1400edo
| ← 1399edo | 1400edo | 1401edo → |
1400 equal divisions of the octave (abbreviated 1400edo or 1400ed2), also called 1400-tone equal temperament (1400tet) or 1400 equal temperament (1400et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1400 equal parts of about 0.857 ¢ each. Each step represents a frequency ratio of 21/1400, or the 1400th root of 2.
Theory
1400edo is consistent in the 5-limit, where provides the optimal patent val for the 5-limit vishnuzmic temperament. Aside from that it is poor at simple harmony. In higher limits, it is good at the 2.3.19.23.29.31 subgroup. . It also tempers out the linus comma and the barium comma.
Aside from the patent val, there is a number of mappings to be considered. 1400cd val uses the 28edo mapping for 5 and gives a tuning close to the POTE tuning for the 11-limit oquatonic temperament. 1400ccdd val is a tuning for the 11-limit silicon temperament. It is worth noting, patent val can be considered a tuning for the 2.3.11 subgroup silicon - for which it conveniently provides a 70-tone mos reaching 3/2 in 1 generator up and 11/8 in 3 generators down. 1400bbbc val is a tuning for the manganese temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.045 | +0.258 | -0.254 | -0.175 | +0.329 | -0.384 | -0.084 | +0.011 | -0.149 | +0.107 |
| Relative (%) | +0.0 | +5.2 | +30.1 | -29.7 | -20.4 | +38.4 | -44.8 | -9.9 | +1.3 | -17.3 | +12.5 | |
| Steps (reduced) |
1400 (0) |
2219 (819) |
3251 (451) |
3930 (1130) |
4843 (643) |
5181 (981) |
5722 (122) |
5947 (347) |
6333 (733) |
6801 (1201) |
6936 (1336) | |
Subsets and supersets
1400edo has subset edos 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700.
One step of 1400edo is the relative cent for 14edo.
Regular temperament properties
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 317\1400 | 271.714 | [66 -23 -9 -3⟩ | Counterorson |
| 2 | 83\1400 | 71.143 | 25/24 | Vishnu (5-limit) |
| 8 | 86\1400 | 73.714 | 24/23 | Octium (2.3.19.23.29.31) |
| 14 | 581\1400 (81\1400) |
498.000 (69.429) |
4/3 (?) |
Silicon (2.3.11) |
| 28 | 581\1400 (31\1400) |
498.000 (26.571) |
4/3 (126/125) |
Oquatonic (1400cd) |
| 56 | 581\1400 (6\1400) |
498.000 (5.143) |
4/3 (126/125) |
Barium |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct
Scales
- Silicon[70]: (19 24 19 19 19)x14
Music
- Apple In Your Mouth – silicon[70], oxygen[24], magnesium[175], vishnu[34]