16edt
| ← 15edt | 16edt | 17edt → |
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.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -52.3 | -40.4 | +0.0 | +9.2 | -42.3 | -52.3 | -31.2 | +14.0 | -40.4 | +39.8 |
| Relative (%) | +0.0 | -44.0 | -34.0 | +0.0 | +7.7 | -35.5 | -44.0 | -26.2 | +11.8 | -34.0 | +33.5 | |
| Steps (reduced) |
16 (0) |
23 (7) |
28 (12) |
32 (0) |
35 (3) |
37 (5) |
39 (7) |
41 (9) |
43 (11) |
44 (12) |
46 (14) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +14.4 | +0.0 | -4.8 | -1.4 | +9.2 | +26.2 | +48.9 | -42.3 | -10.0 | +26.5 | -52.3 |
| Relative (%) | +12.1 | +0.0 | -4.1 | -1.2 | +7.7 | +22.1 | +41.1 | -35.5 | -8.4 | +22.3 | -44.0 | |
| Steps (reduced) |
47 (15) |
48 (0) |
49 (1) |
50 (2) |
51 (3) |
52 (4) |
53 (5) |
53 (5) |
54 (6) |
55 (7) |
55 (7) | |
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