5ed5/4: Difference between revisions

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'''5ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into five parts of 77.2627 [[cent|cents]] each, corresponding to every second step of [[31edo]]. It is related to [[Carlos Alpha]] and the 7-limit temperaments which temper out 2100875/2097152 (including the [[Breedsmic temperaments|tertiaseptal temperament]] and the [[Starling temperaments|valentine temperament]]).

==Intervals==

{| class="wikitable"

|-

Line 272:

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|}

[[Category:~~5/4~~]]

== Harmonics ==

{{Harmonics in equal

| steps = 5

| num = 5

| denom = 4

}}

{{Harmonics in equal

| steps = 5

| num = 5

| denom = 4

| start = 12

| collapsed = 1

}}

==5ED5/4 as a generator==

===Valentine===

Aside from 2100875/2097152, [[valentine]] temperament tempers out 126/125, 1029/1024, 6144/6125, and 64827/64000 in the 7-limit. It can be described as the 31&46 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 22/21) can serve as its generator. In the 11-limit, it tempers out 121/120, 176/175, and 441/440.

===Tertiaseptal===

Aside from 2100875/2097152, [[tertiaseptal]] temperament tempers out 2401/2400, 65625/65536, and 703125/702464 in the 7-limit. It can be described as the 31&171 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 243/242, 375/374, 441/440, 625/624, and 3584/3575.

===Tertia===

Aside from 2100875/2097152, [[tertiaseptal|tertia]] temperament tempers out 385/384, 1331/1323, and 1375/1372 in the 11-limit. It can be described as the 31&140 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 352/351, 385/384, 561/560, 625/624, and 715/714.

[[Category:Major third]]

[[Category:Equal-step tuning]]

~~[[Category:Edonoi]]~~

@@ Line 1: / Line 1: @@
+{{Infobox ET}}
 '''5ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into five parts of 77.2627 [[cent|cents]] each, corresponding to every second step of [[31edo]]. It is related to [[Carlos Alpha]] and the 7-limit temperaments which temper out 2100875/2097152 (including the [[Breedsmic temperaments|tertiaseptal temperament]] and the [[Starling temperaments|valentine temperament]]).
+==Intervals==
 {| class="wikitable"
 |-
@@ Line 272: / Line 274: @@
 |}
-[[Category:5/4]]
+== Harmonics ==
+{{Harmonics in equal
+| steps = 5
+| num = 5
+| denom = 4
+}}
+{{Harmonics in equal
+| steps = 5
+| num = 5
+| denom = 4
+| start = 12
+| collapsed = 1
+}}
+==5ED5/4 as a generator==
+===Valentine===
+Aside from 2100875/2097152, [[valentine]] temperament tempers out 126/125, 1029/1024, 6144/6125, and 64827/64000 in the 7-limit. It can be described as the 31&amp;46 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 22/21) can serve as its generator. In the 11-limit, it tempers out 121/120, 176/175, and 441/440.
+===Tertiaseptal===
+Aside from 2100875/2097152, [[tertiaseptal]] temperament tempers out 2401/2400, 65625/65536, and 703125/702464 in the 7-limit. It can be described as the 31&amp;171 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 243/242, 375/374, 441/440, 625/624, and 3584/3575.
+===Tertia===
+Aside from 2100875/2097152, [[tertiaseptal|tertia]] temperament tempers out 385/384, 1331/1323, and 1375/1372 in the 11-limit. It can be described as the 31&amp;140 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 352/351, 385/384, 561/560, 625/624, and 715/714.
+[[Category:Major third]]
 [[Category:Equal-step tuning]]
-[[Category:Edonoi]]