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| Line 204: |
Line 204: |
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| |} | | |} |
| ==Scale tree==
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| If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.
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| If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.
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|
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| Generator range: 36.09023 cents (4\7/19 = 4\133) to 37.89474 cents (3\5/19 = 3\95)
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| {| class="wikitable center-all"
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| ! colspan="7" | Fifth
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| !Cents
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| ! Comments
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| |-
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| | 4\7|| || || || || || || 36.0902||
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| |-
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| | || || || || || ||27\47||36.2822||
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| |-
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| | || || || || ||23\40|| ||36.3158 ||
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| |-
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| | || || || || || ||42\73 ||36.3374 ||
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| |-
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| | || || || || 19\33|| || ||36.{{Overline|36}}||
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| |-
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| | || || || || || ||53\92||36.3844||
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| |-
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| | || || || || ||34\59|| ||36.3961||
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| |-
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| | || || || || || ||49\85||36.4087 ||
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| |-
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| | || || ||15\26|| || || ||36.43725||
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| |-
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| | || || || || || ||56\97||36.4633||
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| |-
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| | || || || || || 41\71|| ||36.4175||
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| |-
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| | || || || || || ||67\116|| 36.4791||
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| |-
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| | || || || || 26\45|| || ||36.4912||[[Flattone]] is in this region
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| |-
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| | || || || || || ||63\109||36.5041||
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| |-
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| | || || || || ||37\64|| ||36.5132||
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| |-
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| | || || || || || ||48\83 || 36.52505||
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| |-
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| | || ||11\19|| || || || || 36.5651||
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| |-
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| | || || || || || || 51\88||36.6029||
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| |-
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| | || || || || ||40\69 || ||36.6133||
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| |-
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| | || || || || || ||69\119|| 36.6210||
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| |-
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| | || || || || 29\50|| || ||36.6316||
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| |-
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| | || || || || || || 76\131||36.6412||[[Golden meantone]] (696.2145¢)
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| |-
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| | || || || || ||47\81|| ||36.6472||
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| |-
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| | || || || || || ||65\112||36.6541||
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| |-
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| | || || ||18\31|| || || ||36.6723||[[Meantone]] is in this region
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| |-
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| | || || || || || ||61\105||36.6917||
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| |-
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| | || || || || ||43\74|| ||36.6999||
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| |-
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| | || || || || || ||68\117||36.70175||
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| |-
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| | || || || ||25\43|| || ||36.7197||
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| |-
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| | || || || || || ||57\98||36.7347||
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| |-
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| | || || || || ||32\55|| ||36.7464||
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| |-
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| | || || || || || ||39\67||36.76355||
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| |-
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| | ||7\12|| || || || || ||36.8421||
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| |-
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| | || || || || || ||38\65||36.9231||
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| |-
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| | || || || || ||31\53|| ||36.9414||The fifth closest to a just [[3/2]] for EDOs less than 200
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| |-
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| | || || || || || ||55\94||36.9541||[[Garibaldi]] / [[Cassandra]]
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| |-
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| | || || || ||24\41|| || ||36.9705||
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| |-
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| | || || || || || ||65\111||36.98435||
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| |-
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| | || || || || ||41\70|| ||36.9925||
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| |-
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| | || || || || || ||58\99||37.0016||
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| |-
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| | || || ||17\29|| || || ||37.0236||
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| |-
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| | || || || || || ||61\104||37.0445||
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| |-
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| | || || || || ||44\75|| ||37.0526||
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| |-
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| | || || || || || ||71\121||37.0596||Golden neogothic (704.0956¢)
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| |-
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| | || || || ||27\46|| || ||37.0709||[[Neogothic]] is in this region
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| |-
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| | || || || || || ||64\109||37.0835||
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| |-
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| | || || || || ||37\63|| ||37.0927||
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| |-
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| | || || || || || ||47\80||37.1053||
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| |-
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| | || ||10\17|| || || || ||37.1517||
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| |-
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| | || || || || || ||43\73||37.2026||
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| |-
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| | || || || || ||33\56|| ||37.21805||
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| |-
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| | || || || || || ||56\95||37.2299||
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| |-
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| | || || || ||23\39|| || ||37.2470||
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| |-
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| | || || || || || ||59\100||37.2632||
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| |-
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| | || || || || ||36\61|| ||37.2735||
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| |-
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| | || || || || || ||49\83||37.2388||
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| |-
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| | || || ||13\22|| || || ||37.3206||[[Archy]] is in this region
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| |-
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| | || || || || || ||42\71||37.3610||
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| |-
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| | || || || || ||29\49|| ||37.3792||
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| |-
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| | || || || || || ||45\76||37.3961||
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| |-
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| | || || || ||16\27|| || ||37.4269||
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| |-
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| | || || || || || ||35\59||37.46655||
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| |-
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| | || || || || ||19\32|| ||37.5000||
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| |-
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| | || || || || || ||22\37||37.5533||
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| |-
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| |3\5|| || || || || || ||37.8947||
| |
| |}Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include 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.
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| [[Category:Edf]]
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| [[Category:Edonoi]]
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