Well temperament: Difference between revisions

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* [[Werck3]] – Werckmeister temperament III

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

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

*** Werckmeister did not specify whether the syntonic or [[pythagorean comma|Pythagorean]] comma should be used, so either is acceptable

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

* [[Werckmeister IV]] – Werckmeister temperament IV

# five tempered fifths (C–G, D–A, E–B, F#-C# and Bb–F) are tuned flat by 1/3 ~~Pythagorean~~ comma

# five tempered fifths (C–G, D–A, E–B, F#-C# and Bb–F) are tuned flat by 1/3 comma

# two tempered fifths (G#–D# and Eb–Bb) are tuned sharp by 1/3 ~~Pythagorean~~ comma

# two tempered fifths (G#–D# and Eb–Bb) are tuned sharp by 1/3 comma

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

* [[Werckmeister V]] – Werckmeister temperament V

# five tempered fifths (D–A, A-E, F#-C#, C#-G# and F–C) are tuned flat by 1/4 ~~Pythagorean~~ comma

# five tempered fifths (D–A, A-E, F#-C#, C#-G# and F–C) are tuned flat by 1/4 comma

# one tempered fifth (G#–D#) is tuned sharp by 1/4 ~~Pythagorean~~ comma

# one tempered fifth (G#–D#) is tuned sharp by 1/4 comma

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

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

* [[Vallotti]] – Vallotti/Young temperament

* [[Vallotti]] – Vallotti/Young temperament I

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

# six pure fifths

@@ Line 22: / Line 22: @@
 * [[Werck3]] – Werckmeister temperament III
-# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 [[Pythagorean comma]]
+# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma
+*** Werckmeister did not specify whether the syntonic or [[pythagorean comma|Pythagorean]] comma should be used, so either is acceptable
 # eight [[3/2|pure]] fifths
 * [[Werckmeister IV]] – Werckmeister temperament IV
-# five tempered fifths (C–G, D–A, E–B, F#-C# and Bb–F) are tuned flat by 1/3 Pythagorean comma
+# five tempered fifths (C–G, D–A, E–B, F#-C# and Bb–F) are tuned flat by 1/3 comma
-# two tempered fifths (G#–D# and Eb–Bb) are tuned sharp by 1/3 Pythagorean comma
+# two tempered fifths (G#–D# and Eb–Bb) are tuned sharp by 1/3 comma
 # five [[3/2|pure]] fifths
 * [[Werckmeister V]] – Werckmeister temperament V
-# five tempered fifths (D–A, A-E, F#-C#, C#-G# and F–C) are tuned flat by 1/4 Pythagorean comma
+# five tempered fifths (D–A, A-E, F#-C#, C#-G# and F–C) are tuned flat by 1/4 comma
-# one tempered fifth (G#–D#) is tuned sharp by 1/4 Pythagorean comma
+# one tempered fifth (G#–D#) is tuned sharp by 1/4 comma
 # six [[3/2|pure]] fifths
@@ Line 40: / Line 41: @@
 # five [[3/2|pure]] fifths
-* [[Vallotti]] – Vallotti/Young temperament
+* [[Vallotti]] – Vallotti/Young temperament I
 # six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 Pythagorean comma
 # six pure fifths