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S-expression: Difference between revisions

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→Sk/S(k + 1) (ultraparticulars): add more ultraparticulars given all present have a page or will have a page. ultraparticulars added are 23-limit or dividing a superparticular in three except S27/S28 added for completeness
Godtone (talk | contribs)
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→Sk/S(k + 1) (ultraparticulars): add cent values (as ultraparticulars are very small) and a 17-limit ultraparticular, S50/S51, adjacent to S49/S50 for a comparison of cent-size and for completeness in the 23-limit
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|-
|-
| S2/S3 = ([[4/3]])/([[9/8]])
| S2/S3 = ([[4/3]])/([[9/8]])
| ([[4/1]]) / ([[3/2]])<sup>3</sup>
| ([[4/1]])/([[3/2]])<sup>3</sup>
| [[32/27]]
| [[32/27]]
| 294.135
|-
|-
| S3/S4 = ([[9/8]])/([[16/15]])  
| S3/S4 = ([[9/8]])/([[16/15]])
| ([[5/2]]) / ([[4/3]])<sup>3</sup>
| ([[5/2]])/([[4/3]])<sup>3</sup>
| [[135/128]]
| [[135/128]]
| 92.179
|-
|-
| S4/S5 = ([[16/15]])/([[25/24]])
| S4/S5 = ([[16/15]])/([[25/24]])
| ([[2/1]]) / ([[5/4]])<sup>3</sup>
| ([[2/1]])/([[5/4]])<sup>3</sup>
| [[128/125]]
| [[128/125]]
| 41.059
|-
|-
| S5/S6 = ([[25/24]])/([[36/35]])
| S5/S6 = ([[25/24]])/([[36/35]])
| ([[7/4]]) / ([[6/5]])<sup>3</sup>
| ([[7/4]])/([[6/5]])<sup>3</sup>
| [[875/864]]
| [[875/864]]
| 21.902
|-
|-
| S6/S7 = ([[36/35]])/([[49/48]])
| S6/S7 = ([[36/35]])/([[49/48]])
| ([[8/5]]) / ([[7/6]])<sup>3</sup>
| ([[8/5]])/([[7/6]])<sup>3</sup>
| [[1728/1715]]
| [[1728/1715]]
| 13.074
|-
|-
| S7/S8 = ([[49/48]])/([[64/63]])
| S7/S8 = ([[49/48]])/([[64/63]])
| ([[3/2]]) / ([[8/7]])<sup>3</sup>
| ([[3/2]])/([[8/7]])<sup>3</sup>
| [[1029/1024]]
| [[1029/1024]]
| 8.433
|-
|-
| S8/S9 = ([[64/63]])/([[81/80]])
| S8/S9 = ([[64/63]])/([[81/80]])
| ([[10/7]]) / ([[9/8]])<sup>3</sup>
| ([[10/7]])/([[9/8]])<sup>3</sup>
| [[5120/5103]]
| [[5120/5103]]
| 5.758
|-
|-
| S9/S10 = ([[81/80]])/([[100/99]])
| S9/S10 = ([[81/80]])/([[100/99]])
| ([[11/8]]) / ([[10/9]])<sup>3</sup>
| ([[11/8]])/([[10/9]])<sup>3</sup>
| [[8019/8000]]
| [[8019/8000]]
| 4.107
|-
|-
| S10/S11 = ([[100/99]])/([[121/120]])
| S10/S11 = ([[100/99]])/([[121/120]])
| ([[4/3]]) / ([[11/10]])<sup>3</sup>
| ([[4/3]])/([[11/10]])<sup>3</sup>
| [[4000/3993]]
| [[4000/3993]]
| 3.032
|-
|-
| S11/S12 = ([[121/120]])/([[144/143]])
| S11/S12 = ([[121/120]])/([[144/143]])
| ([[13/10]]) /([[12/11]])<sup>3</sup>
| ([[13/10]])/([[12/11]])<sup>3</sup>
| [[17303/17280]]
| [[17303/17280]]
| 2.303
|-
|-
| S12/S13 = ([[144/143]])/([[169/168]])
| S12/S13 = ([[144/143]])/([[169/168]])
| ([[14/11]]) / ([[13/12]])<sup>3</sup>
| ([[14/11]])/([[13/12]])<sup>3</sup>
| [[24192/24167]]
| [[24192/24167]]
| 1.79
|-
|-
| S13/S14 = ([[169/168]])/([[196/195]])
| S13/S14 = ([[169/168]])/([[196/195]])
| ([[5/4]]) / ([[14/13]])<sup>3</sup>
| ([[5/4]])/([[14/13]])<sup>3</sup>
| [[10985/10976]]
| [[10985/10976]]
| 1.419
|-
|-
| S14/S15 = ([[196/195]])/([[225/224]])
| S14/S15 = ([[196/195]])/([[225/224]])
| ([[16/13]]) / ([[15/14]])<sup>3</sup>
| ([[16/13]])/([[15/14]])<sup>3</sup>
| [[43904/43875]]
| [[43904/43875]]
| 1.144
|-
|-
| S15/S16 = ([[225/224]])/([[256/255]])
| S15/S16 = ([[225/224]])/([[256/255]])
| ([[17/14]]) / ([[16/15]])<sup>3</sup>
| ([[17/14]])/([[16/15]])<sup>3</sup>
| [[57375/57344]]
| [[57375/57344]]
| 0.936
|-
|-
| S16/S17 = ([[256/255]])/([[289/288]])
| S16/S17 = ([[256/255]])/([[289/288]])
| ([[6/5]]) / ([[17/16]])<sup>3</sup>
| ([[6/5]])/([[17/16]])<sup>3</sup>
| [[24576/24565]]
| [[24576/24565]]
| 0.775
|-
|-
| S17/S18 = ([[289/288]])/([[324/323]])
| S17/S18 = ([[289/288]])/([[324/323]])
| ([[19/16]])/([[18/17]])<sup>3</sup>
| ([[19/16]])/([[18/17]])<sup>3</sup>
| [[93347/93312]]
| [[93347/93312]]
| 0.649
|-
|-
| S18/S19 = ([[324/323]])/([[361/360]])
| S18/S19 = ([[324/323]])/([[361/360]])
| ([[20/17]])/([[19/18]])<sup>3</sup>
| ([[20/17]])/([[19/18]])<sup>3</sup>
| [[116640/116603]]
| [[116640/116603]]
| 0.549
|-
|-
| S19/S20 = ([[361/360]])/([[400/399]])
| S19/S20 = ([[361/360]])/([[400/399]])
| ([[7/6]])/([[20/19]])<sup>3</sup>
| ([[7/6]])/([[20/19]])<sup>3</sup>
| [[48013/48000]]
| [[48013/48000]]
| 0.469
|-
|-
| S20/S21 = ([[400/399]])/([[441/440]])
| S20/S21 = ([[400/399]])/([[441/440]])
| ([[22/19]])/([[21/20]])<sup>3</sup>
| ([[22/19]])/([[21/20]])<sup>3</sup>
| [[176000/175959]]
| [[176000/175959]]
| 0.403
|-
|-
| S21/S22 = ([[441/440]])/([[484/483]])
| S21/S22 = ([[441/440]])/([[484/483]])
| ([[23/20]])/([[22/21]])<sup>3</sup>
| ([[23/20]])/([[22/21]])<sup>3</sup>
| [[213003/212960]]
| [[213003/212960]]
| 0.35
|-
|-
| S22/S23 = ([[484/483]])/([[529/528]])
| S22/S23 = ([[484/483]])/([[529/528]])
| ([[8/7]])/([[23/22]])<sup>3</sup>
| ([[8/7]])/([[23/22]])<sup>3</sup>
| [[85184/85169]]
| [[85184/85169]]
| 0.305
|-
|-
| S23/S24 = ([[529/528]])/([[576/575]])
| S23/S24 = ([[529/528]])/([[576/575]])
| ([[25/22]])/([[24/23]])<sup>3</sup>
| ([[25/22]])/([[24/23]])<sup>3</sup>
| [[304175/304128]]
| [[304175/304128]]
| 0.268
|-
|-
| S24/S25 = ([[576/575]])/([[625/624]])
| S24/S25 = ([[576/575]])/([[625/624]])
| ([[26/23]])/([[25/24]])<sup>3</sup>
| ([[26/23]])/([[25/24]])<sup>3</sup>
| [[359424/359375]]
| [[359424/359375]]
| 0.236
|-
|-
| S25/S26 = ([[625/624]])/([[676/675]])
| S25/S26 = ([[625/624]])/([[676/675]])
| ([[9/8]])/([[26/25]])<sup>3</sup>
| ([[9/8]])/([[26/25]])<sup>3</sup>
| [[140625/140608]]
| [[140625/140608]]
| 0.209
|-
|-
| S26/S27 = ([[676/675]])/([[729/728]])
| S26/S27 = ([[676/675]])/([[729/728]])
| ([[28/25]])/([[27/26]])<sup>3</sup>
| ([[28/25]])/([[27/26]])<sup>3</sup>
| [[492128/492075]]
| [[492128/492075]]
| 0.186
|-
|-
| S27/S28 = ([[729/728]])/([[784/783]])
| S27/S28 = ([[729/728]])/([[784/783]])
| ([[29/26]])/([[28/27]])<sup>3</sup>
| ([[29/26]])/([[28/27]])<sup>3</sup>
| [[570807/570752]]
| [[570807/570752]]
| 0.167
|-
|-
| S28/S29 = ([[784/783]])/([[841/840]])
| S28/S29 = ([[784/783]])/([[841/840]])
| ([[10/9]])/([[29/28]])<sup>3</sup>
| ([[10/9]])/([[29/28]])<sup>3</sup>
| [[219520/219501]]
| [[219520/219501]]
| 0.15
|-
|-
| S31/S32 = ([[961/960]])/([[1024/1023]])
| S31/S32 = ([[961/960]])/([[1024/1023]])
| ([[11/10]])/([[32/31]])<sup>3</sup>
| ([[11/10]])/([[32/31]])<sup>3</sup>
| [[327701/327680]]
| [[327701/327680]]
| 0.111
|-
|-
| S33/S34 = ([[1089/1088]])/([[1156/1155]])
| S33/S34 = ([[1089/1088]])/([[1156/1155]])
| ([[35/32]])/([[34/33]])<sup>3</sup>
| ([[35/32]])/([[34/33]])<sup>3</sup>
| [[1257795/1257728]]
| [[1257795/1257728]]
| 0.092
|-
|-
| S34/S35 = ([[1156/1155]])/([[1225/1224]])
| S34/S35 = ([[1156/1155]])/([[1225/1224]])
| ([[12/11]])/([[35/34]])<sup>3</sup>
| ([[12/11]])/([[35/34]])<sup>3</sup>
| [[471648/471625]]
| [[471648/471625]]
| 0.084
|-
|-
| S37/S38 = ([[1369/1368]])/([[1444/1443]])
| S37/S38 = ([[1369/1368]])/([[1444/1443]])
| ([[13/12]])/([[38/37]])<sup>3</sup>
| ([[13/12]])/([[38/37]])<sup>3</sup>
| [[658489/658464]]
| [[658489/658464]]
| 0.066
|-
|-
| S40/S41 = ([[1600/1599]])/([[1681/1680]])
| S40/S41 = ([[1600/1599]])/([[1681/1680]])
| ([[14/13]])/([[41/40]])<sup>3</sup>
| ([[14/13]])/([[41/40]])<sup>3</sup>
| [[896000/895973]]
| [[896000/895973]]
| 0.052
|-
|-
| S43/S44 = ([[1849/1848]])/([[1936/1935]])
| S43/S44 = ([[1849/1848]])/([[1936/1935]])
| ([[15/14]])/([[44/43]])<sup>3</sup>
| ([[15/14]])/([[44/43]])<sup>3</sup>
| [[1192605/1192576]]
| [[1192605/1192576]]
| 0.042
|-
|-
| S46/S47 = ([[2116/2115]])/([[2209/2208]])
| S46/S47 = ([[2116/2115]])/([[2209/2208]])
| ([[16/15]])/([[47/46]])<sup>3</sup>
| ([[16/15]])/([[47/46]])<sup>3</sup>
| [[1557376/1557345]]
| [[1557376/1557345]]
| 0.034
|-
|-
| S49/S50 = ([[2401/2400]])/([[2500/2499]])
| S49/S50 = ([[2401/2400]])/([[2500/2499]])
| ([[17/16]])/([[50/49]])<sup>3</sup>
| ([[17/16]])/([[50/49]])<sup>3</sup>
| [[2000033/2000000]]
| [[2000033/2000000]]
| 0.029
|-
| S50/S51 = ([[2500/2499]])/([[2601/2600]])
| ([[52/49]])/([[51/50]])<sup>3</sup>
| [[6500000/6499899]]
| 0.027
|-
|-
| S55/S56 = ([[3025/3024]])/([[3136/3135]])
| S55/S56 = ([[3025/3024]])/([[3136/3135]])
| ([[19/18]])/([[56/55]])<sup>3</sup>
| ([[19/18]])/([[56/55]])<sup>3</sup>
| [[3161125/3161088]]
| [[3161125/3161088]]
| 0.02
|-
|-
| S64/S65 = ([[4096/4095]])/([[4225/4224]])
| S64/S65 = ([[4096/4095]])/([[4225/4224]])
| ([[22/21]])/([[65/64]])<sup>3</sup>
| ([[22/21]])/([[65/64]])<sup>3</sup>
| [[5767168/5767125]]
| [[5767168/5767125]]
| 0.013
|}
|}


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