|  
|
|
Line 2,188: Line 2,187:
| [[98/97]]
| [[98/97]]
| 17.756
| 17.756
| (2*7<sup>2</sup>)/97
| (2×7<sup>2</sup>)/97
|  
| 2.7.97 {{monzo| 1 2 -1 }}
|  
|  
|
|
Line 2,197: Line 2,196:
| [[101/100]]
| [[101/100]]
| 17.226
| 17.226
| 101/(2<sup>2</sup>*5<sup>2</sup>)
| 101/(2×5)<sup>2</sup>
|
| 2.5.101 {{monzo| -2 -2 1 }}
|  
|  
|
|
Line 2,204: Line 2,203:
| [[102/101]]
| [[102/101]]
| 17.057
| 17.057
| (2*3*17)/101
| (2×3×17)/101
|  
| 2.3.17.101 {{monzo| 1 1 1 -1 }}
|  
|  
|  
|  
Line 2,211: Line 2,210:
| [[7777/7776]]
| [[7777/7776]]
| 0.223
| 0.223
| 7*11*101/(2<sup>5</sup>*3<sup>5</sup>)
| 7×11×101/(2×3)<sup>5</sup>
|
| 2.3.7.11.101 {{monzo| -5 -5 1 1 1 }}
|  
| Pulsar comma
|  
|  
|}
|}
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