21edf: Difference between revisions

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'''[[EDF|Division of the just perfect fifth]] into 21 equal parts''' (21EDF) is related to [[36edo|36 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 33.4264 cents. Unlike 36edo, it is only consistent up to the [[~~3-odd-limit|4-~~integer-limit]], with discrepancy for the 5th harmonic.

'''[[EDF|Division of the just perfect fifth]] into 21 equal parts''' (21EDF) is related to [[36edo|36 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 33.4264 cents. Unlike 36edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.

Lookalikes: [[36edo]], [[57edt]]

=Approximations=

==Approximations==

==Harmonics==

===Harmonics===

==3-limit (Pythagorean) approximations (same as 7edf):==

===3-limit (Pythagorean) approximations (same as 7edf):===

2/1 = 1200 cents; 36 degrees of 21edf = 1203.3514... cents.

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128/81 = 792.180... cents; 24 degrees of 21edf = 802.2342... cents.

==7-limit approximations:==

===7-limit approximations:===

===7 only:===

====7 only:====

7/4 = 968.826... cents; 29 degrees of 21edf = 969.3664... cents.

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64/49 = 462.348... cents; 14 degrees of 21edf = 467.97... cents.

===3 and 7:===

====3 and 7:====

7/6 = 266.871... cents; 8 degrees of 21edf = 267.4114... cents.

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63/32 = 1172.736... cents; 35 degrees of 21edf = 1169.925... cents.

==Intervals==

The following table gives an overview of all degrees of 36edo.

{| class="wikitable"

{| class="wikitable mw-collapsible"

|+ Intervals of 21edf

|-

! |Degree

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|

|}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''[[EDF|Division of the just perfect fifth]] into 21 equal parts''' (21EDF) is related to [[36edo|36 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 33.4264 cents. Unlike 36edo, it is only consistent up to the [[3-odd-limit|4-integer-limit]], with discrepancy for the 5th harmonic.
+'''[[EDF|Division of the just perfect fifth]] into 21 equal parts''' (21EDF) is related to [[36edo|36 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 33.4264 cents. Unlike 36edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.
 Lookalikes: [[36edo]], [[57edt]]
-=Approximations=
+==Approximations==
-==Harmonics==
+===Harmonics===
 {{Harmonics in equal|21|3|2|prec=2|columns=15}}
-==3-limit (Pythagorean) approximations (same as 7edf):==
+===3-limit (Pythagorean) approximations (same as 7edf):===
 /1 = 1200 cents; 36 degrees of 21edf = 1203.3514... cents.
@@ Line 24: / Line 24: @@
 /81 = 792.180... cents; 24 degrees of 21edf = 802.2342... cents.
-==7-limit approximations:==
+===7-limit approximations:===
-===7 only:===
+====7 only:====
 /4 = 968.826... cents; 29 degrees of 21edf = 969.3664... cents.
@@ Line 33: / Line 33: @@
 /49 = 462.348... cents; 14 degrees of 21edf = 467.97... cents.
-===3 and 7:===
+====3 and 7:====
 /6 = 266.871... cents; 8 degrees of 21edf = 267.4114... cents.
@@ Line 62: / Line 62: @@
 /32 = 1172.736... cents; 35 degrees of 21edf = 1169.925... cents.
+==Intervals==
 The following table gives an overview of all degrees of 36edo.
-{| class="wikitable"
+{| class="wikitable mw-collapsible"
+|+ Intervals of 21edf
 |-
 ! |Degree
@@ Line 287: / Line 289: @@
 |
 |}
+{{todo|expand}}