22ed5: Difference between revisions

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-'''[[Ed5|Division of the 5th harmonic]] into 22 equal parts''' (22ed5) is a good [[hyperpyth]] tuning. The step size about 126.6506 cents. It is compared to [[15edt]] and every second step of [[19edo]], but with the 5/1 rather than 2/1 or 3/1 being just.
+{{Infobox ET}}
+'''[[Ed5|Division of the 5th harmonic]] into 22 equal parts''' (22ED5) is a good [[hyperpyth]] tuning. The step size about 126.6506 cents. It is compared to [[15edt|15EDT]] and every second step of [[19edo|19EDO]], but with the 5/1 rather than 2/1 or 3/1 being just.
+== Intervals ==
 {| class="wikitable"
 |-
@@ Line 60: / Line 62: @@
 | | 10
 | | 1266.5062
-| |
+| | [[26/25|52/25]], 160/77
 | |
 |-
@@ Line 70: / Line 72: @@
 | | 12
 | | 1519.8075
-| |
+| | [[77/64|77/32]], 125/52
 | |
 |-
@@ Line 116: / Line 118: @@
 | | 2659.6631
 | | 65/14
-| |
+| | +17.7 cents from [[23/20|23/5]]
 |-
 | | 22
@@ Line 124: / Line 126: @@
 |}
-==22ed5 as a generator==
+== Harmonics ==
-ed5 can also be thought of as a generator of the 19-limit [[15edt|mowgli temperament]], which tempers out 351/350, 476/475, 495/494, 969/968, 1445/1444, and 1701/1690, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by [[19edo]], [[161edo]], and [[180edo]] among others.
+{{Harmonics in equal
+| steps = 22
+| num = 5
+| denom = 1
+}}
+{{Harmonics in equal
+| steps = 22
+| num = 5
+| denom = 1
+| start = 12
+| collapsed = 1
+}}
+== 22ED5 as a generator ==
+ED5 can also be thought of as a generator of the 19-limit [[Hemimean clan #Mowglic|mowglic temperament]], which tempers out 351/350, 476/475, 495/494, 513/512, 540/539, and 1701/1690, which is an extension of the [[Syntonic–enneadecal equivalence continuum|mowgli temperament]]. This temperament is supported by [[19edo|19EDO]], [[161edo|161EDO]], and [[180edo|180EDO]] among others.
-[[Category:Ed5]]
+[[Category:Hyperpyth]]
-[[Category:Edonoi]]
+{{todo|expand}}