16ed5/2
| ← 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. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal 12-tone scale.
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 | |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.3 | -18.2 | -20.5 | -10.3 | -28.5 | +2.1 | -30.8 | -36.4 | -20.5 | +12.8 | -38.7 |
| Relative (%) | -10.4 | -18.4 | -20.7 | -10.4 | -28.7 | +2.1 | -31.1 | -36.7 | -20.7 | +12.9 | -39.1 | |
| Steps (reduced) |
12 (12) |
19 (3) |
24 (8) |
28 (12) |
31 (15) |
34 (2) |
36 (4) |
38 (6) |
40 (8) |
42 (10) |
43 (11) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +21.0 | -8.2 | -28.5 | -41.1 | -46.9 | -46.7 | -41.1 | -30.8 | -16.1 | +2.5 | +24.7 |
| Relative (%) | +21.2 | -8.2 | -28.7 | -41.4 | -47.3 | -47.1 | -41.5 | -31.1 | -16.3 | +2.5 | +24.9 | |
| Steps (reduced) |
45 (13) |
46 (14) |
47 (15) |
48 (0) |
49 (1) |
50 (2) |
51 (3) |
52 (4) |
53 (5) |
54 (6) |
55 (7) | |
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 12-, 109-, 121-, 133-, 145-, 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.
Scale tree
Ed5/2 scales can be approximated in EDOs by subdividing their approximations of 5/2.
| Major tenth | Period | Notes | |||
|---|---|---|---|---|---|
| 9\7 | 96.429 | Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins | |||
| 31\24 | 96.875 | ||||
| 22\17 | 97.059 | Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins | |||
| 35\27 | 97.2 | ||||
| 13\10 | 97.5 | Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins | |||
| 17\13 | 98.077 | ||||
| 21\16 | 98.4375 | Subpental Mixolydian mode ends, Pental Mixolydian mode begins | |||
| 25\19 | 98.684 | ||||
| 29\22 | 98.863 | ||||
| 33\25 | 99 | ||||
| 4\3 | 100 | Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins | |||
| 19\14 | 101.786 | ||||
| 15\11 | 102.27 | Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins | |||
| 26\19 | 102.632 | ||||
| 11\8 | 103.125 | Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins | |||
| 18\13 | 103.846 | ||||
| 25\18 | 104.16 | ||||