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m Xenwolf moved page 1-6 Syntonic Comma Meantone to 1/6 syntonic comma meantone: changed into intended lemma (that was not possible in Wikispaces), changed into Sentence case
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1/6 comma meantone is the tuning of [[Meantone_family|meantone temperament]] which tunes the fifth as the sixth root of 45/4, or in other words 698.371 cents. This means the fifth is flattened by 1/6 of the syntonic comma (81/80 ratio) of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone 45/32 is tuned justly, and it can be characterized fully as the regular tuning tempering out 81/80 and tuning 2 and 45/32 justly. It is closely related to [[55edo|55edo]] in terms of its tuning.
'''1/6 comma meantone''' is the tuning of [[Meantone family|meantone temperament]] which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the syntonic comma ([[81/80]] ratio) of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning tempering out 81/80 and tuning 2 and 45/32 justly. It is closely related to [[55edo]] in terms of its tuning.


=Fractional projection matrix=
== Fractional projection matrix ==
The [[Fractional_monzos|fractional projection map]] defining 7-limit 1/6 comma meantone is
The [[Fractional monzos|fractional projection map]] defining [[7-limit]] 1/6 comma meantone is


{| class="wikitable"
{| class="wikitable"
|-
|-
| | [1
| [1
| | 0
| 0
| | 0
| 0
| | 0>
| 0>
|-
|-
| | [2/3
| [2/3
| | 1/3
| 1/3
| | 1/6
| 1/6
| | 0>
| 0>
|-
|-
| | [-4/3
| [-4/3
| | 4/3
| 4/3
| | 2/3
| 2/3
| | 0>
| 0>
|-
|-
| | [-19/3
| [-19/3
| | 10/3
| 10/3
| | 5/3
| 5/3
| | 0>
| 0>
|}
|}


=Links=
== Links ==
[http://music.case.edu/~rwd/baroquetemp/XMT.intro.html Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [http://www.webcitation.org/5zW8FuybZ permalink]
* [http://music.case.edu/~rwd/baroquetemp/XMT.intro.html Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [http://www.webcitation.org/5zW8FuybZ permalink]
* [http://sonic-arts.org/monzo/55edo/55edo.htm Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[Joe Monzo]] [http://www.webcitation.org/5zW910Jax permalink]


[http://sonic-arts.org/monzo/55edo/55edo.htm Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[Joe_Monzo|Joe Monzo]] [http://www.webcitation.org/5zW910Jax permalink]      [[Category:1/6-comma]]
[[Category:1/6-comma]]
[[Category:meantone]]
[[Category:Meantone]]
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