Meantone: Difference between revisions

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| en = Meantone

| de = Mitteltönig

}}{{Infobox regtemp|Generator=3/2|Comma basis=81/80|Mapping=1; 1 4|Edo join 1=19|Edo join 2=12|Optimization method=CWE|Generator tuning=696.7|Subgroups=2.3.5|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]]~~, [[12L 7s]]~~|Title=Meantone}}'''Meantone''' is a familiar historical [[temperament]] based on a chain of fifths (or fourths). The more technical part is discussed in [[meantone family]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}

}}{{Infobox regtemp

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|Edo join 1=7

|Edo join 2=12

|Optimization method=CWE

|Generator tuning=696.7

|Subgroups=2.3.5

|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]]

|Title=Meantone}}

'''Meantone''' is a familiar historical [[temperament]] based on a chain of fifths (or fourths). The more technical part is discussed in [[meantone family]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}

== History ==

Meantone with fifths flatter than 700{{cent}} were the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[well temperament]]s and eventually [[12edo|12-tone equal temperament]] won in popularity. However, even today, the vast majority of common-practice Western music theory is based exclusively on meantone, as 12-tone equal temperament is itself a meantone tuning.

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=== Septimal meantone ===

{{Infobox regtemp|Generator=3/2|Comma basis=81/80, 225/224|Mapping=1; 1 4 10|Edo join 1=31|Edo join 2=19|Optimization method=CWE|Generator tuning=696.7|Subgroups=2.3.5.7|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]|Title=Septimal meantone}}{{Wikipedia| Septimal meantone temperament }}'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh.

{{Infobox regtemp

|Generator=3/2

|Comma basis=81/80, 225/224

|Mapping=1; 1 4 10

|Edo join 1=12

|Edo join 2=19

|Optimization method=CWE

|Generator tuning=696.7

|Subgroups=2.3.5.7

|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]

|Title=Septimal meantone}}{{Wikipedia| Septimal meantone temperament }}

'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh.

See [[meantone vs meanpop]] for a comparison of undecimal (11-limit) extensions.

@@ Line 2: / Line 2: @@
 | en = Meantone
 | de = Mitteltönig
-}}{{Infobox regtemp|Generator=3/2|Comma basis=81/80|Mapping=1; 1 4|Edo join 1=19|Edo join 2=12|Optimization method=CWE|Generator tuning=696.7|Subgroups=2.3.5|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]|Title=Meantone}}'''Meantone''' is a familiar historical [[temperament]] based on a chain of fifths (or fourths). The more technical part is discussed in [[meantone family]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}
+}}{{Infobox regtemp
+|Generator=3/2
+|Comma basis=81/80
+|Mapping=1; 1 4
+|Edo join 1=7
+|Edo join 2=12
+|Optimization method=CWE
+|Generator tuning=696.7
+|Subgroups=2.3.5
+|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]]
+|Title=Meantone}}
+'''Meantone''' is a familiar historical [[temperament]] based on a chain of fifths (or fourths). The more technical part is discussed in [[meantone family]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}
 == History ==
 Meantone with fifths flatter than 700{{cent}} were the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[well temperament]]s and eventually [[12edo|12-tone equal temperament]] won in popularity. However, even today, the vast majority of common-practice Western music theory is based exclusively on meantone, as 12-tone equal temperament is itself a meantone tuning.
@@ Line 12: / Line 23: @@
 === Septimal meantone ===
-{{Infobox regtemp|Generator=3/2|Comma basis=81/80, 225/224|Mapping=1; 1 4 10|Edo join 1=31|Edo join 2=19|Optimization method=CWE|Generator tuning=696.7|Subgroups=2.3.5.7|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]|Title=Septimal meantone}}{{Wikipedia| Septimal meantone temperament }}'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh.
+{{Infobox regtemp
+|Generator=3/2
+|Comma basis=81/80, 225/224
+|Mapping=1; 1 4 10
+|Edo join 1=12
+|Edo join 2=19
+|Optimization method=CWE
+|Generator tuning=696.7
+|Subgroups=2.3.5.7
+|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]
+|Title=Septimal meantone}}{{Wikipedia| Septimal meantone temperament }}
+'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh.
 See [[meantone vs meanpop]] for a comparison of undecimal (11-limit) extensions.