Major minthmic chords: Difference between revisions

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A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank ~~five~~ temperament, and in addition the rank ~~three~~ 2.3.11.13 temperament, tempering out the minthma, [[352/351]].

A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank-5 temperament, and in addition the rank-3 2.3.11.13 temperament, tempering out the minthma, [[352/351]].

We have the four minthmic tetrads, with steps the minthmic tempering of [[11/9]]-[[16/13]]-[[7/6]]-[[8/7]], 11/9-16/13-8/7-7/6, 16/13-11/9-7/6-8/7, and 16/13-11/9-8/7-7/6, leading to temperings of 1-11/9-[[3/2]]-[[7/4]], 1-11/9-3/2-[[12/7]], 1-16/13-3/2-7/4 and 1-16/13-3/2-12/7. These in turn have subchords such as the minthmic temperings of 1-11/9-3/2 and 1-16/13-3/2. Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.

We have the four minthmic tetrads, with steps the minthmic tempering of

* [[11/9]]-[[16/13]]-[[7/6]]-[[8/7]],

* 11/9-16/13-8/7-7/6,

* 16/13-11/9-7/6-8/7, and

* 16/13-11/9-8/7-7/6,

~~Mintha was a nymph turned into a mint plant by a goddess whom she got in the way~~ of, ~~and minthmic tempering has the slightly sharp, minty~~-~~fresh fifths some people appreciate (~~[[~~Margo Schulter~~]] ~~has expressed great fondness for this comma~~, ~~for example.) Equal temperaments with minthmic chords include {{EDOs|22, 29, 46, 53, 80, 87, 111, 121, 140, 198~~ and ~~205}}~~.

leading to temperings of

* 1-11/9-[[3/2]]-[[7/4]],

* 1-11/9-3/2-[[12/7]],

* 1-16/13-3/2-7/4 and

* 1-16/13-3/2-12/7.

[[~~Category:13~~-~~limit~~]]

These in turn have subchords such as the minthmic temperings of

[[Category:~~Chords~~]]

* 1-11/9-3/2 and

* 1-16/13-3/2.

Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.

Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include {{EDOs| 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205 }}.

[[Category:Essentially tempered chords]]

[[Category:Minthmic]]

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-A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank five temperament, and in addition the rank three 2.3.11.13 temperament, tempering out the minthma, [[352/351]].
+A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank-5 temperament, and in addition the rank-3 2.3.11.13 temperament, tempering out the minthma, [[352/351]].
-We have the four minthmic tetrads, with steps the minthmic tempering of [[11/9]]-[[16/13]]-[[7/6]]-[[8/7]], 11/9-16/13-8/7-7/6, 16/13-11/9-7/6-8/7, and 16/13-11/9-8/7-7/6, leading to temperings of 1-11/9-[[3/2]]-[[7/4]], 1-11/9-3/2-[[12/7]], 1-16/13-3/2-7/4 and 1-16/13-3/2-12/7. These in turn have subchords such as the minthmic temperings of 1-11/9-3/2 and 1-16/13-3/2. Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.
+We have the four minthmic tetrads, with steps the minthmic tempering of
+* [[11/9]]-[[16/13]]-[[7/6]]-[[8/7]],
+* 11/9-16/13-8/7-7/6,
+* 16/13-11/9-7/6-8/7, and
+* 16/13-11/9-8/7-7/6,
-Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include {{EDOs|22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205}}.
+leading to temperings of
+* 1-11/9-[[3/2]]-[[7/4]],
+* 1-11/9-3/2-[[12/7]],
+* 1-16/13-3/2-7/4 and
+* 1-16/13-3/2-12/7.
-[[Category:13-limit]]
+These in turn have subchords such as the minthmic temperings of
-[[Category:Chords]]
+* 1-11/9-3/2 and
+* 1-16/13-3/2.
+Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.
+Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include {{EDOs| 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205 }}.
+[[Category:Essentially tempered chords]]
 [[Category:Minthmic]]