Well temperament: Difference between revisions

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== Historical well temperaments ==

* [[Kirnberger]] – Kirnberger temperament

* [[Kirnberger]] – Kirnberger temperament III

# ~~the~~ fifths ~~are [[3/2|pure]], except for~~

# four tempered fifths (C–G, D–A, G–D and A–E) are flat by 1/4 [[syntonic comma]] (→ [[quarter comma meantone]])

~~# the~~ C–G, D–A, G–D and A–E ~~fifths~~ are [[quarter comma meantone]]

# one tempered fifth (F#–Db) is flat by a [[schisma]]

# ~~the~~ F#–Db is ~~the wolf fifth,~~ a [[schisma]] flat

# seventh [[3/2|pure]] fifths

* [[Werck3]] – Werckmeister temperament III

# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 Pythagorean comma

# eight [[3/2|pure]] fifths

* [[Vallotti]] – Vallotti/Young temperament

# ~~the~~ fifths ~~are [[3/2|pure]], except for~~

# six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 [[Pythagorean comma]]

~~# the~~ C–G, D–A, E–B, F–C, G–D and A–E ~~fifths~~ are 1/6 [[Pythagorean comma]] ~~flat.~~

# six pure fifths

* [[Young2]] – Young temperament II

* [[Werck3]] – Werckmeister temperament III

# four tempered fifths (C–G, D–A, G–D and A–E) are tuned flat by 3/16 syntonic comma

# four tempered fifths (E-B, B–F#, Bb–F and F–C) are tuned flat by 1/4 Pythagorean comma less 3/16 syntonic comma

# four pure fifths (F#–C#, C#–G#, G#–Eb and Eb–Bb)

== Generalizations ==

@@ Line 5: / Line 5: @@
 == Historical well temperaments ==
-* [[Kirnberger]] – Kirnberger temperament
+* [[Kirnberger]] – Kirnberger temperament III
-# the fifths are [[3/2|pure]], except for
+# four tempered fifths (C–G, D–A, G–D and A–E) are flat by 1/4 [[syntonic comma]] (→ [[quarter comma meantone]])
-# the C–G, D–A, G–D and A–E fifths are [[quarter comma meantone]]
+# one tempered fifth (F#–Db) is flat by a [[schisma]]
-# the F#–Db is the wolf fifth, a [[schisma]] flat
+# seventh [[3/2|pure]] fifths
+* [[Werck3]] – Werckmeister temperament III
+# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 Pythagorean comma
+# eight [[3/2|pure]] fifths
 * [[Vallotti]] – Vallotti/Young temperament
-# the fifths are [[3/2|pure]], except for
+# six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 [[Pythagorean comma]]
-# the C–G, D–A, E–B, F–C, G–D and A–E fifths are 1/6 [[Pythagorean comma]] flat.
+# six pure fifths
 * [[Young2]] – Young temperament II
-* [[Werck3]] – Werckmeister temperament III
+# four tempered fifths (C–G, D–A, G–D and A–E) are tuned flat by 3/16 syntonic comma
+# four tempered fifths (E-B, B–F#, Bb–F and F–C) are tuned flat by 1/4 Pythagorean comma less 3/16 syntonic comma
+# four pure fifths (F#–C#, C#–G#, G#–Eb and Eb–Bb)
 == Generalizations ==