Meantone family: Difference between revisions

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The '''meantone family''' is the family of rank-2 ~~temperaments~~ that temper out the syntonic comma, [[81/80]], and thus can all be seen as ~~extensions of~~ [[~~meantone~~]]~~. The~~ [[~~period]] is an [[octave]], the [[generator]] is a [[3/2|fifth]], and four fifths go to make up a [[5/1~~]] ~~interval~~.

The '''meantone family''' is the family of [[rank-2 temperament]]s that [[tempering out|temper out]] the syntonic comma, [[81/80]], and thus can all be seen as [[extension]]s of [[meantone]].

== Meantone ==

Meantone is characterized by an [[2/1|octave]] [[period]], a [[3/2|fifth]] [[generator]], and the relationship that four fifths go to make up a [[5/1|5th harmonic]].

[[Subgroup]]: 2.3.5

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[[Badness]] (Smith): 0.007381

=== ~~Extensions~~ ===

=== Overview to extensions ===

The second comma of the normal comma list defines which [[7-limit]] family member we are looking at.

* Flattertone adds {{monzo| -24 17 0 -1 }}, finding the ~7/4 at the double-augmented sixth~~. It is well-tuned~~ flat of 26edo.

* Flattertone adds {{monzo| -24 17 0 -1 }}, finding the [[~]][[7/4]] at the double-augmented sixth, for a tuning between flat of 26edo.

* Flattone adds {{monzo| -17 9 0 1 }}, finding the ~7/4 at the diminished seventh, ~~It is well-tuned~~ between 19edo ~~and 26edo~~.

* Flattone adds {{monzo| -17 9 0 1 }}, finding the ~7/4 at the diminished seventh, for a tuning between 26edo and 19edo.

* Septimal meantone adds [[Harrison's comma|{{monzo| -13 10 0 -1 }}]], finding the ~[[7/4]] at the augmented sixth ~~(diesis-flat minor seventh). It is well-tuned~~ between 12edo ~~and 19edo~~.

* Septimal meantone adds [[Harrison's comma|{{monzo| -13 10 0 -1 }}]], finding the ~7/4 at the augmented sixth, for a tuning between 19edo and 12edo.

* Dominant adds [[64/63|{{monzo| 6 -2 0 -1 }}]], finding the ~7/4 at the minor seventh~~. It is well-tuned~~ between 5edo ~~and 12edo~~.

* Dominant adds [[64/63|{{monzo| 6 -2 0 -1 }}]], finding the ~7/4 at the minor seventh, for a tuning between 12edo and 5edo.

* Sharptone adds [[28/27|{{monzo| 2 -3 0 1 }}]], finding the ~7/4 at the major sixth~~. It is~~ never exactly well-tuned, ~~but~~ 5edo is the only [[diamond monotone]] tuning, ~~and even it has~~ a terrible ~5~~/4. As such, it is an exotemperament~~.

* Sharptone adds [[28/27|{{monzo| 2 -3 0 1 }}]], finding the ~7/4 at the major sixth, for an [[exotemperament]] never exactly well-tuned, and where 5edo is the only [[diamond monotone]] tuning, with a terrible 5-limit part.

Those all have a fifth as generator.

* Injera adds {{monzo| -7 8 0 -2 }} with a half-octave period.

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 }}
 {{Technical data page}}
-The '''meantone family''' is the family of rank-2 temperaments that temper out the syntonic comma, [[81/80]], and thus can all be seen as extensions of [[meantone]]. The [[period]] is an [[octave]], the [[generator]] is a [[3/2|fifth]], and four fifths go to make up a [[5/1]] interval.
+The '''meantone family''' is the family of [[rank-2 temperament]]s that [[tempering out|temper out]] the syntonic comma, [[81/80]], and thus can all be seen as [[extension]]s of [[meantone]].
 == Meantone ==
 {{Main| Meantone }}
+Meantone is characterized by an [[2/1|octave]] [[period]], a [[3/2|fifth]] [[generator]], and the relationship that four fifths go to make up a [[5/1|5th harmonic]].
 [[Subgroup]]: 2.3.5
@@ Line 37: / Line 39: @@
 [[Badness]] (Smith): 0.007381
-=== Extensions ===
+=== Overview to extensions ===
 The second comma of the normal comma list defines which [[7-limit]] family member we are looking at.
-* Flattertone adds {{monzo| -24 17 0 -1 }}, finding the ~7/4 at the double-augmented sixth. It is well-tuned flat of 26edo.
+* Flattertone adds {{monzo| -24 17 0 -1 }}, finding the [[~]][[7/4]] at the double-augmented sixth, for a tuning between flat of 26edo.
-* Flattone adds {{monzo| -17 9 0 1 }}, finding the ~7/4 at the diminished seventh, It is well-tuned between 19edo and 26edo.
+* Flattone adds {{monzo| -17 9 0 1 }}, finding the ~7/4 at the diminished seventh, for a tuning between 26edo and 19edo.
-* Septimal meantone adds [[Harrison's comma|{{monzo| -13 10 0 -1 }}]], finding the ~[[7/4]] at the augmented sixth (diesis-flat minor seventh). It is well-tuned between 12edo and 19edo.
+* Septimal meantone adds [[Harrison's comma|{{monzo| -13 10 0 -1 }}]], finding the ~7/4 at the augmented sixth, for a tuning between 19edo and 12edo.
-* Dominant adds [[64/63|{{monzo| 6 -2 0 -1 }}]], finding the ~7/4 at the minor seventh. It is well-tuned between 5edo and 12edo.
+* Dominant adds [[64/63|{{monzo| 6 -2 0 -1 }}]], finding the ~7/4 at the minor seventh, for a tuning between 12edo and 5edo.
-* Sharptone adds [[28/27|{{monzo| 2 -3 0 1 }}]], finding the ~7/4 at the major sixth. It is never exactly well-tuned, but 5edo is the only [[diamond monotone]] tuning, and even it has a terrible ~5/4. As such, it is an exotemperament.
+* Sharptone adds [[28/27|{{monzo| 2 -3 0 1 }}]], finding the ~7/4 at the major sixth, for an [[exotemperament]] never exactly well-tuned, and where 5edo is the only [[diamond monotone]] tuning, with a terrible 5-limit part.
 Those all have a fifth as generator.
 * Injera adds {{monzo| -7 8 0 -2 }} with a half-octave period.