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User:Moremajorthanmajor/5L 2s (perfect eleventh-equivalent): Difference between revisions

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If we carry this freshman-summing out a little further, new, larger [[EDXI]]<nowiki/>s pop up in our continuum.
If we carry this freshman-summing out a little further, new, larger [[EDXI]]<nowiki/>s pop up in our continuum.


Generator ranges:  
Generator ranges:  
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{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="7" |Generator
!Generator
!Normalized
!Normalized
!L
!L
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!Comments
!Comments
|-
|-
|4\7|| || || || || || ||960¢||1||1||1.000||
|4\7||960.000¢||1||1||1.000||
|-
| 27\47||967.164¢||7||6||1.167||
|-
| 23\40||968.421¢||6||5||1.200||
|-
| 42\73||969.231¢||11||9||1.222||
|-
| 19\33||970.213¢||5||4||1.250||
|-
|-
| || || || || || ||27\47||967.1642¢||7||6||1.167||
| 34\59||971.429¢||9||7||1.286||
|-
|-
| || || || || ||23\40|| ||968.4211¢||6||5||1.200||
| 15\26||972.{{Overline|972}}¢||4||3||1.333||
|-
|-
| || || || || || ||42\73||969.2308¢||11||9||1.222||
| 56\97||973.913¢||15||11||1.364||
|-
|-
| || || || ||19\33|| || ||970.2128¢||5||4||1.250||
| 41\71||974.{{Overline|2574}}¢||11||8||1.375||
|-
|-
| || || || || || ||53\92||970.9924¢||14||11||1.273||
| 67\116||974.{{Overline|54}}¢||18||13||1.385||
|-
|-
| || || || || ||34\59|| ||971.4286¢||9||7||1.286||
| 26\45||975.000¢||7||5||1.400||17/12 [[Flattone]] is in this region
|-
|-
| || || || || || ||49\85||971.9008¢||13||10||1.300||
| 63\109||975.484¢||17||12||1.417||
|-
|-
| || || ||15\26|| || || ||972.{{Overline|972}}¢||4||3||1.333||
| 37\64||975.824¢||10||7||1.429||
|-
|-
| || || || || || ||56\97||973.913¢||15||11||1.364||
| 48\83||976.271¢||13||9||1.444||
|-
|-
| || || || || ||41\71|| ||974.{{Overline|2574}}¢||11||8||1.375||
| 11\19||977.{{Overline|7}}¢||3||2||1.500||
|-
|-
| || || || || || ||67\116||974.{{Overline|54}}¢||18||13||1.385||
| 51\88||979.200¢||14||9||1.556||
|-
|-
| || || || ||26\45|| || ||975¢||7||5||1.400||17/12 [[Flattone]] is in this region
| 40\69||979.592¢||11||7||1.571||
|-
|-
| || || || || || ||63\109||975.4839¢||17||12||1.417||
| 29\50||980.282¢||8||5||1.600||
|-
|-
| || || || || ||37\64|| ||975.8242¢||10||7||1.429||
| 76\131||980.645¢||21|| |13||1.615||17/12 [[Golden meantone]] (980.7157¢)
|-
|-
| || || || || || ||48\83||976.2712¢||13||9||1.444||
| 47\81||980.870¢||13||8||1.625||
|-
|-
| || ||11\19|| || || || ||977.{{Overline|7}}¢||3||2||1.500||
| 18\31||981.{{Overline|81}}¢||5||3||1.667||17/12 [[Meantone]] is in this region
|-
|-
| || || || || || ||51\88||979.2¢||14||9||1.556||
| 43\74||982.857¢||12||7||1.714||
|-
|-
| || || || || ||40\69|| ||979.5918¢||11||7||1.571||
| 25\43||983.607¢||7||4||1.750||
|-
|-
| || || || || || ||69\119||979.8817¢||19||12||1.583||
| 32\55||984.615¢||9||5||1.800||
|-
|-
| || || || ||29\50|| || ||980.2817¢||8||5||1.600||
| 39\67||985.263¢||11||6||1.833||
|-
|-
| || || || || || ||76\131||980.6452¢||21|| |13||1.615||17/12 [[Golden meantone]] (980.7157¢)
|46\79
|985.714¢
|13
|7
|1.857
|
|-
|-
| || || || || ||47\81|| ||980.8696¢||13||8||1.625||
|53\91
|986.047¢
|15
|8
|1.875
|
|-
|-
| || || || || || ||65\112||981.1321¢||18||11||1.636||
|60\103
|986.301¢
|17
|9
|1.889
|
|-
|-
| || || ||18\31|| || || ||981.{{Overline|81}}¢||5||3||1.667||17/12 [[Meantone]] is in this region
|67\115
|986.503¢
|19
|10
|1.900
|
|-
|-
| || || || || || ||61\105||982.5503¢||17||10||1.700||
|74\127
|986.{{Overline|6}}¢
|21
|11
|1.909
|
|-
|-
| || || || || ||43\74|| ||982.857¢||12||7||1.714||
|81\139
|986.802¢
|23
|12
|1.917
|
|-
|-
| || || || || || ||68\117||983.1325¢||19||11||1.727||
|88\151
|986.916¢
|25
|13
|1.923
|
|-
|-
| || || || ||25\43|| || ||983.6066¢||7||4||1.750||
|95\163
|987.013¢
|27
|14
|1.929
|
|-
|-
| || || || || || ||57\98||984.1727¢||16||9||1.778||
| 7\12||988.235¢||2||1||2.000||Basic 17/12 diatonic <br>(Generators smaller than this are proper)
|-
|-
| || || || || ||32\55|| ||984.6154¢||9||5||1.800||
|45\77
|990.826¢
|13
|6
|2.167
|
|-
|-
| || || || || || ||39\67||985.2632¢||11||6||1.833||
| 38\65||991.304¢||11||5||2.200||
|-
|-
| ||7\12|| || || || || ||988.2353¢||2||1||2.000||Basic 17/12 diatonic <br>(Generators smaller than this are proper)
| 31\53||992.000¢||9||4||2.250||The generator closest to 17/12 of a just [[3/2]] for EDXIs less than 200
|-
|-
| || || || || || ||38\65||991.3043¢||11||5||2.200||
| 55\94||992.481¢||16||7||2.286||17/12 [[Garibaldi]] / [[Cassandra]]
|-
|-
| || || || || ||31\53|| ||992¢||9||4||2.250||The generator closest to 17/12 of a just [[3/2]] for EDXIs less than 200
| 24\41||993.103¢||7||3||2.333||
|-
|-
| || || || || || ||55\94||992.4812¢||16||7||2.286||17/12 [[Garibaldi]] / [[Cassandra]]
| 41\70||993.{{Overline|93}}¢||12||5||2.400||
|-
|-
| || || || ||24\41|| || ||993.1034¢||7||3||2.333||
| 58\99||994.2857¢||17||7||2.428||
|-
|-
| || || || || || ||65\111||993.6306¢||19||8||2.375||
| 17\29||995.122¢||5||2||2.500||
|-
|-
| || || || || ||41\70|| ||993.{{Overline|93}}¢||12||5||2.400||
| 44\75||996.226¢||13||5||2.600||
|-
|-
| || || || || || ||58\99||994.2857¢||17||7||2.428||
| 71\121||996.491¢||21||8||2.625||17/12 Golden neogothic (996.3946¢)
|-
|-
| || || ||17\29|| || || ||995.1220¢||5||2||2.500||
| 27\46||996.923¢||8||3||2.667||17/12 [[Neogothic]] is in this region
|-
|-
| || || || || || ||61\104||995.9184¢||18||7||2.571||
| 37\63||997.753¢||11||4||2.750||
|-
|-
| || || || || ||44\75|| ||996.2264¢||13||5||2.600||
| 47\80||998.230¢||14||5||2.800||
|-
|-
| || || || || || ||71\121||996.4912¢||21||8||2.625||17/12 Golden neogothic (996.3946¢)
|57\97
|998.540¢
|17
|6
|2.833
|
|-
|-
| || || || ||27\46|| || ||996.9231¢||8||3||2.667||17/12 [[Neogothic]] is in this region
|67\114
|998.758¢
|20
|7
|2.857
|
|-
|-
| || || || || || ||64\109||997.4026¢||19||7||2.714||
|77\131
|998.{{Overline|918}}¢
|23
|8
|2.875
|
|-
|-
| || || || || ||37\63|| ||997.7528¢||11||4||2.750||
|87\148
|999.043¢
|26
|9
|2.889
|
|-
|-
| || || || || || ||47\80||998.2301¢||14||5||2.800||
| 10\17||1000.000¢||3||1||3.000||
|-
|-
| || ||10\17|| || || || ||1000¢||3||1||3.000||
| 43\73||1001.942¢||13||4||3.250||
|-
|-
| || || || || || ||43\73||1001.9417¢||13||4||3.250||
| 33\56||1002.532¢||10||3||3.333||
|-
|-
| || || || || ||33\56|| ||1002.5316¢||10||3||3.333||
| 23\39||1003.{{Overline|63}}¢||7||2||3.500||
|-
|-
| || || || || || ||56\95||1002.9851¢||17||5||3.400||
| 36\61||1004.651¢||11||3||3.667||
|-
|-
| || || || ||23\39|| || ||1003.{{Overline|63}}¢||7||2||3.500||
| 49\83||1005.128¢||15||4||3.750||
|-
|-
| || || || || || ||59\100||1004.2553¢||18||5||3.600||
| 13\22||1006.452¢||4||1||4.000||17/12 [[Archy]] is in this region
|-
|-
| || || || || ||36\61|| ||1004.6512¢||11||3||3.667||
|55\93
|1007.634¢
|17
|4
|4.250
|
|-
|-
| || || || || || ||49\83||1005.1282¢||15||4||3.750||
| 42\71||1008.000¢||13||3||4.333||
|-
|-
| || || ||13\22|| || || ||1006.4516¢||4||1||4.000||17/12 [[Archy]] is in this region
| 29\49||1008.696¢||9||2||4.500||
|-
|-
| || || || || || ||42\71||1008¢||13||3||4.333||
| 45\76||1009.346¢||14||3||4.667||
|-
|-
| || || || || ||29\49|| ||1008.6957¢||9||2||4.500||
| 16\27||1010.526¢||5||1||5.000||
|-
|-
| || || || || || ||45\76||1009.3458¢||14||3||4.667||
|51\86
|1011.570¢
|16
|3
|5.333
|
|-
|-
| || || || ||16\27|| || ||1010.5263¢||5||1||5.000||
| 35\59||1012.048¢||11||2||5.500||
|-
|-
| || || || || || ||35\59||1012.0482¢||11||2||5.500||
| 19\32||1013.{{Overline|3}}¢||6||1||6.000||
|-
|-
| || || || || ||19\32|| ||1013.{{Overline|3}}¢||6||1||6.000||
|41\69
|1014.432¢
|13
|2
|6.500
|
|-
|-
| || || || || || ||22\37||1015.3846¢||7||1||7.000||
| 22\37||1015.385¢||7||1||7.000||
|-
|-
|3\5|| || || || || || ||1028.5714¢||1||0||→ inf||
|3\5||1028.571¢||1||0||→ inf||
|}
|}


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