1400edo: Difference between revisions

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== 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. . It also tempers out the [[~~linus~~ comma]] and the [[~~barium~~ comma]].

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.

=== Prime harmonics ===

=== 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| 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 ==

{| class="wikitable center-all left-5"

~~!Periods per 8ve~~

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

~~!Generator (Reduced)~~

~~!Cents (Reduced)~~

~~!Associated Ratio~~

~~!Temperaments~~

|-

|1

! Periods per 8ve

~~|317\1400~~

! Generator*

~~|271.714~~

! Cents*

~~|[66 -23 -9 -3⟩~~

! Associated ratio*

~~|[[Counterorson]]~~

! Temperaments

|-

|2

| 2

|83\1400

| 83\1400

|71.143

| 71.143

|25/24

| 25/24

|[[Vishnu]] (5-limit)

| [[Vishnu]] (5-limit)

|-

|8

| 8

|86\1400

| 86\1400

|73.714

| 73.714

|24/23

| 24/23

|[[Octium]] (2.3.19.23.29.31)

| [[Octium]] (2.3.19.23.29.31)

|-

|14

| 14

|581\1400 (81\1400)

| 581\1400 (81\1400)

|498.000 (69.429)

| 498.000 (69.429)

|4/3 (?)

| 4/3 (?)

|[[Silicon]] (2.3.11)

| [[Silicon]] (2.3.11)

|-

|28

| 28

|581\1400 (31\1400)

| 581\1400 (31\1400)

|498.000 (26.571)

| 498.000 (26.571)

|4/3 (126/125)

| 4/3 (126/125)

|[[Oquatonic]] (1400cd)

| [[Oquatonic]] (1400cd)

|-

|56

| 56

|581\1400 (6\1400)

| 581\1400 (6\1400)

|498.000 (5.143)

| 498.000 (5.143)

|4/3 (126/125)

| 4/3 (126/125)

|[[Barium]]

| [[Barium]]

|}

<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

<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 ==

* Silicon[70]: (19 24 19 19 19)×14

* Silicon[70]: (19 24 19 19 19)~~x14~~

== Music ==

; ~~'''~~[[Mercury Amalgam]]~~'''~~

; [[Mercury Amalgam]]

* [https://www.youtube.com/watch?v=o9aAB4csKBQ ''Apple In Your Mouth''] – Silicon[70], Oxygen[24], Magnesium[175], Vishnu[34]

* ''[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:Vishnu]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1400}}
+{{ED intro}}
 == Theory ==
-edo 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]].
+edo 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.
 === Prime harmonics ===
-{{harmonics in equal|1400}}
+{{Harmonics in equal|1400}}
 === Subsets and supersets ===
-edo 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}}.
+edo 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 ==
 {| class="wikitable center-all left-5"
-!Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-!Generator<br>(Reduced)
-!Cents<br>(Reduced)
-!Associated<br>Ratio
-!Temperaments
 |-
-|1
+! Periods<br>per 8ve
-|317\1400
+! Generator*
-|271.714
+! Cents*
-|[66 -23 -9 -3⟩
+! Associated<br>ratio*
-|[[Counterorson]]
+! Temperaments
 |-
-|2
+| 2
-|83\1400
+| 83\1400
-|71.143
+| 71.143
-|25/24
+| 25/24
-|[[Vishnu]] (5-limit)
+| [[Vishnu]] (5-limit)
 |-
-|8
+| 8
-|86\1400
+| 86\1400
-|73.714
+| 73.714
-|24/23
+| 24/23
-|[[Octium]] (2.3.19.23.29.31)
+| [[Octium]] (2.3.19.23.29.31)
 |-
-|14
+| 14
-|581\1400<br>(81\1400)
+| 581\1400<br>(81\1400)
-|498.000<br>(69.429)
+| 498.000<br>(69.429)
-|4/3<br>(?)
+| 4/3<br>(?)
-|[[Silicon]] (2.3.11)
+| [[Silicon]] (2.3.11)
 |-
-|28
+| 28
-|581\1400<br>(31\1400)
+| 581\1400<br>(31\1400)
-|498.000<br>(26.571)
+| 498.000<br>(26.571)
-|4/3<br>(126/125)
+| 4/3<br>(126/125)
-|[[Oquatonic]] (1400cd)
+| [[Oquatonic]] (1400cd)
 |-
-|56
+| 56
-|581\1400<br>(6\1400)
+| 581\1400<br>(6\1400)
-|498.000<br>(5.143)
+| 498.000<br>(5.143)
-|4/3<br>(126/125)
+| 4/3<br>(126/125)
-|[[Barium]]
+| [[Barium]]
 |}
+<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
-<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 ==
+* Silicon[70]: (19 24 19 19 19)×14
-* Silicon[70]: (19 24 19 19 19)x14
 == Music ==
-; '''[[Mercury Amalgam]]'''
+; [[Mercury Amalgam]]
+* [https://www.youtube.com/watch?v=o9aAB4csKBQ ''Apple In Your Mouth''] – Silicon[70], Oxygen[24], Magnesium[175], Vishnu[34]
-* ''[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:Vishnu]]
 [[Category:Listen]]