72nd-octave temperaments: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 1:

[[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting.

Line 20:

===17-limit===

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

Line 33:

Line 34:

===2.3.5.7.11.13.17.31 subgroup===

=== 2.3.5.7.11.13.17.31 subgroup ===

Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.

Line 46:

Line 47:

Optimal tuning (CTE): ~3/2 = 701.948

===2.3.5.7.11.13.17.31.37 subgroup===

=== 2.3.5.7.11.13.17.31.37 subgroup ===

[[37/22]] is mapped to exact three-quarters of the octave.

Line 72:

Line 73:

[[Optimal tuning]] ([[CTE]]): ~73205/53248 = 550.602

~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~|72~~, 1872f~~, 1944, 2016~~, 2088f, 2160fm~~, 3960}}

@@ Line 1: / Line 1: @@
-{{Fractional-octave navigation|72}}
+{{Infobox fractional-octave|72}}
 [[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting.
@@ Line 20: / Line 20: @@
 {{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
-===17-limit===
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
@@ Line 33: / Line 34: @@
 {{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
-===2.3.5.7.11.13.17.31 subgroup===
+=== 2.3.5.7.11.13.17.31 subgroup ===
 Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.
@@ Line 46: / Line 47: @@
 Optimal tuning (CTE): ~3/2 = 701.948
-===2.3.5.7.11.13.17.31.37 subgroup===
+=== 2.3.5.7.11.13.17.31.37 subgroup ===
 [[37/22]] is mapped to exact three-quarters of the octave.
@@ Line 72: / Line 73: @@
 [[Optimal tuning]] ([[CTE]]): ~73205/53248 = 550.602
-[[Support]]ing [[ET]]s: {{EDOs|72, 1872f, 1944, 2016, 2088f, 2160fm, 3960}}
+{{Optimal ET sequence|legend=1|72, 1944, 2016, 3960}}
+{{Navbox fractional-octave}}