16ed5/2
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 | ED38\29 | Golden | ED5/2 | ED(7φ+6)\5(φ+1) | ED4\3=r¢ | ||
---|---|---|---|---|---|---|---|---|
1 | 1#/2b | F#/Gb | 98.276 | 98.3795 | 99.145 | 99.2705 | 100 | |
2 | 2 | G | 196.552 | 196.759 | 198.289 | 198.541 | 200 | |
3 | 2#/3b | G#/Jb | G#/Ab | 294.828 | 295.138 | 297.433 | 297.8115 | 300 |
4 | 3 | J | A | 393.103 | 393.518 | 396.578 | 397.082 | 400 |
5 | 3#/4b | J#/Ab | A#/Bb | 491.379 | 491.897 | 495.723 | 496.3525 | 500 |
6 | 4 | A | B | 589.655 | 590.277 | 594.868 | 595.623 | 600 |
7 | 5 | B | H | 687.931 | 688.656 | 694.012 | 694.894 | 700 |
8 | 5#/6b | B#/Hb | H#/Cb | 786.207 | 787.036 | 793.157 | 794.164 | 800 |
9 | 6 | H | C | 884.483 | 885.415 | 892.3015 | 893.435 | 900 |
10 | 6#/7b | H#/Cb | C#/Db | 982.759 | 983.795 | 991.446 | 992.705 | 1000 |
11 | 7 | C | D | 1081.0345 | 1082.174 | 1090.591 | 1091.976 | 1100 |
12 | 7#/8b | C#/Db | D#/Sb | 1179.31 | 1180.554 | 1189.735 | 1191.246 | 1200 |
13 | 8 | D | S | 1277.586 | 1278.933 | 1288.88 | 1290.517 | 1300 |
14 | 8#/9b | D#/Eb | S#/Eb | 1375.862 | 1377.313 | 1388.0245 | 1389.787 | 1400 |
15 | 9 | E | 1474.138 | 1475.692 | 1487.169 | 1489.058 | 1500 | |
16 | 1 | F | 1572.414 | 1574.0715 | 1586.314 | 1588.328 | 1600 |
Coincidentally, 133 steps of the pyrite EDX of this size exceed 11 octaves by only 2.978¢.
Regular temperaments
- Main article: Quintaleap family
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.