7ed5/4: Difference between revisions

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'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to ~~every fourth step of~~ [[~~87edo~~]]. It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to 21.7440 [[EDO|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

== Harmonics ==

{{Harmonics in equal

| steps = 7

| num = 5

| denom = 4

}}

{{Harmonics in equal

| steps = 7

| num = 5

| denom = 4

| start = 12

| collapsed = 1

}}

==Intervals==

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==7ED5/4 as a generator==

===Alphaquarter===

7ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]].

7ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]] among others.

===1783&7980 temperament===

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POTE generator: 55.188

~~Map~~: [<1 6 2|, <0 -96 7|]

Mapping: [<1 6 2|, <0 -96 7|]

EDOs: ~~[[1783edo|~~1783]], 4414, 6197, ~~[[7980edo|~~7980]], 9763, 11546, 14177

EDOs: 1783, 4414, 6197, 7980, 9763, 11546, 14177

Badness: 0.1157

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

[[Category:Major third]]

[[Category:Equal-step tuning]]

~~[[Category:Edonoi]]~~

@@ Line 1: / Line 1: @@
-'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
+{{Infobox ET}}
+'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to 21.7440 [[EDO|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
+== Harmonics ==
+{{Harmonics in equal
+| steps = 7
+| num = 5
+| denom = 4
+}}
+{{Harmonics in equal
+| steps = 7
+| num = 5
+| denom = 4
+| start = 12
+| collapsed = 1
+}}
 ==Intervals==
@@ Line 379: / Line 394: @@
 ==7ED5/4 as a generator==
 ===Alphaquarter===
-ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]].
+ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]] among others.
 ===1783&amp;7980 temperament===
@@ Line 388: / Line 403: @@
 POTE generator: 55.188
-Map: [&lt;1 6 2|, &lt;0 -96 7|]
+Mapping: [&lt;1 6 2|, &lt;0 -96 7|]
-EDOs: [[1783edo|1783]], 4414, 6197, [[7980edo|7980]], 9763, 11546, 14177
+EDOs: 1783, 4414, 6197, 7980, 9763, 11546, 14177
 Badness: 0.1157
-[[Category:5/4]]
+[[Category:Major third]]
 [[Category:Equal-step tuning]]
-[[Category:Edonoi]]