User:Moremajorthanmajor/5L 2s (8/3-equivalent): Difference between revisions

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Generator ranges:  
Generator ranges:  
*Chroma-positive generator: 960 cents (4\7, normalized) to 1028.5714 cents (3\5, normalized)
*Chroma-positive generator: 970.311 cents (4\7) to 1018.827 cents (3\5)
*Chroma-negative generator: 685.7143 cents (2\5, normalized) to 720 cents (3\7, normalized)
*Chroma-negative generator: 679.218 cents (2\5) to 727.734 cents (3\7)


{| class="wikitable center-all"
{{Scale tree|5L 2s<8/3>}}
! colspan="7" |Generator
!Normalized
!L
!s
!L/s
!Comments
|-
|4\7|| || || || || || ||960¢||1||1||1.000||
|-
| || || || || || ||27\47||967.1642¢||7||6||1.167||
|-
| || || || || ||23\40|| ||968.4211¢||6||5||1.200||
|-
| || || || || || ||42\73||969.2308¢||11||9||1.222||
|-
| || || || ||19\33|| || ||970.2128¢||5||4||1.250||
|-
| || || || || || ||53\92||970.9924¢||14||11||1.273||
|-
| || || || || ||34\59|| ||971.4286¢||9||7||1.286||
|-
| || || || || || ||49\85||971.9008¢||13||10||1.300||
|-
| || || ||15\26|| || || ||972.{{Overline|972}}¢||4||3||1.333||
|-
| || || || || || ||56\97||973.913¢||15||11||1.364||
|-
| || || || || ||41\71|| ||974.{{Overline|2574}}¢||11||8||1.375||
|-
| || || || || || ||67\116||974.{{Overline|54}}¢||18||13||1.385||
|-
| || || || ||26\45|| || ||975¢||7||5||1.400||17/12 [[Flattone]] is in this region
|-
| || || || || || ||63\109||975.4839¢||17||12||1.417||
|-
| || || || || ||37\64|| ||975.8242¢||10||7||1.429||
|-
| || || || || || ||48\83||976.2712¢||13||9||1.444||
|-
| || ||11\19|| || || || ||977.{{Overline|7}}¢||3||2||1.500||
|-
| || || || || || ||51\88||979.2¢||14||9||1.556||
|-
| || || || || ||40\69|| ||979.5918¢||11||7||1.571||
|-
| || || || || || ||69\119||979.8817¢||19||12||1.583||
|-
| || || || ||29\50|| || ||980.2817¢||8||5||1.600||
|-
| || || || || || ||76\131||980.6452¢||21|| |13||1.615||17/12 [[Golden meantone]] (980.7157¢)
|-
| || || || || ||47\81|| ||980.8696¢||13||8||1.625||
|-
| || || || || || ||65\112||981.1321¢||18||11||1.636||
|-
| || || ||18\31|| || || ||981.{{Overline|81}}¢||5||3||1.667||17/12 [[Meantone]] is in this region
|-
| || || || || || ||61\105||982.5503¢||17||10||1.700||
|-
| || || || || ||43\74|| ||982.857¢||12||7||1.714||
|-
| || || || || || ||68\117||983.1325¢||19||11||1.727||
|-
| || || || ||25\43|| || ||983.6066¢||7||4||1.750||
|-
| || || || || || ||57\98||984.1727¢||16||9||1.778||
|-
| || || || || ||32\55|| ||984.6154¢||9||5||1.800||
|-
| || || || || || ||39\67||985.2632¢||11||6||1.833||
|-
| ||7\12|| || || || || ||988.2353¢||2||1||2.000||Basic 17/12 diatonic <br>(Generators smaller than this are proper)
|-
| || || || || || ||38\65||991.3043¢||11||5||2.200||
|-
| || || || || ||31\53|| ||992¢||9||4||2.250||The generator closest to 17/12 of a just [[3/2]] for EDXIs less than 200
|-
| || || || || || ||55\94||992.4812¢||16||7||2.286||17/12 [[Garibaldi]] / [[Cassandra]]
|-
| || || || ||24\41|| || ||993.1034¢||7||3||2.333||
|-
| || || || || || ||65\111||993.6306¢||19||8||2.375||
|-
| || || || || ||41\70|| ||993.{{Overline|93}}¢||12||5||2.400||
|-
| || || || || || ||58\99||994.2857¢||17||7||2.428||
|-
| || || ||17\29|| || || ||995.1220¢||5||2||2.500||
|-
| || || || || || ||61\104||995.9184¢||18||7||2.571||
|-
| || || || || ||44\75|| ||996.2264¢||13||5||2.600||
|-
| || || || || || ||71\121||996.4912¢||21||8||2.625||17/12 Golden neogothic (996.3946¢)
|-
| || || || ||27\46|| || ||996.9231¢||8||3||2.667||17/12 [[Neogothic]] is in this region
|-
| || || || || || ||64\109||997.4026¢||19||7||2.714||
|-
| || || || || ||37\63|| ||997.7528¢||11||4||2.750||
|-
| || || || || || ||47\80||998.2301¢||14||5||2.800||
|-
| || ||10\17|| || || || ||1000¢||3||1||3.000||
|-
| || || || || || ||43\73||1001.9417¢||13||4||3.250||
|-
| || || || || ||33\56|| ||1002.5316¢||10||3||3.333||
|-
| || || || || || ||56\95||1002.9851¢||17||5||3.400||
|-
| || || || ||23\39|| || ||1003.{{Overline|63}}¢||7||2||3.500||
|-
| || || || || || ||59\100||1004.2553¢||18||5||3.600||
|-
| || || || || ||36\61|| ||1004.6512¢||11||3||3.667||
|-
| || || || || || ||49\83||1005.1282¢||15||4||3.750||
|-
| || || ||13\22|| || || ||1006.4516¢||4||1||4.000||17/12 [[Archy]] is in this region
|-
| || || || || || ||42\71||1008¢||13||3||4.333||
|-
| || || || || ||29\49|| ||1008.6957¢||9||2||4.500||
|-
| || || || || || ||45\76||1009.3458¢||14||3||4.667||
|-
| || || || ||16\27|| || ||1010.5263¢||5||1||5.000||
|-
| || || || || || ||35\59||1012.0482¢||11||2||5.500||
|-
| || || || || ||19\32|| ||1013.{{Overline|3}}¢||6||1||6.000||
|-
| || || || || || ||22\37||1015.3846¢||7||1||7.000||
|-
|3\5|| || || || || || ||1028.5714¢||1||0||→ inf||
|}


Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include 17/12 meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.
Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include 17/12 meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.