1/6-comma meantone: Difference between revisions
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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 [[ | '''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 [[ | The [[Fractional monzos|fractional projection map]] defining [[7-limit]] 1/6 comma meantone is | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| [1 | |||
| 0 | |||
| 0 | |||
| 0> | |||
|- | |- | ||
| [2/3 | |||
| 1/3 | |||
| 1/6 | |||
| 0> | |||
|- | |- | ||
| [-4/3 | |||
| 4/3 | |||
| 2/3 | |||
| 0> | |||
|- | |- | ||
| [-19/3 | |||
| 10/3 | |||
| 5/3 | |||
| 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] | |||
[[Category:1/6-comma]] | |||
[[Category: | [[Category:Meantone]] | ||
Revision as of 21:43, 24 October 2018
1/6 comma meantone is the tuning of 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 in terms of its tuning.
Fractional projection matrix
The fractional projection map defining 7-limit 1/6 comma meantone is
| [1 | 0 | 0 | 0> |
| [2/3 | 1/3 | 1/6 | 0> |
| [-4/3 | 4/3 | 2/3 | 0> |
| [-19/3 | 10/3 | 5/3 | 0> |