1400edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro | {{EDO intro}} | ||
== Theory == | == Theory == | ||
1400edo is consistent in the 5-limit, where provides the optimal patent val for the 5-limit [[vishnuzma|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 | 1400edo is consistent in the 5-limit, where provides the optimal patent val for the 5-limit [[vishnuzma|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. | 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. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
1400edo has subset edos {{EDOs|1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700}}. | 1400edo has subset edos {{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. | One step of 1400edo is the relative cent for 14edo. | ||
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| 317\1400 | | 317\1400 | ||
| 271.714 | | 271.714 | ||
| | | {{monzo| 66 -23 -9 -3 }} | ||
| [[Counterorson]] | | [[Counterorson]] | ||
|- | |- | ||
| Line 60: | Line 60: | ||
| [[Barium]] | | [[Barium]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
| Line 67: | Line 67: | ||
== Music == | == Music == | ||
; '''[[Mercury Amalgam]]''' | ; '''[[Mercury Amalgam]]''' | ||
* ''[https://www.youtube.com/watch?v=o9aAB4csKBQ&pp=ygUHMTQwMGVkbw%3D%3D Apple In Your Mouth]'' | * ''[https://www.youtube.com/watch?v=o9aAB4csKBQ&pp=ygUHMTQwMGVkbw%3D%3D Apple In Your Mouth]'' – silicon[70], oxygen[24], magnesium[175], vishnu[34] | ||
[[Category:Vishnuzmic]] | [[Category:Vishnuzmic]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 16:55, 15 January 2025
| ← 1399edo | 1400edo | 1401edo → |
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 distinct
Scales
- Silicon[70]: (19 24 19 19 19)x14
Music
- Apple In Your Mouth – silicon[70], oxygen[24], magnesium[175], vishnu[34]