16ed5/2

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← 15ed5/216ed5/217ed5/2 →
Prime factorization 24
Step size 99.1446¢
Fifth 7\16ed5/2 (694.012¢)
(semiconvergent)
Octave 12\16ed5/2 (1189.74¢) (→3\4ed5/2)
Semitones (A1:m2) 1:1 (99.14¢ : 99.14¢)
Consistency limit 11
Distinct consistency limit 3

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=
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.

See also