1400edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods<br>per 8ve | ||
per 8ve | !Generator<br>(Reduced) | ||
!Generator | !Cents<br>(Reduced) | ||
(Reduced) | !Associated<br>Ratio | ||
!Cents | |||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperaments | !Temperaments | ||
|- | |- | ||
|2 | |2 | ||
| | |83\1400 | ||
| | |71.143 | ||
| | |25/24 | ||
|Vishnu (5-limit) | |[[Vishnu]] (5-limit) | ||
|- | |- | ||
|14 | |14 | ||
| | |581\1400<br>(81\1400) | ||
| | |498.000<br>(69.429) | ||
| | |4/3<br>(?) | ||
|Silicon (2.3.11) | |[[Silicon]] (2.3.11) | ||
|- | |- | ||
|28 | |28 | ||
| | |581\1400<br>(31\1400) | ||
| | |498.000<br>(26.571) | ||
| | |4/3<br>(126/125) | ||
|Oquatonic (1400cd) | |[[Oquatonic]] (1400cd) | ||
|- | |- | ||
|56 | |56 | ||
| | |581\1400<br>(6\1400) | ||
| | |498.000<br>(5.143) | ||
| | |4/3<br>(126/125) | ||
|Barium | |[[Barium]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Scales == | == Scales == | ||
* Silicon[70]: (19 24 19 19 19)x14 | * Silicon[70]: (19 24 19 19 19)x14 | ||
Revision as of 17:37, 21 October 2023
| ← 1399edo | 1400edo | 1401edo → |
Theory
1400edo is consistent in the 5-limit, and 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 provides the optimal patent val for the 5-limit vishnuzmic temperament. 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 is a tuning for the 11-limit oquatonic temperament, and 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.
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 (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 2 | 83\1400 | 71.143 | 25/24 | Vishnu (5-limit) |
| 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