1400edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1400edo is consistent in the 5-limit, where provides the optimal patent val for the 5-limit [[ | 1400edo is only [[consistent]] in the [[5-odd-limit]], where it provides the [[optimal patent val]] for the 5-limit [[vishnu]] temperament. Aside from that it is poor at simple harmony. In the higher limits, it is good at the 2.3.19.23.29.31 subgroup. It also tempers out the [[barium comma]] and the [[linus comma]] using the patent val. | ||
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. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|1400}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1400edo has subset edos {{EDOs| | 1400edo has subset edos {{EDOs| 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. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 43: | Line 36: | ||
|- | |- | ||
| 14 | | 14 | ||
| 581\1400<br | | 581\1400<br>(81\1400) | ||
| 498.000<br | | 498.000<br>(69.429) | ||
| 4/3<br | | 4/3<br>(?) | ||
| [[Silicon]] (2.3.11) | | [[Silicon]] (2.3.11) | ||
|- | |- | ||
| 28 | | 28 | ||
| 581\1400<br | | 581\1400<br>(31\1400) | ||
| 498.000<br | | 498.000<br>(26.571) | ||
| 4/3<br | | 4/3<br>(126/125) | ||
| [[Oquatonic]] (1400cd) | | [[Oquatonic]] (1400cd) | ||
|- | |- | ||
| 56 | | 56 | ||
| 581\1400<br | | 581\1400<br>(6\1400) | ||
| 498.000<br | | 498.000<br>(5.143) | ||
| 4/3<br | | 4/3<br>(126/125) | ||
| [[Barium]] | | [[Barium]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
* Silicon[70]: (19 24 19 19 19) | * Silicon[70]: (19 24 19 19 19)×14 | ||
== Music == | == Music == | ||
; | ; [[Mercury Amalgam]] | ||
* | * [https://www.youtube.com/watch?v=o9aAB4csKBQ ''Apple In Your Mouth''] – Silicon[70], Oxygen[24], Magnesium[175], Vishnu[34] | ||
[[Category: | [[Category:Vishnu]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||