1/5-comma meantone: Difference between revisions

(4 intermediate revisions by 3 users not shown)

Line 1:

{{Interwiki

| en = 1/5-comma meantone

| de = Fünftelkomma-mitteltönig

}}

'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1|2]] and [[16/15]] purely.

The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat.

The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat. The augmented sixth is exactly [[225/128]], and for septimal meantone, this means the [[7/4]] is sharp by a [[225/224|septimal kleisma (225/224)]].

1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)

Line 21:

Line 25:

[[Tuning map]]: {{val| 1200 1897.6537 2790.6150 3376.5374 }}

[[~~Mistuning~~ map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }}

[[Error map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }}

== Music ==

; [[septimal lemon]]

* [https://youtu.be/jlbpQqahZh0 ''Bubbles''] (2025)

[[Category:Meantone]]

[[Category:Historical]]

@@ Line 1: / Line 1: @@
+{{Interwiki
+| en = 1/5-comma meantone
+| de = Fünftelkomma-mitteltönig
+}}
 '''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1|2]] and [[16/15]] purely.
-The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat.
+The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat. The augmented sixth is exactly [[225/128]], and for septimal meantone, this means the [[7/4]] is sharp by a [[225/224|septimal kleisma (225/224)]].
 /5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)
@@ Line 21: / Line 25: @@
 [[Tuning map]]: {{val| 1200 1897.6537 2790.6150 3376.5374 }}
-[[Mistuning map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }}
+[[Error map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }}
+== Music ==
+; [[septimal lemon]]
+* [https://youtu.be/jlbpQqahZh0 ''Bubbles''] (2025)
 [[Category:Meantone]]
 [[Category:Historical]]