16ed5/2: Difference between revisions
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| Line 7: | Line 7: | ||
! Degrees | ! Degrees | ||
! colspan="3" | Enneatonic | ! colspan="3" | Enneatonic | ||
! | ! Cents | ||
|- | |- | ||
| 1 | | 1 | ||
| 1#/2b | | 1#/2b | ||
| colspan="2" | F#/Gb | | colspan="2" | F#/Gb | ||
| 99.145 | | 99.145 | ||
|- | |- | ||
| 2 | | 2 | ||
| 2 | | 2 | ||
| colspan="2" | G | | colspan="2" | G | ||
| 198.289 | | 198.289 | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 35: | Line 23: | ||
| G#/Jb | | G#/Jb | ||
| ''G#/Ab'' | | ''G#/Ab'' | ||
| 297.433 | | 297.433 | ||
|- | |- | ||
| 4 | | 4 | ||
| Line 45: | Line 29: | ||
| J | | J | ||
| ''A'' | | ''A'' | ||
| 396.578 | | 396.578 | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 55: | Line 35: | ||
| J#/Ab | | J#/Ab | ||
| ''A#/Bb'' | | ''A#/Bb'' | ||
| 495.723 | | 495.723 | ||
|- | |- | ||
| 6 | | 6 | ||
| Line 65: | Line 41: | ||
| A | | A | ||
| ''B'' | | ''B'' | ||
| 594.868 | | 594.868 | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 75: | Line 47: | ||
| B | | B | ||
| ''H'' | | ''H'' | ||
| 694.012 | | 694.012 | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 85: | Line 53: | ||
| B#/Hb | | B#/Hb | ||
| ''H#/Cb'' | | ''H#/Cb'' | ||
| 793.157 | | 793.157 | ||
|- | |- | ||
| 9 | | 9 | ||
| Line 95: | Line 59: | ||
| H | | H | ||
| ''C'' | | ''C'' | ||
| 892.3015 | | 892.3015 | ||
|- | |- | ||
| 10 | | 10 | ||
| Line 105: | Line 65: | ||
| H#/Cb | | H#/Cb | ||
| ''C#/Db'' | | ''C#/Db'' | ||
| 991.446 | | 991.446 | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 115: | Line 71: | ||
| C | | C | ||
| ''D'' | | ''D'' | ||
| 1090.591 | | 1090.591 | ||
|- | |- | ||
| 12 | | 12 | ||
| Line 125: | Line 77: | ||
| C#/Db | | C#/Db | ||
| ''D#/Sb'' | | ''D#/Sb'' | ||
| 1189.735 | | 1189.735 | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 135: | Line 83: | ||
| D | | D | ||
| ''S'' | | ''S'' | ||
| 1288.88 | | 1288.88 | ||
|- | |- | ||
| 14 | | 14 | ||
| Line 145: | Line 89: | ||
| D#/Eb | | D#/Eb | ||
| ''S#/Eb'' | | ''S#/Eb'' | ||
| 1388.0245 | | 1388.0245 | ||
|- | |- | ||
| 15 | | 15 | ||
| 9 | | 9 | ||
| colspan="2" | E | | colspan="2" | E | ||
| 1487.169 | | 1487.169 | ||
|- | |- | ||
| 16 | | 16 | ||
| 1 | | 1 | ||
| colspan="2" | F | | colspan="2" | F | ||
| 1586.314 | | 1586.314 | ||
|} | |} | ||
Revision as of 01:51, 4 May 2023
| ← 15ed5/2 | 16ed5/2 | 17ed5/2 → |
(semiconvergent)
16ED5/2 is the equal division of the 5/2 interval into 16 parts of 99.1446 cents each. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval.
Intervals
| Degrees | Enneatonic | Cents | ||
|---|---|---|---|---|
| 1 | 1#/2b | F#/Gb | 99.145 | |
| 2 | 2 | G | 198.289 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | 297.433 |
| 4 | 3 | J | A | 396.578 |
| 5 | 3#/4b | J#/Ab | A#/Bb | 495.723 |
| 6 | 4 | A | B | 594.868 |
| 7 | 5 | B | H | 694.012 |
| 8 | 5#/6b | B#/Hb | H#/Cb | 793.157 |
| 9 | 6 | H | C | 892.3015 |
| 10 | 6#/7b | H#/Cb | C#/Db | 991.446 |
| 11 | 7 | C | D | 1090.591 |
| 12 | 7#/8b | C#/Db | D#/Sb | 1189.735 |
| 13 | 8 | D | S | 1288.88 |
| 14 | 8#/9b | D#/Eb | S#/Eb | 1388.0245 |
| 15 | 9 | E | 1487.169 | |
| 16 | 1 | F | 1586.314 | |
Coincidentally, 133 steps of the pyrite EDX of this size exceed 11 octaves by only 2.978¢.
Regular temperaments
16ed5/2 can also be thought of as a generator of the 2.3.5.17.19 subgroup temperament which tempers out 256/255, 361/360, and 4624/4617, which is a cluster temperament with 12 clusters of notes in an octave (quintaleap temperament). This temperament is supported by Template:Val list, and 157edo.
Tempering out 400/399 (equating 20/19 and 21/20) leads to quintupole (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to quinticosiennic (12&145).
Another temperament related to 16ed5/2 is quintapole (12&85). It is practically identical to the Galilei tuning, which is generated by the ratios 2/1 and 18/17.