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List of superparticular intervals: Difference between revisions

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Line 348: Line 348:
| 13/(2<sup>2</sup>×3)
| 13/(2<sup>2</sup>×3)
| {{Monzo| -2 -1 0 0 0 1 }}
| {{Monzo| -2 -1 0 0 0 1 }}
| (Large) tridecimal 2/3-tone, tridecimal neutral second
| Large tridecimal 2/3-tone, tridecimal neutral second
|
|
|-
|-
Line 355: Line 355:
| (2×7)/13
| (2×7)/13
| {{Monzo| 1 0 0 1 0 -1 }}
| {{Monzo| 1 0 0 1 0 -1 }}
| (Small) tridecimal 2/3-tone, trienthird
| Small tridecimal 2/3-tone, trienthird
|
|
|-
|-
Line 362: Line 362:
| (2×13)/5<sup>2</sup>
| (2×13)/5<sup>2</sup>
| {{Monzo| 1 0 -2 0 0 1 }}
| {{Monzo| 1 0 -2 0 0 1 }}
| (Large) tridecimal 1/3-tone
| Large tridecimal 1/3-tone
|
|
|-
|-
Line 369: Line 369:
| 3<sup>3</sup>/(2×13)
| 3<sup>3</sup>/(2×13)
| {{Monzo| -1 3 0 0 0 -1 }}
| {{Monzo| -1 3 0 0 0 -1 }}
| (Small) tridecimal 1/3-tone
| Small tridecimal 1/3-tone
|
|
|-
|-
Line 1,795: Line 1,795:
| 29/(2<sup>2</sup>×7)
| 29/(2<sup>2</sup>×7)
| 2.7.29 {{monzo| -2 -1 1 }}
| 2.7.29 {{monzo| -2 -1 1 }}
| Large vicesimononal 1/4-tone
| Vicesimononal thirdtone, vicesimononal subchroma, large vicesimononal 2/7-tone
|
|
|-
|-
Line 1,802: Line 1,802:
| (2×3×5)/29
| (2×3×5)/29
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
| Small vicesimononal 1/4-tone
| Small vicesimononal 2/7-tone
|
|
|-
|-
Line 1,809: Line 1,809:
| (2×29)/(3×19)
| (2×29)/(3×19)
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
|  
| Vicesimononal 1/7-tone
|
|
|-
|-
Line 1,956: Line 1,956:
| 29<sup>2</sup>/(2<sup>3</sup>×3×5×7)
| 29<sup>2</sup>/(2<sup>3</sup>×3×5×7)
| 2.3.5.7.29 {{monzo| -3 -1 -1 -1 2 }}
| 2.3.5.7.29 {{monzo| -3 -1 -1 -1 2 }}
|  
| Arabellisma
| S29
| S29
|-
|-
Line 2,110: Line 2,110:
| (13/(2×5×7))<sup>2</sup>×29
| (13/(2×5×7))<sup>2</sup>×29
| 2.5.7.13.29 {{monzo|-2 -2 -2 2 1}}
| 2.5.7.13.29 {{monzo|-2 -2 -2 2 1}}
|
| Large grapevine comma
|
|
|-
|-
Line 2,152: Line 2,152:
| (3<sup>3</sup>×5<sup>2</sup>×11)/(2<sup>8</sup>×29)
| (3<sup>3</sup>×5<sup>2</sup>×11)/(2<sup>8</sup>×29)
| 2.3.5.11.29 {{monzo|-8 3 2 1 -1}}
| 2.3.5.11.29 {{monzo|-8 3 2 1 -1}}
|
| Small grapevine comma
|
|
|-
|-
Line 2,806: Line 2,806:
| (2<sup>5</sup>×3×31)/(5<sup>2</sup>×7×17)
| (2<sup>5</sup>×3×31)/(5<sup>2</sup>×7×17)
| 2.3.5.7.17.31 {{monzo| 5 1 -2 -1 -1 1 }}
| 2.3.5.7.17.31 {{monzo| 5 1 -2 -1 -1 1 }}
|
|
|-
| [[3565/3564]]
| 0.48569
| (5×23×31)/((2×3<sup>2</sup>)<sup>2</sup>×11)
| 2.3.5.11.23.31 {{monzo| -2 -4 1 -1 1 1 }}
|
|
|-
| [[3751/3750]]
| 0.46160
| (11<sup>2</sup>×31)/(2×3×5<sup>4</sup>)
| 2.3.5.11.31 {{monzo| -1 -1 -4 2 1 }}
|
|
|-
| [[3876/3875]]
| 0.44671
| (2<sup>2</sup>×3×17×19)/(5<sup>3</sup>×31)
| 2.3.5.17.19.31 {{monzo| 2 1 -3 1 1 -1 }}
|  
|  
|
|
Line 2,967: Line 2,988:
| 2.5.41 {{monzo| -3 -1 1 }}
| 2.5.41 {{monzo| -3 -1 1 }}
| Large quadracesimoprimal 1/5-tone
| Large quadracesimoprimal 1/5-tone
|
|  
|-
|-
| [[42/41]]
| [[42/41]]
Line 2,974: Line 2,995:
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small quadracesimoprimal 1/5-tone
| Small quadracesimoprimal 1/5-tone
|
|  
|-
|-
| [[82/81]]
| [[82/81]]
Line 2,981: Line 3,002:
| 2.3.41 {{monzo| 1 -4 1 }}
| 2.3.41 {{monzo| 1 -4 1 }}
| 41st-partial chroma
| 41st-partial chroma
|
|  
|-
|-
| [[1025/1024]]
| [[124/123]]
| 1.6898
| 14.018
| (5<sup>2</sup>×41)/2<sup>10</sup>
| (2<sup>2</sup>×31)/(3×41)
| 2.5.41 {{monzo| -10 2 1 }}
| 2.3.31.41 {{monzo| 2 -1 1 -1 }}
|
|  
|  
|
|-
|-
| [[1600/1599]]
| [[165/164]]
| 1.0824
| 10.524
| (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41)
| (3×5×11)/(2<sup>2</sup>×41)
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
| 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }}
|
|  
| S40
|  
|-
|-
| [[1681/1680]]
| [[205/204]]
| 1.0302
| 8.4657
| 41<sup>2</sup>/(2<sup>4</sup>×3×5×7)
| (5×41)/(2<sup>2</sup>×3×17)
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
| 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }}
|
|
| S41
|
|-
| [[246/245]]
| 7.0519
| (2×3×41)/(5×7<sup>2</sup>)
| 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }}
|  
|  
|-
|-
| [[1682/1681]]
| [[247/246]]
| 1.0296
| 7.0233
| (2×29<sup>2</sup>)/41<sup>2</sup>
| (13×19)/(2×3×41)
| 2.29.41 {{monzo| 1 2 -2 }}
| 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }}
| Shaftesburisma
|  
|  
|  
|-
|-
| [[Megabyte comma|1048576/1048575]]
| [[287/286]]
| 0.0016510
| 6.0427
| 2<sup>20</sup>/(3×5<sup>2</sup>×11×31×41)
| (7×41)/(2×11×13)
| 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }}
| 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }}
| Megabyte comma
|  
| S1024
|  
|}
 
=== 43-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[43/42]]
| [[288/287]]
| 40.737
| 6.0217
| 43/(2×3×7)
| (2<sup>5</sup>×3<sup>2</sup>)/(7×41)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| 2.3.7.41 {{monzo| 5 2 -1 -1 }}
| Large quadracesimotertial 1/5-tone
|  
|
|  
|-
|-
| [[44/43]]
| [[369/368]]
| 39.800
| 4.6981
| (2<sup>2</sup>×11)/43
| (3<sup>2</sup>×41)/(2<sup>4</sup>×23)
| 2.11.43 {{monzo| 2 1 -1 }}
| 2.3.23.41 {{monzo| -4 2 -1 1 }}
| Small quadracesimotertial 1/5-tone
|  
|
|  
|-
|-
| [[86/85]]
| [[451/450]]
| 20.249
| 3.8429
| (2×43)/(5×17)
| (11×41)/(2×(3×5)<sup>2</sup>)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }}
|
|  
|  
|
|-
|-
| [[87/86]]
| [[493/492]]
| 20.014
| 3.5152
| (3×29)/(2×43)
| (17×29)/(2<sup>2</sup>×3×41)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }}
|
|  
|  
|
|-
|-
| [[129/128]]
| [[1025/1024]]
| 13.473
| 1.6898
| (3×43)/2<sup>7
| (5<sup>2</sup>×41)/2<sup>10</sup>
| 2.3.43 {{monzo| -7 1 1 }}
| 2.5.41 {{monzo| -10 2 1 }}
| 43rd-partial chroma
|  
|
|
|-
|-
| [[1764/1763]]
| [[1600/1599]]
| 0.98170
| 1.0824
| (2×3×7)<sup>2</sup>/(41×43)
| (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41)
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
|
| S40
|-
| [[1681/1680]]
| 1.0302
| 41<sup>2</sup>/(2<sup>4</sup>×3×5×7)
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
|
|
| S42
| S41
|-
|-
| [[1849/1848]]
| [[1682/1681]]
| 0.93656
| 1.0296
| 43<sup>2</sup>/(2<sup>3</sup>×3×7×11)
| (2×29<sup>2</sup>)/41<sup>2</sup>
| 2.3.7.11.43 {{monzo| -3 -1 -1 -1 2 }}
| 2.29.41 {{monzo| 1 2 -2 }}
| Shaftesburisma
|  
|  
| S43
|-
|-
| [[1936/1935]]
| [[Megabyte comma|1048576/1048575]]
| 0.98170
| 0.0016510
| 2<sup>20</sup>/(3×5<sup>2</sup>×11×31×41)
| 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }}
| Megabyte comma
| S1024
|}
 
=== 43-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[43/42]]
| 40.737
| 43/(2×3×7)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large quadracesimotertial 1/5-tone
|
|-
| [[44/43]]
| 39.800
| (2<sup>2</sup>×11)/43
| 2.11.43 {{monzo| 2 1 -1 }}
| Small quadracesimotertial 1/5-tone
|
|-
| [[86/85]]
| 20.249
| (2×43)/(5×17)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| Large quadracesimotertial 1/10-tone
|
|-
| [[87/86]]
| 20.014
| (3×29)/(2×43)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| Small quadracesimotertial 1/10-tone
|
|-
| [[129/128]]
| 13.473
| (3×43)/2<sup>7</sup>
| 2.3.43 {{monzo| -7 1 1 }}
| 43rd-partial chroma
|
|-
| [[130/129]]
| 13.369
| (2×5×13)/(3×43)
| 2.3.5.13.43 {{monzo| 1 -1 1 1 -1 }}
|
|
|-
| [[172/171]]
| 10.095
| (2<sup>2</sup>×43)/(3<sup>2</sup>×19)
| 2.3.19.43 {{monzo| 2 -2 -1 1 }}
|
|
|-
| [[216/215]]
| 8.0336
| (2×3)<sup>3</sup>/(5×43)
| 2.3.5.43 {{monzo| 3 3 -1 -1 }}
|
|
|-
| [[259/258]]
| 6.6972
| (7×37)/(2×3×43)
| 2.3.7.37.43 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[301/300]]
| 5.7612
| (7×43)/((2×5)<sup>2</sup>×3)
| 2.3.5.7.43 {{monzo| -2 -1 -2 1 1 }}
|
|
|-
| [[344/343]]
| 5.0400
| (2<sup>3</sup>×43)/(7<sup>3</sup>)
| 2.7.43 {{monzo| 3 -3 1 }}
|
|
|-
| [[345/344]]
| 5.0254
| (3×5×23)/(2<sup>3</sup>×43)
| 2.3.5.23.43 {{monzo| -3 1 1 1 -1 }}
|
|
|-
| [[430/429]]
| 4.0308
| (2×5×43)/(3×11×13)
| 2.3.5.11.13.43 {{monzo| 1 -1 1 -1 -1 1 }}
|
|
|-
| [[1764/1763]]
| 0.98170
| (2×3×7)<sup>2</sup>/(41×43)
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
|
| S42
|-
| [[1849/1848]]
| 0.93656
| 43<sup>2</sup>/(2<sup>3</sup>×3×7×11)
| 2.3.7.11.43 {{monzo| -3 -1 -1 -1 2 }}
|
| S43
|-
| [[1936/1935]]
| 0.98170
| (2<sup>2</sup>×11)<sup>2</sup>/(3<sup>2</sup>×5×43)
| (2<sup>2</sup>×11)<sup>2</sup>/(3<sup>2</sup>×5×43)
| 2.3.5.11.43 {{monzo| 4 -2 -1 2 -1 }}
| 2.3.5.11.43 {{monzo| 4 -2 -1 2 -1 }}
|
|
| S44
| S44
|}
|}
 
 
=== 47-limit (incomplete) ===
=== 47-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
! width="5%" | Meta<ref name="ssp"/>
|-
| [[47/46]]
| 37.232
| 47/(2×23)
| 2.23.47 {{monzo| -1 -1 1 }}
|
|
|-
| [[48/47]]
| 36.448
| (2<sup>4</sup>×3)/47
| 2.3.47 {{monzo| 4 1 -1 }}
|
|
|-
| [[94/93]]
| 18.516
| (2×47)/(3×31)
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
|
|
|-
| [[95/94]]
| 18.320
| (5×19)/(2×47)
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[141/140]]
| 12.322
| (3×47)/(2<sup>2</sup>×5×7)
| 2.3.5.7.47 {{monzo| -2 1 -1 -1 1 }}
|
|
|-
| [[188/187]]
| 9.2333
| (2<sup>2</sup>×47)/(11×17)
| 2.11.37.47 {{monzo| 2 -1 -1 1 }}
|
|
|-
| [[189/188]]
| 9.1843
| (3<sup>3</sup>×7)/(2<sup>2</sup>×47)
| 2.3.7.47 {{monzo| -2 3 1 -1 }}
|
|
|-
| [[235/234]]
| 7.3827
| (5×47)/(2×3<sup>2</sup>×13)
| 2.3.5.13.47 {{monzo| -1 -2 1 -1 1 }}
|
|
|-
| [[329/328]]
| 5.2701
| (7×47)/(2<sup>3</sup>×41)
| 2.7.41.47 {{monzo| -3 1 -1 1 }}
|
|
|-
| [[330/329]]
| 5.2541
| (2×3×5×11)/(7×47)
| 2.3.5.7.11.47 {{monzo| 1 1 1 -1 1 -1 }}
|
|
|-
|-
| [[47/46]]
| [[376/375]]
| 37.232
| 4.6105
| 47/(2×23)
| (2<sup>3</sup>×47)/(3×5<sup>3</sup>)
| 2.23.47 {{monzo| -1 -1 1 }}
| 2.3.5.47 {{monzo| 3 -1 -3 1 }}
|  
|  
|
|-
| [[48/47]]
| 36.448
| (2<sup>4</sup>×3)/47
| 2.3.47 {{monzo| 4 1 -1 }}
|  
|  
|
|-
|-
| [[94/93]]
| [[377/376]]
| 18.516
| 4.5982
| (2×47)/(3×31)
| (13×29)/(2<sup>3</sup>×47)
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
| 2.13.29.47 {{monzo| -3 1 1 -1 }}
|  
|  
|
|-
| [[95/94]]
| 18.320
| (5×19)/(2×47)
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
|  
|  
|
|-
|-
| [[2116/2115]]
| [[2116/2115]]
Retrieved from "https://en.xen.wiki/w/List_of_superparticular_intervals"