# 16edt

 ← 15edt 16edt 17edt →
Prime factorization 24
Step size 118.872¢
Octave 10\16edt (1188.72¢) (→5\8edt)
Consistency limit 8
Distinct consistency limit 4

16EDT is equal division of the third harmonic into 16 parts of 118.872 cents each (corresponding to 10.0949 EDO).

## Properties

As the double of 8EDT, this division of the tritave is harmonically fraternal to 10EDO. Its unit step is ~1.128 cents flat of 1\10EDO. Unlike 10EDO, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent 13:21 and a decent 7:13. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.

## Intervals

Degree Size in
Cents Hekts
1 118.87219 81.25
2 237.74438 162.5
3 356.61656 243.75
4 475.48875 325
5 594.36094 406.25
6 713.23312 487.5
7 832.10531 568.75
8 950.9775 650
9 1069.84969 731.25
10 1188.72188 812.5
11 1307.59406 893.75
12 1426.46625 975
13 1545.33844 1056.25
14 1664.21063 1137.5
15 1783.08281 1218.75
16 1901.955 1300

## Related temperament

16EDT is also be thought of as a generator of the subsedia temperament, which is a cluster temperament with 10 clusters of notes in an octave.

Subsedia (10 & 111)

7-limit
Comma list: 16875/16807, 65536/64827
Mapping: [1 0 5 4], 0 16 -27 -12]]
POTE generator: ~15/14 = 118.965
Optimal ET sequence10, 101, 111, 121, 232d

11-limit
Comma list: 540/539, 1375/1372, 65536/64827
Mapping: [1 0 5 4 -1], 0 16 -27 -12 45]]
POTE generator: ~15/14 = 118.968
Optimal ET sequence10, 101, 111, 121, 232d

13-limit
Comma list: 352/351, 540/539, 676/675, 1375/1372
Mapping: [1 0 5 4 -1 4], 0 16 -27 -12 45 -3]]
POTE generator: ~15/14 = 118.968
Optimal ET sequence10, 101, 111, 121, 232d