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| Line 117: |
Line 117: |
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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) |
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| {| 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||
| |
| |}
| |
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| |
|
| 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. |