Quarter-comma meantone: Difference between revisions

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Because of all of these features, it has a certain claim to be considered the canonical meantone tuning and often "meantone" is taken to mean quarter-comma specifically. The traditional interval names, listed below, may be considered to have their older traditional tuning in the quarter-comma meantone tunings listed below. However, other tunings (besides [[12edo]] which is ubiquitous but not an especially good tuning for meantone) may be preferred. Note, for instance, that the doubly augmented second and the doubly diminished fourth are both neutral thirds, about six cents apart. If we want a tuning which will equate the two, we need to use [[31edo]] instead.

== Tuning profile ==

[[Projection map]]:

{| class="right-all"

|-

| [⟨ || 1 || 1 || 0 || -3 || ]

|-

| ⟨ || 0 || 0 || 0 || 0 || ]

|-

| ⟨ || 0 || 1/4 || 1 || 5/2 || ]

|-

| ⟨ || 0 || 0 || 0 || 0 || ]]

|}

[[Tuning map]]: {{val| 1200 1896.5784 2786.3137 3365.7843 }}

[[Mistuning map]]: {{val| 0 -5.3766 0 -3.0416 }}

== Intervals of quarter-comma meantone ==

@@ Line 9: / Line 9: @@
 Because of all of these features, it has a certain claim to be considered the canonical meantone tuning and often "meantone" is taken to mean quarter-comma specifically. The traditional interval names, listed below, may be considered to have their older traditional tuning in the quarter-comma meantone tunings listed below. However, other tunings (besides [[12edo]] which is ubiquitous but not an especially good tuning for meantone) may be preferred. Note, for instance, that the doubly augmented second and the doubly diminished fourth are both neutral thirds, about six cents apart. If we want a tuning which will equate the two, we need to use [[31edo]] instead.
+== Tuning profile ==
+[[Projection map]]:
+{| class="right-all"
+|-
+| [⟨ || 1 || 1 || 0 || -3 || ]
+|-
+| ⟨ || 0 || 0 || 0 || 0 || ]
+|-
+| ⟨ || 0 || 1/4 || 1 || 5/2 || ]
+|-
+| ⟨ || 0 || 0 || 0 || 0 || ]]
+|}
+[[Tuning map]]: {{val| 1200 1896.5784 2786.3137 3365.7843 }}
+[[Mistuning map]]: {{val| 0 -5.3766 0 -3.0416 }}
 == Intervals of quarter-comma meantone ==