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 sequence: 10, 101, 111, 121, 232d
Badness: 0.157658

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 sequence: 10, 101, 111, 121, 232d
Badness: 0.066838

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 sequence: 10, 101, 111, 121, 232d
Badness: 0.031635

17-limit
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
Mapping: [⟨1 0 5 4 -1 4 3], ⟨0 16 -27 -12 45 -3 11]]
POTE generator: ~15/14 = 118.968
Optimal ET sequence: 10, 101, 111, 121, 232dg
Badness: 0.019707

Music

A Short Tune in 16EDT by Peter 'Rush' Kosmorsky