36edo: Difference between revisions

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63/32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.

~~== Tuning by Ear ==~~

After [[9edo]] and [[19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6]]'s with a comma of less than 2 cents) connected by [[3/2]]'s, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo]] and obviously a much smaller absolute error. It's a good system to use on large organs that have three manuals.

~~Tuning file: [[9x4just]]~~

== Rank-2 temperaments ==

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Line 535:

5 5 5 6 5 5 5

== Tuning by Ear ==

After [[9edo]] and [[19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6]]'s with a comma of less than 2 cents) connected by [[3/2]]'s, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo]] and obviously a much smaller absolute error. It's a good system to use on large organs that have three manuals.

Tuning file: [[9x4just]]

== Instruments ==

@@ Line 410: / Line 410: @@
 /32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.
-== Tuning by Ear ==
-After [[9edo]] and [[19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6]]'s with a comma of less than 2 cents) connected by [[3/2]]'s, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo]] and obviously a much smaller absolute error. It's a good system to use on large organs that have three manuals.
-Tuning file: [[9x4just]]
 == Rank-2 temperaments ==
@@ Line 540: / Line 535: @@
 5 5 6 5 5 5
+== Tuning by Ear ==
+After [[9edo]] and [[19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6]]'s with a comma of less than 2 cents) connected by [[3/2]]'s, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo]] and obviously a much smaller absolute error. It's a good system to use on large organs that have three manuals.
+Tuning file: [[9x4just]]
 == Instruments ==