EDT: Difference between revisions
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| | 160edt is 101edo with ~0.61 cent stretched octaves. | | | 160edt is 101edo with ~0.61 cent stretched octaves. | ||
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|[[161edt]] | | | [[161edt]] | ||
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|161edt falls exactly halfway between 101 and 102 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\203 of an octave. | | | 161edt falls exactly halfway between 101 and 102 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\203 of an octave. | ||
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|[[162edt]] | | | [[162edt]] | ||
|[[102edo]] | | | [[102edo]] | ||
|Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 5-limit. | | | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 5-limit. | ||
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|[[163edt]] | | | [[163edt]] | ||
|[[103edo]] | | | [[103edo]] | ||
|163edt is 103edo with ~1.85 cent stretched octaves | | | 163edt is 103edo with ~1.85 cent stretched octaves. | ||
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|[[164edt]] | |[[164edt]] | ||
| Line 1,027: | Line 1,027: | ||
| | 165edt is 104edo with ~1.2 cent compressed octaves. | | | 165edt is 104edo with ~1.2 cent compressed octaves. | ||
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|[[166edt]] | | | [[166edt]] | ||
|[[105edo]] | | | [[105edo]] | ||
|166edt is 105edo with ~3 cent stretched octaves. | | | 166edt is 105edo with ~3 cent stretched octaves. | ||
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|[[167edt]] | | | [[167edt]] | ||
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|167edt falls exactly halfway between 105 and 106 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\211 of an octave. | | | 167edt falls exactly halfway between 105 and 106 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\211 of an octave. | ||
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| | [[168edt]] | | | [[168edt]] | ||
| Line 1,039: | Line 1,039: | ||
| | Same ~0.04 cent octave stretch as 84edt~53edo. | | | Same ~0.04 cent octave stretch as 84edt~53edo. | ||
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|[[169edt]] | | | [[169edt]] | ||
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|169edt falls exactly halfway between 106 and 107 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\213 of an octave. | | | 169edt falls exactly halfway between 106 and 107 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\213 of an octave. | ||
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|[[170edt]] | | | [[170edt]] | ||
|[[107edo]] | | | [[107edo]] | ||
|170edt is 107edo with ~2.9 cent compressed octaves. | | | 170edt is 107edo with ~2.9 cent compressed octaves. | ||
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| | [[171edt]] | | | [[171edt]] | ||
| Line 1,051: | Line 1,051: | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. | | | Same ~1.2 cent octave stretch as 19edt~12edo. | ||
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|[[172edt]] | | | [[172edt]] | ||
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|172edt falls exactly halfway between 108 and 109 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\217 of an octave. | | | 172edt falls exactly halfway between 108 and 109 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\217 of an octave. | ||
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| | [[173edt]] | | | [[173edt]] | ||
| Line 1,059: | Line 1,059: | ||
| | 173edt is 109edo with ~1.7 cent compressed octaves. | | | 173edt is 109edo with ~1.7 cent compressed octaves. | ||
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|[[174edt]] | | | [[174edt]] | ||
|[[110edo]] | | | [[110edo]] | ||
|174edt is 110edo with ~2.4 cent stretched octaves. | | | 174edt is 110edo with ~2.4 cent stretched octaves. | ||
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|[[175edt]] | | | [[175edt]] | ||
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|Same ~4.5 cent octave compression as 35edt~22edo, but actually more strongly resembles the scale with generator 2\221 of an octave. | | | Same ~4.5 cent octave compression as 35edt~22edo, but actually more strongly resembles the scale with generator 2\221 of an octave. | ||
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| | [[176edt]] | | | [[176edt]] | ||
| Line 1,071: | Line 1,071: | ||
| | 176edt is 111edo with ~0.47 cent compressed octaves. | | | 176edt is 111edo with ~0.47 cent compressed octaves. | ||
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|[[177edt]] | | | [[177edt]] | ||
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|177edt is 112edo with a ~3.5 cent compressed octave, but also 223ed4 with a ~3.75 cent compressed 4/1. | | | 177edt is 112edo with a ~3.5 cent compressed octave, but also 223ed4 with a ~3.75 cent compressed 4/1. | ||
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|[[178edt]] | | | [[178edt]] | ||
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|Same ~3.3 cent octave stretch as 89edt~56edo, but actually more strongly resembles the scale with generator 2\225 of an octave. | | | Same ~3.3 cent octave stretch as 89edt~56edo, but actually more strongly resembles the scale with generator 2\225 of an octave. | ||
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| | [[179edt]] | | | [[179edt]] | ||
| Line 1,083: | Line 1,083: | ||
| | 179edt is 113edo with ~0.68 cent stretched octaves. | | | 179edt is 113edo with ~0.68 cent stretched octaves. | ||
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|[[180edt]] | | | [[180edt]] | ||
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|Same ~4.6 cent octave stretch as 30edt~19edo, but actually more strongly resembles the scale with generator 2\227 of an octave. | | | Same ~4.6 cent octave stretch as 30edt~19edo, but actually more strongly resembles the scale with generator 2\227 of an octave. | ||
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|[[181edt]] | | | [[181edt]] | ||
|[[114edo]] | | | [[114edo]] | ||
|181edt is 114edo with ~2.1 cent compressed octaves | | | 181edt is 114edo with ~2.1 cent compressed octaves. | ||
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|[[182edt]] | | | [[182edt]] | ||
|[[115edo]] | | | [[115edo]] | ||
|182edt is 115edo with ~1.8 cent stretched octaves | | | 182edt is 115edo with ~1.8 cent stretched octaves. | ||
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|[[183edt]] | | | [[183edt]] | ||
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|183edt falls exactly halfway between 115 and 116 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\231 of an octave. | | | 183edt falls exactly halfway between 115 and 116 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\231 of an octave. | ||
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| | [[184edt]] | | | [[184edt]] | ||
| Line 1,103: | Line 1,103: | ||
| | Same ~0.94 cent octave compression as 46edt~29edo. | | | Same ~0.94 cent octave compression as 46edt~29edo. | ||
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|[[185edt]] | | | [[185edt]] | ||
|[[117edo]] | | | [[117edo]] | ||
|185edt is 117edo with a ~2.9 cent stretched octave. | | | 185edt is 117edo with a ~2.9 cent stretched octave. | ||
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|[[186edt]] | | | [[186edt]] | ||
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|Same ~3.6 cent octave compression as 62edt~39edo, but actually more strongly resembles the scale with generator 2\235 of an octave. | | | Same ~3.6 cent octave compression as 62edt~39edo, but actually more strongly resembles the scale with generator 2\235 of an octave. | ||
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| | [[187edt]] | | | [[187edt]] | ||
| Line 1,115: | Line 1,115: | ||
| | 187edt is 118edo with ~0.16 cent stretched octaves. | | | 187edt is 118edo with ~0.16 cent stretched octaves. | ||
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|[[188edt]] | | | [[188edt]] | ||
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|188edt is 119edo with ~3.9 cent stretched octaves, but also 237ed4 with an ~2.3 cent compressed 4/1. | | | 188edt is 119edo with ~3.9 cent stretched octaves, but also 237ed4 with an ~2.3 cent compressed 4/1. | ||
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|[[189edt]] | | | [[189edt]] | ||
|[[119edo]] | | | [[119edo]] | ||
|Same ~2.5 cent octave compression as 27edt~17edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit. | | | Same ~2.5 cent octave compression as 27edt~17edo, but there is a lot of mismatch between the pure-octave and pure-tritave tunings. Patent vals differ in the 5-limit. | ||
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| | [[190edt]] | | | [[190edt]] | ||
| Line 1,127: | Line 1,127: | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. | | | Same ~1.2 cent octave stretch as 19edt~12edo. | ||
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|[[191edt]] | | | [[191edt]] | ||
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|191edt falls exactly halfway between 120 and 121 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\241 of an octave. | | | 191edt falls exactly halfway between 120 and 121 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\241 of an octave. | ||
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| | [[192edt]] | | | [[192edt]] | ||
| Line 1,135: | Line 1,135: | ||
| | 192edt is 121edo with ~1.4 cent compressed octaves. | | | 192edt is 121edo with ~1.4 cent compressed octaves. | ||
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|[[193edt]] | | | [[193edt]] | ||
|[[122edo]] | | | [[122edo]] | ||
|193edt is 122edo with ~2.3 cent stretched octaves. | | | 193edt is 122edo with ~2.3 cent stretched octaves. | ||
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|[[194edt]] | | | [[194edt]] | ||
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|Same ~3.9 cent octave compression as 97edt~61edo, but actually more strongly resembles the scale with generator 2\245 of an octave. | | | Same ~3.9 cent octave compression as 97edt~61edo, but actually more strongly resembles the scale with generator 2\245 of an octave. | ||
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| | [[195edt]] | | | [[195edt]] | ||
| Line 1,147: | Line 1,147: | ||
| | Same ~0.31 cent octave compression as 65edt~41edo. | | | Same ~0.31 cent octave compression as 65edt~41edo. | ||
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|[[196edt]] | | | [[196edt]] | ||
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|Same ~3.3 cent octave compression as 49edt~31edo, but actually more strongly resembles the scale with generator 2\247 of an octave. | | | Same ~3.3 cent octave compression as 49edt~31edo, but actually more strongly resembles the scale with generator 2\247 of an octave. | ||
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|[[197edt]] | | | [[197edt]] | ||
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|197edt is 124edo with a ~2.9 cent compressed octave, but also 249ed4 with a ~4 cent stretched 4/1. | | | 197edt is 124edo with a ~2.9 cent compressed octave, but also 249ed4 with a ~4 cent stretched 4/1. | ||
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| | [[198edt]] | | | [[198edt]] | ||
| Line 1,159: | Line 1,159: | ||
| | 198edt is 125edo with ~0.73 cent stretched octaves. | | | 198edt is 125edo with ~0.73 cent stretched octaves. | ||
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|[[199edt]] | | | [[199edt]] | ||
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|199edt falls exactly halfway between 125 and 126 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\251 of an octave. | | | 199edt falls exactly halfway between 125 and 126 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\251 of an octave. | ||
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|[[200edt]] | | | [[200edt]] | ||
|[[126edo]] | | | [[126edo]] | ||
|Same ~1.8 cent octave compression as 100edt~63edo. | | | Same ~1.8 cent octave compression as 100edt~63edo. | ||
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|[[201edt]] | | | [[201edt]] | ||
|[[127edo]] | | | [[127edo]] | ||
|201edt is 127edo with ~1.7 cent compressed octave. | | | 201edt is 127edo with ~1.7 cent compressed octave. | ||
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|[[202edt]] | | | [[202edt]] | ||
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|202edt falls exactly halfway between 127 and 128 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\255 of an octave. | | | 202edt falls exactly halfway between 127 and 128 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\255 of an octave. | ||
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| | [[203edt]] | | | [[203edt]] | ||
| Line 1,179: | Line 1,179: | ||
| | 203edt is 128edo with ~0.74 cent compressed octaves. | | | 203edt is 128edo with ~0.74 cent compressed octaves. | ||
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|[[204edt]] | | | [[204edt]] | ||
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|Same ~2.7 cent octave stretch as 68edt~43edo, but actually more strongly resembles the scale with generator 2\257 of an octave. | | | Same ~2.7 cent octave stretch as 68edt~43edo, but actually more strongly resembles the scale with generator 2\257 of an octave. | ||
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|[[205edt]] | | | [[205edt]] | ||
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|205edt is 129edo with a ~3.2 cent compressed octave, but also 259ed4 with a ~3 cent stretched 4/1. | | | 205edt is 129edo with a ~3.2 cent compressed octave, but also 259ed4 with a ~3 cent stretched 4/1. | ||
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| | [[206edt]] | | | [[206edt]] | ||
| Line 1,191: | Line 1,191: | ||
| | Same ~2.4 cent octave stretch as 103edt~65edo. | | | Same ~2.4 cent octave stretch as 103edt~65edo. | ||
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|[[207edt]] | | | [[207edt]] | ||
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| | | | 207edt falls exactly halfway between 130 and 131 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\261 of an octave. | ||
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|[[208edt]] | | | [[208edt]] | ||
|[[131edo]] | | | [[131edo]] | ||
|208edt is 131edo with ~2.1 cent compressed octaves. | | | 208edt is 131edo with ~2.1 cent compressed octaves. | ||
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| | [[209edt]] | | | [[209edt]] | ||
| Line 1,203: | Line 1,203: | ||
| | Same ~1.2 cent octave stretch as 19edt~12edo. | | | Same ~1.2 cent octave stretch as 19edt~12edo. | ||
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|[[210edt]] | | | [[210edt]] | ||
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|210edt falls exactly halfway between 132 and 133 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\265 of an octave. | | | 210edt falls exactly halfway between 132 and 133 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\265 of an octave. | ||
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| | [[211edt]] | | | [[211edt]] | ||
| Line 1,211: | Line 1,211: | ||
| | 211edt is 133edo with ~1.1 cent compressed octaves. | | | 211edt is 133edo with ~1.1 cent compressed octaves. | ||
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|[[212edt]] | | | [[212edt]] | ||
|[[134edo]] | | | [[134edo]] | ||
|Same ~2.2 cent octave stretch as 106edt~67edo, but patent vals surprisingly actually match through the 7-limit, though the 7s nevertheless cannot be said to match with a straight face. | |Same ~2.2 cent octave stretch as 106edt~67edo, but patent vals surprisingly actually match through the 7-limit, though the 7s nevertheless cannot be said to match with a straight face. | ||
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|[[213edt]] | | | [[213edt]] | ||
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|213edt falls exactly halfway between 134 and 135 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\269 of an octave. | | | 213edt falls exactly halfway between 134 and 135 edos. It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\269 of an octave. | ||
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| | [[214edt]] | | | [[214edt]] | ||
| Line 1,223: | Line 1,223: | ||
| | 214edt is 135edo with ~0.17 cent compressed octaves. | | | 214edt is 135edo with ~0.17 cent compressed octaves. | ||
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|[[215edt]] | | | [[215edt]] | ||
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|[[216edt]] | | | [[216edt]] | ||
|[[136edo]] | | | [[136edo]] | ||
|Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 5-limit. | | | Same ~2.5 cent octave compression as 27edt~17edo. Patent vals match through the 5-limit. | ||
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| | [[217edt]] | | | [[217edt]] | ||
| | [[137edo]] | | | [[137edo]] | ||
| | 217edt is 137edo with ~0.77 cent stretched octaves. | | | 217edt is 137edo with ~0.77 cent stretched octaves. | ||
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| | [[222edt]] | |||
| | [[140edo]] | |||
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| | [[225edt]] | |||
| | [[142edo]] | |||
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| | [[228edt]] | |||
| | [[144edo]] | |||
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| | [[230edt]] | |||
| | [[145edo]] | |||
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| | [[233edt]] | |||
| | [[147edo]] | |||
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| | [[236edt]] | |||
| | [[149edo]] | |||
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| | [[241edt]] | |||
| | [[152edo]] | |||
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| | [[244edt]] | |||
| | [[154edo]] | |||
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| | [[249edt]] | |||
| | [[157edo]] | |||
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| | [[252edt]] | |||
| | [[159edo]] | |||
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|} | |} | ||