23edo and octave stretching: Difference between revisions
Changed from 1216 to 1206 as the statement in the synopsis is incorrect about 1216, but true about 1206. Read through the full article and changed anything that no longer held true in 1206 (it was not too much, it's mostly the same). Changed the lists of tunings to more reasonable ones. |
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! Interval !! Width in steps !! Width in cents !! Approximations | ! Interval !! Width in steps !! Width in cents !! Approximations | ||
|- | |- | ||
| Quarter-tone || 1 || 52.45 || | | Quarter-tone || 1 || 52.45 || 33:32 | ||
|- | |- | ||
| Semitone || 2 || 105.89 || 16: | | Semitone || 2 || 105.89 || 16:15, 15:14 | ||
|- | |- | ||
| 3/4-tone || 3 || 157.34 || 12:11, 11:10, 10:9 | | 3/4-tone || 3 || 157.34 || 12:11, 11:10, 10:9 | ||
|- | |- | ||
| Whole tone || 4 || 209.79 || 9:8 | | Whole tone || 4 || 209.79 || 9:8 | ||
|- | |- | ||
| Septimal subminor third || 5 || 262.23 || 7:6 | | Septimal subminor third || 5 || 262.23 || 7:6 | ||
| Line 28: | Line 28: | ||
| Major third || 7 || 367.13 || 5:4 | | Major third || 7 || 367.13 || 5:4 | ||
|- | |- | ||
| Septimal supermajor third || 8 || 418.58 || 9:7 | | Septimal supermajor third || 8 || 418.58 || 14:11, 9:7 | ||
|- | |- | ||
| Minor fourth || 9 || 472.92 || | | Minor fourth || 9 || 472.92 || 13:10 | ||
|- | |- | ||
| Major fourth || 10 || 524.47 || | | Major fourth || 10 || 524.47 || 15:11 | ||
|- | |- | ||
| Septimal tritone || 11 || 576.92 || 7:5 | | Septimal tritone || 11 || 576.92 || 7:5 | ||
|- | |- | ||
| Tridecimal tritone || 12 || 629.36 || 13:9 | | Tridecimal tritone || 12 || 629.36 || 10:7, 13:9 | ||
|- | |- | ||
| Natural fifth || 13 || 681.81 || 3:2 | | Natural fifth || 13 || 681.81 || 3:2 | ||
|- | |- | ||
| Augmented fifth || 14 || 734.26 || | | Augmented fifth || 14 || 734.26 || 20:13 | ||
|- | |- | ||
| Undecimal minor sixth || 15 || 786.70 || 11:7 | | Undecimal minor sixth || 15 || 786.70 || 11:7 | ||
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| Major sixth || 17 || 891.60 || 5:3 | | Major sixth || 17 || 891.60 || 5:3 | ||
|- | |- | ||
| Septimal subminor seventh;<br />septimal supermajor sixth || 18 || 944.04 || 7 | | Septimal subminor seventh;<br />septimal supermajor sixth || 18 || 944.04 || 12:7 | ||
|- | |- | ||
| Minor seventh || 19 || 996.49 || 9:5 | | Minor seventh || 19 || 996.49 || 7:4, 9:5 | ||
|- | |- | ||
| Neutral seventh || 20 || 1048.94 || 11:6 | | Neutral seventh || 20 || 1048.94 || 11:6 | ||
|- | |- | ||
| Major seventh || 21 || 1101.38 || | | Major seventh || 21 || 1101.38 || 15:8 | ||
|- | |- | ||
| Diminished octave || 22 || 1153.83 || | | Diminished octave || 22 || 1153.83 || | ||