14th-octave temperaments

Fractional-octave temperaments

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← 13th-octave • 14th-octave • 15th-octave →

While 14edo is poor in simple harmonics, some of its multiples (such as 224edo and 742edo) are members of zeta edo list.

Silicon

The name of silicon temperament comes from the 14th element. Defined upwards to the 13-limit. When tuned in 742edo, it is generated by a 53edo fifth intermingled with 14edo periods.

Subgroup: 2.3.5.7

Comma list: 14348907/14336000, 56358560858112/56296884765625

Mapping: [⟨14 0 -145 239], ⟨0 1 8 -9]]

Mapping generators: ~6125/5832, ~3

Optimal tuning (CTE): ~3/2 = 701.870

Optimal ET sequence: 224, 518, 742, 966, 1708, 2674

Badness: 0.196

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 1240029/1239040, 2359296/2358125

Mapping: [⟨14 0 -145 239 115], ⟨0 1 8 -9 -3]]

Optimal tuning (CTE): ~3/2 = 701.872

Optimal ET sequence: 224, 518, 742, 966, 1708, 4382e

Badness: 0.0450

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 4096/4095, 6656/6655, 9801/9800, 24192/24167

Mapping: [⟨14 0 -145 239 115 74], ⟨0 1 8 -9 -3 -1]]

Optimal tuning (CTE): ~3/2 = 701.8733

Optimal ET sequence: 224, 518, 742, 966, 1708f

Badness: 0.0269